**Seminar**

**for researchers,
students and teachers**

** _{t}**=
[P,L]
AB = qBA

PQ - QP = - ihI
S** _{0}**S

**Centre for
Mathematical Sciences**

**Lund****, ****Sweden**

Sergei Silvestrov, Photo of Sergei Silvestrov

e-mail: sergei.silvestrov@math.lth.se Tel: (+46) (0) 46-2228854 FAX: (+46)
46-2224010

Click on these pointers to
jump to:

Next and
Planed talks and events

Past seminars About NANG seminar in general

**
NANG Seminar
Activities: ****workshops,
conferences, mini-courses, networks and journals **

*(click on the links bellow for more
info on these series of events)*

**Networks **

AGMF network: “Algebra, Geometry and
Mathematical Physics” Baltic Nordic network

**Journal
created and edited under the auspices of the NANG seminar**

Journal of Generalized Lie
Theory and Applications

**Conferences**

Göteborg 2007, October 11- October 13, 2007, “Algebra, Geometry and Mathematical Physics” conference

organized by AGMF: “Algebra, Geometry and Mathematical Physics” Baltic Nordic network

*This conference is dedicated to the memory of Professor Isaiah Kantor (1936-2006)*

Lund 2007, October 8, Workshop on interpolation, inequalities, invariants, multilinearforms and related topic, October 8, 2007

Lund, 2007, June 13, Workshop on wavelet analysis, fractal geometry, iterated function systems and applications

Lund, 2007, May 8, Workshop on homological devices and non-commutative algebra

Lund 2006, October 12- October 14, 2006, “Algebra, Geometry and Mathematical Physics” conference

organized by AGMF: “Algebra, Geometry and Mathematical Physics” Baltic Nordic network

Öresund symposiums on non-commutative geometry,
non-commutative analysis and applications

**Mini-courses
organized under the auspices of the NANG seminar**

**
STINT ****
intensive advanced mini-course **

Wavelets, fractals, iterated function systems and operator representations.

*
Minikurs om wavelets, fraktaler, itererade funktions system och
operatorrepresentationer *

**
Palle
Jorgensen,
Iowa****,
USA**** **

**Time:**
June
11 –

**Place:
**
MH: 333,**
** Centre for Mathematical Sciences,

**Intensive advanced mini-course in algebraic geometry
with applications**

*Minikurs i algebraisk geometri och
tillämpningar*

**
Nacer Makhlouf, **
** Mulhouse, France**

**Time****:**Week of March 27 – March 31, 2006

**Place****:**Centre for Mathematical Sciences,

TALKS or EVENTS

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NEXT

**
SPRING**** 2008**

**Time: **
13.15-14.30, Friday, April 25

Place: MH: 332B, Centre for Mathematical Sciences,

**Speaker:
**Magnus Goffeng, Department of
Mathematical Sciences, Chalmers University of Technology/Göteborg University

**Title: **
Extensions of *-algebras and finitely
summable Fredholm modules

**Abstract: **

When studying problems in difficult algebras one often tries to reduce the problem to a simpler problem in a simpler algebra. For example when studying pseudodifferential operators, problems are often reduced to studying the commutative algebra of symbols. This can be formalized by studying extensions of algebras. For C*-algebras this theory is welldeveloped and is studied via an algebraic invariant. This algebraic invariant has relations with KK-theory and index theory. I will present a generalization of this algebraic invariant to a class of *-algebras and indicate how this can be used to derive explicit index formulaes such as Atiyah-Singers index theorem.

**Time: **
13.15-14.30, Wednesday, April 9

Place:
MH:333, Centre for Mathematical Sciences,

**Speaker:
**Abdenacer Makhlouf,

**Title: **
Deforming binary and ternary algebras:
cohomological tool and some structure results.

**OBS! ** Colloquium in
Mathematics

**Abstract: **

In the this talk, I describe the deformation theory introduced by Gerstenhaber for associative algebras and by Nijenhuis-Richardson for Lie algebras. Then I extend it to ternary algebras. These deformation theories are an algebraic point of view based on the cohomology which lead to several structure results on rigid algebras and the global study of the algebraic varieties of a given finite dimensional algebras.

**Time: **
15.30-16.30, Wednesday, February 27

Place:
MH:333, Centre for Mathematical Sciences,

**Speaker:
**Christian Svensson, Matematikcentrum, Lunds universitet

**Title: **
Crossed Product
Structures Associated With Discrete Dynamical Systems

**OBS! **Licentiate seminarium** **

**Abstract: **

The origin of the research done in the papers included in this thesis is the theory of crossed product C*-algebras. In our context, discrete dynamical systems generated by a homeomorphism of a topological space correspond to crossed product C*-algebras obtained from the actions of the group of integers on the C*-algebra of complex-valued continuous functions on the space, induced by the homeomorphism. There exist many well-known striking equivalences between topological properties of such dynamical systems and their associated C*-crossed products, one of the most famous ones being the equivalence between minimality of a system and simplicity of its C*-algebra.

In the papers included in this thesis we introduce an algebraic crossed product structure induced by an automorphism of a commutative Banach algebra, and investigate its connections with a naturally associated topological dynamical system on the character space of the Banach algebra. Many analogues of the known equivalences from the theory of crossed product C*-algebras hold true in this context, as well as results that appear to lack correspondents in the C*-algebra case. We consider e.g. the ideal structure and maximal abelian subalgebras of the crossed product and how these algebraic properties can be related to topological features of the system. We also start the investigation of a Banach algebra crossed product whose C*-envelope is the usual crossed product C*-algebra.

**Time: **
15.30-16.30, Tuesday, February 26

Place:
MH:333, Centre for Mathematical Sciences,

**Speaker:
**Sten Kaijser,
Department of Mathematics, Uppsala University

**Title: **The Mellin transform
and some well-known inequalities.

Mellin-transformen och några välkända olikheter

**Abstract: **

The starting point for this seminar is the observation that

L** ^{p}** spaces are invariant under a change
of density. This implies that

a change of density is always possible and this can often lead to new

knowledge. An important example of this is replacing the additively

invariant Lebesgue measure by the multiplicatively invariant

Euler-Lebesgue measure.

Sammanfattning: Utgångspunkten för detta föredrag är iakttagelsen att

L

byte av täthet kan göras problemfritt, något som ofta leder till helt ny

insikter. Ett viktigt exempel på detta är övergången från det additivt

invarianta Lebesgue-måttet till det multiplikativt invarianta

Euler-Lebesgue-måttet.

**Time: **
16.15-17.15, Friday, February 22

Place:
MH:333, Centre for Mathematical Sciences,

**Speaker:
****
Klas Modin,** Numerisk analys, Matematikcentrum, Lunds universitet

**Title: **Explicit adaptive
geometric integration based on splitting

and its connection to Nambu–Poisson brackets

**Abstract: **

Geometric integrators are numerical integration methods
where the discrete phase flow

preserve some underlying geometric structure. The two most common examples are
symplectic methods and reversible

methods. For problems in Hamiltonian dynamics (or Poisson dynamics),

geometric integrators are preferable over standard methods, because they

usually conserve, or ``almost conserve'', first integrals over very long time
intervals.

Implementation of adaptive step size control for geometric numerical integration
schemes

is non-trivial, since conventional strategies destroy the structure preserving
properties.

The common approach is to introduce a dynamic time transformation of the
original

system, and then to utilize a geometric (structure preserving) discretization of
the transformed system.

An explicit fully reversible integrating step size control algorithm for
reversible systems is suggested in [HS]

The idea is to consider an augmented dynamical system, with an additional first
integral that corresponds to the step

size control objective, and then to carry out explicit reversible discretization
of this system.

Theoretical justification is given of the good long time behaviour of the
algorithm when applied to integrable

reversible systems. However, when applied to Hamiltonian systems, the resulting
adaptive integrator

is not symplectic, which for many problems (e.g. non-reversible and/or non-integrable
problems)

is a drawback.

In the first part of the talk I will sketch the basic principle behind

splitting methods (for construction of symplectic methods) and show

how the Baker--Campbell--Hausdorff (BCH) formula

is used to obtain theoretical results on the long time energy behaviour.

In the second part I will show that the time transformed augmented system used
as a basis in [HS]

admits a generalized Poisson structure, which is some cases

correspond to a Nambu--Poisson structure. Furthermore, it turns out that the
adaptive numerical scheme

suggested in [HS], can be viewed as a splitting method in the framework of Nambu--Poisson
brackets.

Possible theoretical implications and open problems connected to this will also
be discussed.

Bibliography

[HS] E.Hairer and G. Söderlind. Explicit, time reversible, adaptive step size
control.

SIAM J. Sci. Comput., 26:1838--1851, 2005.

list is incomplete, more web info on past
seminars and events will be added

info on activities during 2005 is under construction
and will be added soon

**
AUTUMN 2007**

**Time: **
10.15-11.00, Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
Michael Cwikel**, Technion – Israel Institute of Technology, Haifa,
Israel:

**Title: **Complex interpolation of
compact operators. Creeping towards an answer?

**Abstract: **

The problem that we are struggling with
goes back to Alberto Calderon's celebrated and beautiful work on complex
interpolation spaces. Thus it has been open since August 15, 1963.

Suppose that T is a linear operator which acts compactly on both of the Banach
spaces X and Y. We still do not know whether, in general, T is also compact on
Calderon's space [X,Y]_{θ}.

Partial answers to this question have been given by Calderon himself, by Lions
and Peetre, Arne Persson, and many others.

I will report on some recent partial
answers which at least give the impression (illusion?) that we might be creeping
closer to a full answer.

Unless the audience prefers otherwise, I will begin by recalling some of the
history and applications of interpolation theory and the definitions and some of
the basic relevant facts about Calderon's spaces. I will also indicate various
connections with Fourier series. Indeed Fourier series are apparently a
significant part of the arsenal we have for attacking this problem.
(As some of you may recall, Svante Janson has characterised Calderon's spaces
via sequence spaces of Fourier coefficients, and Fedor Nazarov has used Fourier
series to give an "almost counterexample" to a closely related question.)

Some background about these things can be found at

http://www.math.technion.ac.il/~mcwikel/compact

**Time: **
11.10-11.55, Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Lars-Erik Persson**,
Luleå University of Technology, Luleå, Sweden:

**Title: **Hardy-type inequalities and
convexity- historical remarks and some

recent results and questions

**Abstract: **

`
I will first shortly present some
remarkably facts from the period 1915-1925, which finally led Hardy to present
and prove his inequality in his famous 1925 paper (in particular, the Swedish
mathematician Riesz was important for this development !), see [1]. After that I
will present the easiest (and, in my opinion, most natural) proof of this
inequality I know. This proof depends only on a convexity argument and this way
of thinking is also related to interpolation theory. Finally, I present some
facts from the books [2] and [3] but also some even more recent results and open
questions.`

`
[1]A. Kufner, L. Maligranda and L.E.
Persson, The prehistory of the Hardy`

`
inequality, Amer. Math. Monthly 113
(2006), No. 8, 715-732.`

`
[2]C.P. Niculescu and L.E. Persson,
CONVEX FUNCTIONS AND THEIR APPLICATIONS-A`
`
CONTEMPORARY APPROACH, Canad. Math. Series Books in Mathematics, Springer, 2006`
`
(252 pages).`

`
[3] A. Kufner, L. Maligranda and L.E.
Persson, THE HARDY INEQUALITY. ABOUT ITS`
`HISTORY AND SOME RELATED RESULTS, Vydavatelsky Servis Publishing House,
Pilsen,`
`
2007 (161 pages).`

**Time: **
13.15-13:45, Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Jaak Peetre**,
Lund University, Lund, Sweden:

**Title: **Neoclassical Invariant theory

**Abstract: **

Some topics and ideas related to this interesting neoclassical subject will be presented.

**Time: **
13.50-14.10**, **Monday, October 8** **

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Christian Svensson**:
Lund University, Lund, Sweden

**Title: **Crossed product algebras and
Banach algebras associated to dynamical systems.

**Abstract: **

Given a discrete dynamical system, one may construct an associative (non-commutative) complex algebra with multiplication determined via the action defining the system, being an example of a crossed product. It turns out that for large classes of systems, one obtains striking equivalences between, in particular, topological properties of the system and algebraic properties of the crossed product. In this talk we will discuss the ideal structure of crossed products and ideal intersection properties of (commutative) subalgebras between the canonical "coefficient algebra" and its commutant.

**Time: **
14.10-14.30, Monday, October 8 ** **

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Johan Oinert**,
Lund University, Lund, Sweden

**Title: **Crystalline graded rings and
generalized crossed products

**Abstract: **

In this talk we will focus on a certain 'intersection property' of ideals in certain kinds of rings and algebras. We start by looking at C*-crossed product algebras associated with dynamical systems, which is our main motivating example. We will then show that the 'intersection property' also holds in a purely algebraic framework, namely for algebraic crossed products. Thereafter we generalize this result to a more general class of rings, the so called 'crystalline graded rings'. Both of these classes of rings are group graded, but we will define a new class of rings (with motivation coming from irreversible dynamical systems) which is only assumed to be monoid graded. After giving the definition, we shall give some concrete examples of such rings and show that in general the 'intersection property' need not hold for these rings.

**Time: **
14.35-14.55**, **Monday, October 8** **

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Erik Darpö**,
Uppsala University, Lund, Sweden

**Title: **On the classification of
finite-dimensional division algebras

**Abstract: **

Let *k* be a field. A division algebra
over *k* is a vector space A over *k* endowed with a bilinear
multiplication map AxA --> A; (x,y) --> xy such that left and right
multiplication with any non-zero element in A are invertible linear operators on
A. In general, a division algebra is not assumed to be associative or
commutative, nor to have an identity element.

We shall give a survey of the classification problem for finite-dimensional
division algebras, with focus on algebras over the real ground field. This
includes the construction of the four classical real

division algebras, theorems by Frobenius and Zorn on associative and alternative
division algebras respectively, and the celebrated (1,2,4,8)-theorem, which
asserts that every finite-dimensional division algebra over **R** has
dimension either 1, 2, 4 or 8.

We will also touch upon some recent development in the field, originating mainly
from Osborns work on quadratic division algebras in the sixties.

**Time: **
15.30-15.50, Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Olivier Verdier**,
Lund University, Lund, Sweden

**Title: **Application of interpolation
between anisotropic Sobolev spaces to PDEs

**Abstract:
**

The interpolation between anisotropic Sobolev spaces with p=2 is elementary but turns out to be an effective tool, coupled with the vectorial Sobolev inequalities, to obtain estimates of nonlinear terms. I will show some applications to the Burgers equation with highly irregular source terms.

**Time: **
15.50-16.35**. **Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Svante Janson**,
Uppsala University, Sweden

**Title: **Interpolation of subcouples
and quotient couples

**Abstract: **

A subcouple (Y_{0},Y_{1})
of a Banach couple (X_{0},X_{1}) is K-closed if, for elements in
Y_{0}+Y_{1}, the K-functional evaluated in the smaller couple is
equivalent to the K-functional evaluated in the larger couple.

This is not true in general, but it is a useful property when it holds. This
property was used and investigated by Pisier, in connection with interpolation
of H^{p}-spaces. I will discuss this and general results concerning
interpolation by the real method of subcouples and quotient couples. It seems
that very little is known about corresponding results for the complex method.

This is a survey based on my paper with the same title in Ark. Mat. 31 (1993),
no. 2, 307--338.

**Time: **
16.40-17.10, Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Sten Kaijser**,
Uppsala University, Uppsala, Sweden:

**Title: **Pseudodeterminants

**Abstract: **

This talk will be devoted to Pseudodeterminants.

**Time: **
17.15-18.00**, **Monday, October 8

Place:
MH:332A, Centre for Mathematical Sciences,

**Speaker:
****Frank Hansen**,
Copenhagen University, Copenhagen, Denmark

**Title: **The application of operator
monotone functions in economics

**Abstract: **

Two notions in microeconomics, decreasing
relative risk premium and risk vulnerability, are connected to matrix or
operator monotonicity. We show that a decision maker with an increasing utility
function has preferences representing decreasing relative risk premium, if and
only if his utility function is matrix monotone of order two. We then show that
this property may be equivalently formulated in terms of preferences on binary
lotteries. We finally explain the notion of risk vulnerability and show that an

operator monotone function necessarily is risk vulnerable.

**SPRING 2007**

**
STINT ****
intensive advanced mini-course by Palle E. T. Jorgensen
**

**Time: **kl** **13:15-15:00,

**
Monday, June 11, **

**
Tuesday June 12, **

**
Wednesday, June 13**

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **
Palle E. T. Jorgensen**,
The University of Iowa , USA

**Title:**
Wavelets, fractals, iterated function systems and operator representations.

**(http://www.maths.lth.se/matematiklth/personal/ssilvest/PalleJorgensenWaveletsLundJune2007.htm
)**

**Abstract: **

These lectures, combining analysis and tools from mathematical probability, give a systematic presentation of recent trends in three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals.

From operator algebra theory, a key topic in the talks will be representations of the Cuntz algebras.

They aim to bring together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students.

Special:

• motivation;

• glossary of terms, their use in mathematics and in engineering;

• graphic renditions of algorithms, and separate illustrations;

• explaining engineering terms to mathematicians, and operator theory to engineers;

• guide to the literature.

Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa.

He has taught some of this in courses over the last several years.

He is the author of a GTM Springer book v 234 in 2006.

**
Analysis and Probability: Wavelets, Signals,
Fractals, **
Graduate Texts in Mathematics, Vol. 234,
Springer**.**

And his other most recent book was written jointly with Ola Bratteli and is entitled

*
Wavelets through a Looking Glass*, Applied and Numerical
Harmonic Analysis,
Birkhäuser, 2002.

**Time: **kl** **
10.15-11:05, Wednesday, June 13,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **
Örjan Stenflo**,
Uppsala University:

**Title:** Random V-variable fractals.

*
Workshop
on wavelet analysis, fractal
geometry, iterated function systems and applications, Lund, June 13, 2007*

**Abstract: **

A standard way to generate probability measures supported on fractal sets is to regard them as limiting probability distributions for processes obtained from random iterations of functions. It is typically not possible to generate natural random fractals like e.g. Brownian motion in a similar way due to the complexity of these objects. This has restricted applications in fractal modeling. In joint work with Michael Barnsley and John Hutchinson we introduced V-variable fractals as a way of resolving this. Random V-variable fractals can be generated quickly as "points" along trajectories of a fractal-valued random iteration process. Simultaneously they can be used to approximate "standard" random fractals.

**Time: **kl** **
11.10-12:00, Wednesday, June 13,

**Place:** MH:309B, Centre for
Mathematical Sciences,

**Speaker:** **
Ole Christensen**, Danmarks Tekniske Universitet:

**Title:** Gabor systems and frames.

*
Workshop
on wavelet analysis, fractal
geometry, iterated function systems and applications, Lund, June 13, 2007*

**Abstract: **

In signal processing and pure mathematics it is useful to represent complicated signals or functions f in terms of linear combinations of simpler building blocks ek; the classical case, where ek is assumed to be an orthonormal basis for a Hilbert space H to which the relevant signals belong, leads to the representation f= Σ< f,ek> ek. However, the assumption that ek forms an ONB is quite restrictive, and it limits the other properties one can expect from ek. We discuss concrete cases from wavelet analysis and Gabor theory, where desirable properties of ek can not be combined with ek being an ONB. It turns out that much more freedom can be attained by assuming that ek is a frame rather than an ONB. We will discuss recent results concerning frames, with particular focus on Gabor frames.

**Time: **kl** **13:15-14:00, Tuesday, May 8,

**Place:** MH:309B, Centre for
Mathematical Sciences,

**Speaker:** **Sergei****
Silvestrov**, ** **

**Title:** Twisted
Derivations and Introduction to Quasi Lie Algebras.

*Workshop on homological devices and
non-commutative algebra, **Lund**, **May 8,
2007**
*

**Abstract: **

In this
talk, I will present a review on quasi-Lie algebras, quas-hom-Lie
algebrasand hom-Lie
algebras generalizing color Lie algebras, Lie superalgebras and Lie algebras and providing a unifying framework
for quasi-Lie quasi-deformations via twisted derivations of infinite-dimensional
Lie algebras of vector fields of Witt and Virasoro
type.

**Time: **kl** **14:05-15:00, Tuesday, May 8,

**Place:** MH:309B, Centre for
Mathematical Sciences,

**Speaker:** **Lars Hellström**,
Umeå university

**Title:** A
Generic Diamond Lemma with applications for nonassociative
algebra, operads,

Hopf algebras, and beyond

*Workshop on homological devices and
non-commutative algebra, **Lund**, **May 8,
2007**
*

**Abstract: **

When
studying algebraic structures defined by generators and relations, one often
relies on a diamond lemma (or some more specialised counterpart, such as may be
found in e.g. Gröbner basis theory) to obtain an
effective model for the structure studied. A problem is however that diamond
lemmas tend to be stated only for a specific family of algebraic structures, so
that each new kind of algebraic structures (with different axioms, a different
set of operations, or whatever) requires its own diamond lemma. In this talk, I
will present my Generic Diamond Lemma and explain how one can apply it for a
large variety of algebraic structures. Focus will be on (i)
how a single result can handle many different kinds of multiplicative
structures (commutative, associative, free non-associative, path algebra, etc.)
and (ii) how to handle many-sorted algebraic structures (operads,
PROPs, symocats, etc.).

**Time: **kl** **15:30-16:30, Tuesday, May 8,

**Place:** MH:309B, Centre for
Mathematical Sciences,

**Speaker:** **Goro****
Kato**,

**Title:** N-Complexes
and Precohomologies, [NCPC]

*Workshop on homological devices and
non-commutative algebra, **Lund**, **May 8,
2007**
*

**Abstract: **

For an abelian category A, we can from the category Se(A) of
sequences and morphisms of A. Recall that in
order to define cohomologies we need the
category of complexes. There is a new invariant, generalizing the
notion of a cohomology, defined from Se (A) to
A. This invariant is said to be a precohomology.
There exist two functors from Se(A) to the
category of N-complexes, where N>1. Those functors
are said to be complexifying functors.
Then we can define a cohomology on the complexified objects in the category of N-complexes, which
is the precohomology of (i,k)-type.
In order to define the Derived Category on N-complexes, we need several
projects including the notions of quasi-isomorphism of N-complexes, homotopy of N-complexes, spectral sequences based on
N-complexes and precohomologies of composite functors, hyperprecohomologies.
Also one can define a notion of inverse limits connecting to precohomologies. We will outline those
projects and main statements.

**Time: **kl** **16:30-17:30, Tuesday, May 8,

**Place:** MH:309B, Centre for
Mathematical Sciences,

**Speaker:** **Daniel Larsson**,
Institute Mittag-Leffler,

**Title:** Some
Applications and Origins of N-complexes.

*Workshop
on homological devices and non-commutative algebra, **Lund**, **May 8,
2007**
*

**Abstract: **

In this talk I will discuss definitions,
motivations and applications, present and future, of so-called N-complexes.
These generalize ordinary complexes in homological algebra in that one do not
assume the differentials to be square-zero. Instead they are nilpotent of some
higher order.

**Time: **kl 11:00-12:00, Tuesday, February 27,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **Tomo****
Matsusita****, Ritsumeikan University****, Japan.**** **

**Title:** Static Hedging in Supermarkets.

*Joint with
Mathematical Statistics seminar*

**Abstract: **

We introduce a notion of supermarkets and show
that in the supermarkets there are plenty of assets and "static hedging
" is always possible. Typical examples are concerning
Cox-Ross-Rubinstein's binary markets and Black-Sholes
markets. Mathematically, expansions with respect to exponential martingales
play central roles.

**Time:** kl 15:15-16.15, Tuesday, February 27,

**Place:** MH:333, Centre for Mathematical
Sciences,

**Speaker:** **Jun Tomiyama,
****Tokyo Metropolitan University****, ****Japan**** Women’s University. **

**Title:** Matrix
Monotone, Convex Functions and Truncated Moment Problem.

**Abstract: **

For a nontrivial interval I in the real line, a real valued
continuous function f defined in I is said to be n-matrix monotone if the
function calculus of f on the selfadjoint part of n
by n matrix algebra M(n) keeps the order in M(n), and n-matrix convex when the
calculus keeps the convexity. Notions of operator monotonicity
and operator convexity of f are similarly defined replacing M(n) by the algebra
of all bounded linear operators on an infinite-dimensional Hilbert space. Write
the sets of those functions as P_n(I) and K_n(I) and the latter classes as P_{\infty}(I)
and K_{\infty}(I).

In this talk, I shall show a deep relationship between the existence of
polynomials in P_n(I) as well as in K_n(I) and truncated moment problems for a finite interval
I, from which we can see an important aspect of structure of pilings of those P_n(I)'s and K_n(I)'s down to
P_{\infty} and to K_{\infty}.
This also brings an insight of the pilings for an infinite interval.

**Time: **kl 16:20-17:20, Tuesday, February 27,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **Tamotsu Teruya****, Ritsumeikan University****, Japan.**** **

**Title:** Equivalence bimodules
arising from index two inclusions of C*-algebras.

**Abstract: **

`Let A be a unital C*-algebra. We shall introduce involutive`

`A-A-equivalence bimodules and prove that any C*-algebra`

`containing $A$ with Watatani index 2 is constructed by an involutive`

`A-A-equivalence bimodule.`

**AUTUMN 2006**

Lund 2006,
October 12- October 14, 2006, “Algebra, Geometry and Mathematical
Physics” conference organized by AGMF: “Algebra, Geometry and
Mathematical Physics” Baltic Nordic network

**SPRING 2006**

**Time:** kl. 13.15-15.00,
Wednesday, May 24,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** Jun Tomiyama,
** **

**Title:** On the structure of the spaces of matrix monotone
functions and matrix
convex functions.

**Abstract: **

Let I be a
nontrivial interval in the real line, and denote by P_n(I)
and K_n(I) the spaces of monotone functions and
convex functions defined on the matrix algebra M_n
and the interval I respectively. We investigate what kinds of polynomials are
contained in those spaces and how rich they are besides those so-called
operator monotone functions and operator convex functions contained in P_n(I) and K_n(I) for every n.
Discussions may contain the characterizations of 2-convex functions as well as
(if possible) the consideration of convex functions on C*-algebras.

**Time: ** kl. 15.15-16.15, Wednesday, May 24,

**Place:**
MH:333, Centre for Mathematical Sciences,

**Speaker:** Yacin Ameur, Kalmar
Högskolan:

**Title:** On
the structure of the spaces of matrix monotone functions and matrix convex functions.

**Abstract: **

The
talk will concern some results related to a joint work with Sergei Silvestrov and Sten Kaijser. I will also discuss
generalizations of interpolation functions, for example to Hilbertian operator spaces.

**Time:** kl. 16.30-17.30,
Wednesday, May 24,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** Hiroyuki Osaka, Ritsumeikan
University, Kusatsu, Japan

**Title:** Stable
rank of inclusion of C*-algebras of depth 2

**Abstract: **

The notion of topological stable rank for
a C*-algebra $A$, denoted by $\tsr(A)$, was
introduced by Rieffel, which generalizes the concept
of dimension of a topological space.

He presented the basic properties and
stability theorem related to K-Theory for

C*-algebras. He also proved that $\tsr(A \rtimes_\alpha {\mathbb Z}) \leq \tsr(A) + 1$, and asked if an irrational rotation algebra
$A_\theta$ has topological stable rank two. I. Putnum
(\cite{pu}) gave a complete answer to this question,
that is, $\tsr(A_\theta) = 1$.

**Time:** kl
13.15-14.15, Friday, March 31,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **Nacer****
Makhlouf**,

**Title:** Hopf Algebras and Hom-Hopf Algebras.

**Abstract: **

The
discovery of quantum groups gives impulse to a strong development in the theory of Hopf algebras. In my talk
I will summarize the recent developments
and give some results on rigidity of Hopf
algebras and irreducible components of Hopf algebraic
varieties. This geometric and local study uses the algebraic formal
deformations introduced by Gerstenber. Then, I will
introduce the basic concepts of Hom-Hopf algebras.
This structure is based on a modified associative algebra structure by a
homomorphism. Using the reversing arrow ansatz, one
defines the Hom-comultiplication, Hom-bialgebras
and Hom-Hopf algebras.

**Intensive advanced mini-course in algebraic geometry
with applications**

Detailed information is at the course home page:

*Minikurs i algebraisk geometri och
tillämpningar*

**Nacer Makhlouf,
**

**Exploring Algebraic Sets with
Computer Algebra Systems.**

**Time:**

Monday 27 mars, 15.15-17.00,

Wednesday 29 March, 13.15-15.00,

Thursday 30 March, 10.15-12.00

**Place:**
MH:228, Centre for Mathematical Sciences,

**Time:** kl
15.30-16.30, Tuesday, March 21,

**Place:** MH:333, Centre for
Mathematical Sciences,

**Speaker:** **Kjetil**** Røysland, ****University of Oslo****, ****Norway**

**Title:** Symmetric MRA Wavelets in L2(R^n).

**Abstract: **

Given
various group actions on L2(R^n) , we will consider MRA's generated by invariant scaling functions.

Inspired by a paper of Packer and Rieffel, we will
give conditions for

the existence of invariant MRA wavlets.

Packer, Judith A. and Rieffel, Marc A. (2003).
Wavelet filter functions,

the matrix completion problem, and projective modules over C( T^n). J.

Fourier Anal. Appl. 9 No.2, 101-116.

**PhD
thesis defence of Daniel Larsson, Lund University, Sweden**

**Time:** kl
15.30-16.30, Friday, February 24.

**Place:** MH:C, Centre for
Mathematical Sciences,

**Title of the PhD Thesis:** Quasi-Lie Algebras and Quasi-Deformations. Algebraic Structures Associated with Twisted
Derivations

**Opponent: **Professor
Jürgen Fuchs, Institutionen för ingenjörsvetenskap, fysik och matematik,
Karlstad Universitet ** **

**Abstract: **

This thesis introduces a new deformation scheme for Lie algebras, which we
refer to as “quasi-deformations” to clearly distinguish it from the
classical Grothendieck-Schlessinger and Gerstenhaber
deformation schemes. The main difference is that quasi-deformations are not in
general category-preserving, i.e., quasi-deforming a Lie algebra gives an
object in the larger category of “quasi-Lie algebras”, a notion
which is also introduced in this thesis. The quasi-deformation scheme can be
loosely described as follows: represent a Lie algebra by derivations acting on
a commutative, associative algebra with unity and replace these derivations
with twisted versions. An algebra structure is then imposed, thus arriving at
the quasi-deformed algebra. Therefore the quasi-deformation takes place on the
level of representations: we “deform” the representation, which is
then “pulled-back” to an algebra structure.

The different Chapters of this thesis is concerned with different aspects of
this quasi-deformation scheme, for instance: Burchnall-Chaundy
theory for the q-deformed Heisenberg algebra (Chapter II), the (quasi-Lie)
algebraic structure on the vector space of twisted derivations (Chapter III),
deformed Witt, Virasoro and loop algebras (Chapter
III and IV), Central extension theory (Chapter III and IV), the Lie algebra sl(2) and some associated quadratic algebras.

**Time:** kl
15.30-16.30, Friday, February 17.

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Lionel Richard, ****Antwerp University****, ****Belgium**

**Title**: On the Gelfand-Kirillov conjecture, its
quantum version and a mixed version.

**Abstract:
**

Initiated in their paper of 1966, the Gelfand-Kirillov
problem is dealing with the

rational equivalence (isomorphism of
skew-fields of fractions) of universal enveloping algebras of algebraic Lie
algebras and Weyl algebras (differential operators on
the affine space). In the 90's appeared an analogue of this problem for quantum
groups.

In this talk I will first present the Gelfand-Kirillov conjecture and its quantum version. In the

quantum case, I will present a theorem of G. Cauchon (2003), dealing with a large class of

**AUTUMN 2005**** **

**Time: **kl. 11.00-12.00, Tuesday,
December 6.

**Place:** MH:333, Centre for Mathematical Sciences,

Examensarbete. Master Thesis.

**Speaker: ****Johan Öinert**, **F00, ****Lund**** ****University**** (LTH)**

**Title**: Connections between Topological Dynamical Systems and
Non-Commutative C*-algebras.

**SPRING 2005**** **

**Time: **kl. 15.30-16.30, Monday,
21 February.

**Place:** MH:332:B, Centre for Mathematical
Sciences,

**Speaker: ****Jun Tomiyama,** **Tokyo**** ****Metropolitan**** ****University****:**

**Title**: Non-Linear Calculus for Monotone Operator Functions on C*-Algebras.

**Time: **kl. 15.30-16.30, Monday,
17 February.

**Place:** MH:C, Centre for Mathematical Sciences,

*Matematiska** Kollokviet. Colloquium. *

**Speaker: ****Jun Tomiyama,** **Tokyo**** ****Metropolitan**** ****University****:**

**Title**: Interplay between Topological Dynamical Systems and
C*-Algebras (Case of Recurrent Sets).

**Time: **kl. 10.15-11.00,
Friday, 4
February

**Place:** MH:333, Centre for Mathematical Sciences,

Examensarbete. Master Thesis.

**Speaker: Christian Svensson**, **F99, ****Lund**** ****University**** (LTH)**

**Title**: Commuting Differential Operators and Commuting
Elements in Non-commutative Algebras.

**Time: **kl. 10.15-11.00, Friday,
28 January*.*

**Place:** MH:333, Centre for Mathematical Sciences,

Examensarbete. Master Thesis.

**Speaker: ****Roland Mezöfi**, **E00, ****Lund**** ****University**** (LTH)**

**Title**: On the q-Deformed Gelfand-Dickey Hierarchy, the q-Deformed Volterra Equation and Their Generalizations.

**AUTUMN 2004**** **

**Time:** kl 15.30-16.30,
Friday, August 27.

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker:
Yacin Ameur, **
**Kalmar**** Högskolan,**

**Title**: Intepolation functions on unital C*-algebras

**Abstract:
(English)**

Let $a$ be a strictly positive element of a unital
C*-algebra $A$, and define

the '$a$-norm' on $A$ by $\|x\|_a=\|a^{1/2}xa^{-1/2}\|$,
$x\in A$. A

positive function $h$ defined on $\sigma(a)$ is called an interpolation
function with

respect to $a$ if the inequality $\|x\|_h(a)\le \max(\|x\|,\|x\|_a)$ holds for

all $x\in A$. We shall give a necessary and sufficient condition for $h$ to be
an

interpolation function, and also discuss the relations between interpolation
functions and the recently studied classes of monotone functions defined on the
positive elements of a C*-algebra.

**Abstract:
(Swedish)**

Låt $a$ vara ett
strikt positivt

element i en C*-algebra $A$ med enhet. Sätt

$\|x\|_a=\|a^{1/2}xa^{-1/2}\|$.
En positiv

funktion $h$ definierad på $\sigma(a)$ säges

vara en interpolationsfunktion m.a.p. $A$ om

olikheten

$\|x\|_{h(a)}\le \max(\|x\|,\|x\|_a)$ är

uppfylld för alla $x\in A$. Vi skall ge ett

nödvändigt och tillräckligt villkor på $h$ för

att vara en interpolationsfunktion. Vi skall

även diskutera relationerna mellan

interpolationsfunktioner och de nyligen

studerade klasserna av monotona funktioner

definierade på de positiva elementen av en

C*-algebra.

**4'nd Öresund Symposium on Non-commutative Geometry and
Non-commutative Analysis**** **

Centre
for Mathematical Sciences, Lund University,

Sergei Silvestrov, (e-mail: sergei.silvestrov@math.lth.se), Centre for mathematical
Sciences, Lund University,

Soeren Eulers (e-mail:
eilers@math.ku.dk)

**Program
and abstracts can be downloaded at**

Öresund symposiums on non-commutative geometry,
non-commutative analysis and applications

**or as
separate file here: PDF**

Öresund symposiums on non-commutative geometry,
non-commutative analysis and applications

**AUTUMN
2003:**

**Time:** kl 11.15-12.00, Torsdag, December 11.

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker:** Jakob Willborg,
student (F96),

**Title:** Non-commutative operator method for equations of difference and

q-difference type

OBS! Master
thesis presentation

**Abstract:** (English)

Non-commuting operators are of great interest in many different disciplines

e.g. applied physics and applied economics besides the pure mathematics. One

needs only to point to the fact that some very fundamental theorems in

quantum mechanics involve the aspect of non-commuting operators to see the

use of this theory. Different generators and defining relations result in

different quantum mechanic interpretations. This thesis centers
on the

application of operator methods for solving differential, difference,

q-difference and q,H-difference equations. Methods
for solving these

equations are developed by considering the commutation relations satisfied

by the operators. First some necessary notions are introduced and then a

general and effective operator method is presented to solve all of those

different types of equations. This operator method is expanded to all such

operator equations of order n with constant coefficients. The nature of the

operator commutation relations are studied and some results e.g. reordering

formulas, covariance commutation relations and more or less explicit

formulas for the powers of the operators are presented. Examples are given

of solutions to different equations. Both homogenous equations and

particular solutions of the non-homogeneous equations are studied. The

convergence of the q-deformed difference equation is investigated in some

detail with the help of visualizations done numerically with a Matlab

program. Finally, D{q,H}-equations are investigated.

**Time:**

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Ralf Fröberg, Department of Mathematics, ****Stockholm**** ****University**

e-mail: ralff@math.su.se

**Title**: Noncommutative Groebner bases, Koszulity, and coherence

**Abstract:
(English)**

I am going to show how one with algebra can calculate the number

of steps of length n in a digraph. This leads naturally to the definition

of Koszul algebras, which I am going to review.

If someone
wants to prepare oneself for Koszul algebras, then
they can

read the review article which I have written:

Ralf Fröberg, Koszul algebras, Proc. Fez Conf.
1997, eds. Dobbs,

Fontana, Kabbaj, lect.
Notes Pure Appl. Math. 205,
Marcel Dekker.

**Abstract:
(Swedish)**

Jag kommer att visa hur man med algebra kan räkna ut antalet stigar av

längd $n$ i en digraf. Detta leder naturligt till definitionen av

Koszulalgebror, som jag kommer att tala översiktligt
om.

Om någon vill
förbereda sig på Koszulalgebror kan de läsa en

översiktsartikel jag har skrivit:

Ralf Fröberg, Koszul algebras, Proc. Fez Conf.
1997, eds. Dobbs,

Fontana, Kabbaj, lect. Notes Pure Appl.
Math. 205, Marcel Dekker.

**Time:**

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker:Dmitri**** Piontkovski**

Central Institute of Economics and Mathematics

Nakhimovsky prosp. 47,

e-mail: piont@mccme.ru

**Title**: Noncommutative Groebner bases, Koszulity, and coherence

**Abstract:**

We will consider a class of associative graded algebras (so-called
algebras

with non-commutative generalized Koszul filtrations)
which includes

coherent algebras (in partivular, Noetherian
algebras) and many important Koszul

rings. Our main examples are algebras where every right-sided finitely
generated

ideal has a finite Groebner basis. If time will allow,
also the commutative examples

arising from algebraic geometry will be under consideration.

**Time:**

**Place:** MH:309C, Centre for Mathematical Sciences,

**Speaker: V.Manuilov, **

**Title**:

Operators under non-rigid relations and almost
representations of groups.

**Abstract:**

Let r_{1},...,r_{m} be a set of
relations on elements a_{1},...,a_{n}.

An $\varepsilon$-almost representation of this set of
relations is a set

b_{1},...,b_{n} of operators on a
Hilbert space (often finite-dimensional)

such that ||r_j(b_{1},...,b_{n})||<
or =\varepsilon. A set of continuous

families b_{1}(t),...,b_{n}(t), t \in
[0,\infty), of operators is an

asymptotic representation if it is an $\varepsilon(t)$-representation
for

each t and if lim_{t}_{->\infty\varepsilon}(t)=0.
Some properties of

almost representations can be seen already in the case of the commutation

relation r(a_{1},a_{2})=a_{1}a_{2}-a_{2}a_{1}.
In the case of finite-dimensional Hilbert

spaces (with increasing dimension) there are topologically nontrivial

almost representations and the corresponding topological invariant (which is

the Chern character) is stable under small
deformations and distinguishes

also unbounded representations. In the special case when the relations define

a group almost representations, we define almost flat vector bundles over

classifying spaces of groups and we discuss the relation to the Novikov

conjecture. We also discuss a possibility to extend an almost representation

to an asymptotic one.

**SPRING 2003:**

**Time:**

**Place:** MH:332a, Centre for Mathematical Sciences,

**Speaker: Pär Kjellberg,
Department of Chemical Physics, ****Lund**** ****University**

**Title:**''Molecular Symmetry.''

**Abstract: **The mission of the natural sciences is to find relations or
rules,

which can be used in order to understand nature.

The world is a complex place and it is often not

an easy task to describe it in a simple way.

When exploring an object in this our diverse universe

it is a well-known fact that if one finds some general symmetrical

properties of it, what ever it may be, this symmetry will

simplify the problem.

The talk will be about symmetry and group theory in the field of

Molecular Physics. The classification of molecules according to their

symmetries will be explained. An overview of the major point groups

will be given, as well as their application to vibrational
modes,

chemical bonding and electronic transitions. Examples of more

complicated problems will be given in relation to the work at the

department of Chemical Physics at

2'nd Öresund Symposium on
Non-commutative Analysis and Non-commutative Geometry

Department
of Mathematics,

Time:
11.00 -- 17.20

Organizers:

Sergei Silvestrov,

Soeren Eulers, Gert
Pedersen,

Want
the program ? Click here

**Time:** 15.30-16.30,

**Place:** MH:C, Centre for Mathematical Sciences,

**Speaker: Professor Erik Alfsen, Department of
Mathematics, ****Oslo University****, ****Norway**

Colloquium
talk !

**Title:**''

of quantum mechanics.''

**Abstract: **Non-commutative associative algebras were

introduced as a model of quantum mechanis by
Heisenberg and Born in the

mid-twenties. Shortly afterwards P. Jordan proposed an alternative model

measurement theory of quantum mechanical observables can be dealt with

in both approaches. However, it is an imortant
feature of quantum

mechanics that the physical variables play a dual role, as observables,

and as generators of of one-parameter groups of
transformations which

describe the time development of the quantum system. An associative

product can be decomposed in a

associative models of quantum mechanics, the measurement theory relates

to the

Thus both aspects of a physical variable can be accounted for in an

associative model. Not so in the

necessary to describe the time development. What is needed, is the

existence of a "dynamical correspondence", defined in terms of

one-parameter groups of order preserving transformations generated by

"order derivations". Such a dynamical correspondence will give each

element of the

application to physics. Mathematically, the theory of dynamical

correspondences carracterizes the relevant

associative algebras (C*-algebras) among the corresponding

algebras (JB-algebras). In the talk this will be explained

with precise statements of definitions and results together with some

brief comments on the ideas of the proofs.

**Time:** 13.15-15.00,

**Place:** MH:140, Centre for Mathematical Sciences,

**Speaker: Professor Erik Alfsen, Department of
Mathematics, ****Oslo University****, ****Norway**

**Title:**''On the state space geometry of Jordan
and C*-algebras.''

**Abstract: **For a JB-algebra, as well as a C*-algebra, one

can define the concept of a "state space", wich
models the "mixed states"

of quantum theory. In both cases, the state space is a compact convex set.

In the JB-algebra case, this compact convex set completely determines the

algebra. But in the C*-algebra case, more structure is necessary to recover

the non-commutative product. It turns out that what is needed, is a
"global

orientation" which "locally distinguishes multiplication from the
left from

multiplication from the right". In fact, the existence of such an

orientation characterizes the state spaces of C*-algebras among those of

JB-algebras. In the talk this will be explained with precise statements
of

definitions and results together with some brief comments on the ideas of

the proofs.

**Time:** 17.15-18.00,

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Jakob Wilborg,
student, ****Lund**

**Title:**"Operator method for solution of differential, difference and
q-difference equations"

**Abstract: **This is a well prepared introductory lecture

about the famous operator method for obtaining solutions for

differential, difference and q-difference equations.

The central role of non-commutativity will be
explained.

**Time:** 15.30-16.30,

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Stefan Heimgård, Student, **
**Lund**

**Title:**"Transfer operators, wavelets and Cuntz
operator algebras"

**Abstract: This is a well prepared introductory lecture,**

based on a section from the recent excellent book by Ola
Bratteli and Palle
Jorgensen:

Ola Bratteli, Palle E. T. Jorgensen,

Wavelets through a Looking Glass. The World of the Spectrum,

Series "Applied and Numerical Harmonic Analysis",

Birkhäuser, Boston, 2002. (ISBN: 0-8176-3962-4)

**AUTUMN 2002:**

**Time:** 13.30-14.30, Friday, December 13, 2002.

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Professor Jun Tomiyama, **
**Tokyo****, Japan**

**Title:**"Projection theorem revisited. "

**Abstract: **In a basic interplay between topological dynamics and
C*-theory,

the Projection theorem plays a central role. With a simple proof recently
found,

I will discuss important consequences of this result together with further
recent

development.

**Time:** 13.30-14.30,

**Place:** MH:309B, Centre for Mathematical Sciences,

**Speaker: Professor Jun Tomiyama, **
**Tokyo****, Japan**

Colloquium
talk !

**Title:**"Interplay between topological dynamics and theory of
C*-algebras. "

**Abstract: **Here I will discus, with brief history, general background and

basic relations between two theories:

how noncommutative C*-algebras naturally appear in relation

with topological dynamical systems ?

**Time:** 13.30-14.30, Wendesday,

**Place:** MH:333, Centre for Mathematical Sciences,

**Speaker: Niels Jakob Laustsen, **Department of Mathematics,

http://www.math.ku.dk/~laustsen/

**Title**:"Commutators of operators on Banach
spaces "

**Abstract: **The *commutator* of two
operators S and T is given by

[S,T] := ST - TS. The original motivation for studying commutators
of

operators comes from quantum mechanics, in which case the operators S

and T are unbounded and act on a Hilbert space. Commutators
are also

useful from a purely mathematical point of view when studying

non-commutativity. Indeed, the theme of this talk is
that we can gain

insight into the non-commutative structure of the Banach

algebra B(X) consisting of all (bounded, linear) operators on

a Banach space X by studying the commutators
of operators on X and the

subspace that they span.

First I
shall review some classical results about commutators
of operators

on a Hilbert space, in particular Halmos's theorem
that each operator on

an infinite-dimensional Hilbert space is the sum of two commutators.
Then

I shall explain how this result can be generalized to operators on many

other Banach spaces, including c_{0},
C([0,1]), l_{p}, and L_{p}([0,1])

for 1<=p<=infinity. The proof has a strong algebraic flavour

and so may appeal to algebraists as well as analysts.

Halmos's
theorem does not extend to all Banach spaces: there
are Banach

spaces X such that B(X) admits a non-zero trace, and so not

all operators on such a Banach space X can be a sum
of commutators. One

family of Banach spaces with this property is the
quasi-reflexive James

space J_{p}. I shall introduce this important
Banach space and outline a

proof of the fact that there is a unique normalized trace

on B(J).

**Time:** 13.15-14.15,

**Place:** MH:333, Centre for Mathematical Sciences, Lund

**Speaker: Magdalene Grantson, **Department of Computer
Science, Lund

**Title:**"An Introduction to Sphere Packing
, Kissing Numbers and Symmetry "

**Abstract:**

Sphere packing is a problem where mathematicians try to determine how tightly

spheres can be packed in a box. The problem asks for the densest packing of
equal

spheres in n-dimensional space. A typical example is a grocer trying to stack

apples in his store or pack them in a box. Arranging the apples in any random
way

may result in an inefficient miss-use of space. Even though there exists several

forms of packing, I will be looking at lattice periodic packing

for identical spheres in 1,2, 3-dimensions. In lattice packing the centers of the spheres

form a lattice in R^{n}. Actually, because of
their regularity lattice packings

are easier to study than non-lattice ones.

In three
dimensions ,the Kissing number problem ask how many spheres

can be arranged so that they all just touch or "kiss" another sphere
of the same size.

Note that for a lattice packing this is simply the number of balls touching any
given one,

since every ball touches the same number of others.

Mathematicians
define symmetry in terms of reflections, rotations, and

inversions that produce an object that is indistinguishable from the original.

There is a
relation between symmetry and lattice packing of spheres, since

Lattices give rise to symmetry groups

**SPRING 2002 and AUTUMN 2001**

**Time:** Friday, May 31, 2002,
14.00-15.00.

**Place: **Room: MH 333, Centre for Mathematical Sciences, Lund

**Speaker: **Jonas Hartwig, Centre for
Mathematical Sciences, Lund

**Title:** "Generalized Derivations on Algebras"

**Abstract:**

We consider linear operators on associative algebras

which satisfy a generalized version of the Leibniz rule for differentiating the
product of

two functions. Examples of such operators include coloured (or graded)
derivations,

in particular superderivations, and varius kinds of difference and shift operators.

Some
necessary equations for generalized derivations on the quantum plane is stated.

We define a module structure on spaces of derivations, and

then state a theorem which determines the structure of some generalized

derivations on associative algebras which are unique factorization domains

as rings, in particular on polynomial algebras. Finally we generalize the Witt
algebra

to a skew-symmetric algebra of generalized derivations on a commutative
associative algebra.

**Titel på
svenska:**
"Generaliserade Deriveringar på Algebror"

**Sammanfattning på svenska:**

Vi studerar lineära operatorer på associativa algebror

som uppfyller en generaliserad version av

Leibniz regel för derivatan av produkten av två
funktioner.

Exempel på sådana operatorer omfattar färgare (eller graderade)

deriveringar, speciellt superderiveringar,

och olika typer av differens- och skiftoperatorer.

Några nödvändiga
ekvationer för generaliserade deriveringar

på kvantumplanet formuleras. Vi definierar en modul-struktur
på rum av deriveringar,

och formulerar en sats som bestämmer strukturen på några

generaliserade deriveringar på associativa algebror med

unik faktorisering, speciellt på polynomalgebror.

Slutligen generaliserar vi Witt algebran till en skev-symmetrisk

algebra av generaliserade derinveringar på en
kommutativ associativ algebra.

**Time:**

**Place: **Room: MH 333, Centre for Mathematical Sciences,

**Speaker: **Lars Hellström, Department of
Mathematics, Umeå Universitet.

**Title:** "On semigroups for filtered
structures."

**Abstract:**

In Mora's unified theory for Gröbner and standard
bases using filtered

structures, the term order serves two purposes. On one hand it is (as

usual) discerning the head term of a polynomial, and on the other it

defines the topology of the algebra. A consequence of the latter is that

the elements in the neighbourhood basis of zero will be indexed by the

elements from a pretty arbitrary semigroup. In
topologies that are defined

by a real-valued norm, elements in the neighbourhood basis of zero would

instead be indexed by positive real numbers. Since semigroups
are more

general, one might expect that filtered structures can define topologies

that real-valued norms cannot, but in fact the opposite is true: every

topology that is induced by a filtered structure that fulfills
all

conditions in Mora's theory can alternatively be defined using a norm that

merely takes rational numbers as values. The reason for this is that the

semigroup of any such filtered structure must have an
order-preserving

homomorphism to the integers.

**Titel på
svenska: **"Om
semigrupper hos filtrerade strukturer"

**Sammanfattning på svenska:**

I Moras förenade teori för Gröbner/standard-baser med hjälp av

filtrerade strukturer så används termordningen för två olika saker:

dels för att som vanligt urskilja den ledande termen i ett polynom,

men även för att definiera den topologi som används. En följd av det senare är
att

elementen i topologins omgivningsbas till punkten
noll kan vara indexerade med

element ur en i stort sett godtycklig semigrupp; som en jämförelse kan

nämnas att en topologi som istället definieras av en reellvärd norm har

en omgivningsbas där elementen är indexerade med
positiva reella tal. Man

skulle därför kunna förvänta sig att man utifrån filtrerade strukturer

kan definiera topologier som inte hör ihop med någon reellvärd norm, men

det visar sig faktiskt vara tvärt om; en filtrerad struktur som uppfyller

alla villkor i Moras teori inducerar en topologi som lika gärna kan

definieras av en rationellvärd norm. Orsaken till detta är att varje sådan

semigrupp har en ordningsbevarande homomorfi till heltalen.

**Time:** Tuesday, May 14, 2002, 15.15-16.15.

**Place: **Room: MH 333, Centre for Mathematical Sciences, Lund

**Speaker: **Samuel Rydh, Department of
Mathematical Physics, KTH, Stockholm.

**Title:** "NCG field theory models and anomalies."

**Abstract:**

I will give a brief introduction to NCG field theory

models in the Hamiltonian framework with the focus on the

quantization of chiral fermions. I will discuss the cocyles

describing the chiral symmetry breaking and address
the issue

of locality.

**Titel på
svenska:**

**Sammanfattning
på svenska:**

Jag kommer att ge en kort introduktion till

icke kommutativa kvantfältmodeller med fokus pa
kvantiseringen

av chirala fermioner i den hamiltonska formuleringen. Jag

kommer att diskutera de cocykler som beskriver det chirala

symmetribrottet och ta upp fragan om lokalitet.

**Time:** Friday,

**Place: **Room: MH 333, Centre for Mathematical Sciences,

**Speaker: **Soeren Eilers,
Department of Mathematics,

**Title:** "Invariants for substitutional subshifts."

**Abstract:**

Based on a *substitution* on a finite alphabet, such as

T(0)=01
T(1)=10

one may define a dynamical system, a *substitution subshift*,

where the points are doubly infinite

sequences such as

.....
10100110010110100101100110100110010110011010010110 .....

where each
finite subword is a subword
of T^{n}(a) for suitable n and a,

and where the automorphism is the forward shift.

Such
dynamical systems are of interest not only as tractable examples

in the theory of dynamical systems, but also as models for complex

behaviour in other branches of mathematics and applications. Work in

such diverse areas as formal languages, number theory, tiling geometry

and mathematical physics employs substitutions and their subshifts.

One basic
problem is to determine whether or not two such systems are

equal is the sense of *conjugacy*. Attacking
this problems

requires a rich and diverse supply of computable invariants.

In the
talks, after a careful introduction to the subject, it will be

my goal to demonstrate how the seemingly unrelated non-commutative

discipline of

operator algebras becomes an important source of invariants

here. The focus in the first talk will be on seminal work by Durand,

Host and Skau. In the second, I hope to cover recent
work by myself

and T. M. Carlsen.

**Titel på
svenska:**

**Sammanfattning
på svenska:**

**Time:**

**Place: **Room: MH 333, Centre for Mathematical Sciences,

**Speaker: **Prof. Dmitrii Silvestrov

Department of Mathematics and Physics,

**Title:**Non-linearly Perturbed Non-negative
Matrices

and Ergodic Type Theorems

**Abstract:**

The lecture presents results of asymptotical analysis for the powers P(t)^{n}

of non-linearly perturbed non-negative matrices

P(t) = P_{1} t + P_{2} t^{2} + ... + P_{k} t^{k}
+ o(t^{k} ).

The explicit algorithm is described for calculations of the corresponding

expansions for invariant and quasi-invariant projectors and other functionals.

The method is based on techniques of perturbed renewal equations.

It turns out that the balance between perturbation parameter t and n has a
delicate

influence upon the form of the expansions. This balance can be of

the form t^{r} n **-->** const as t **-->**
0 and n **-->** infinity, where 0 < r < k+1.

Applications to analysis of ergodic and
quasi-stationary phenomena for non-linearly perturbed

stochastic systems are described. Prospective generalisations for presented
results are discussed.

**Titel på
svenska:**

**Sammanfattning
på svenska:**

**Time:** Friday, March 22, 13.15-15.00

**Place: **MH:333, Matematikcentrum

**Speaker: **Nadia S. Larsen, Department of Mathematics,

University of Copenhagen

**Title:**"Hecke algebras and their
C^*-algebra completions"

**Abstract:**

A group G together with a subgroup G_{0} form a

Hecke-pair if for each element g in G, the double coset

G_{0}g G_{0} is a finite union of left cosets
g_{i}_{ }G_{0}.

A trivial example is that when the subgroup G_{0} is

normal, in which case every double coset is a single
left coset. One

associates to a Hecke pair a *-algebra, and then a
natural question is

whether a *-algebra completion may be constructed in a manner similar

to the completion of the group algebra to the group *-algebra.

Following Bost and Connes's
construction of a Hecke *-algebra arising

in number theory, several authors have recently considered the

problem of constructing completions of more general Hecke
algebras. The

aim of this talk is to introduce the necessary terminology and to review

some of these approaches.

**Titel på
svenska:**

**Sammanfattning
på svenska:**

**Time:** Thursday, March 7, 15.30-17.00

**Place: **MH:333, Matematikcentrum

**Speaker: Jaak Peetre**
(Centre for Mathematical Sciences,

**Title:**"Loewner theory and interpolation
functions"

**Abstract:**

Loewner theory is about matrix monotone
functions.

It has many important applications, e.g. in mathematical physics

and in net work analysis (Duffin and his school).

In this talk I discuss Loewner theory in connection
with

the theory of interpolation functions.

In fact, interpolation functions involve an additional

parameter *p* so in the latter theory may be viewed

as a kind of generalized Loewner theory. This is this

aspect which will be emphasized in the talk.

No previous knowledge of interpolation is supposed.

**Titel**** på svenska:** Operatormonotona
funktioner och Löwners sats

**Sammanfattning
på svenska:**

**Time:** Tuesday, Fabruary
19, 16.00-17.00

**Place: **MH:333, Matematikcentrum

**Speaker: Nail Ibragimov **(Centre for
Mathematical Sciences,

**Title:** "Non-linear superposition principles and

the Vessiot-Guldberg-Lie
algebras"

(Obs ! Nail Ibragimov will give
also lecture on Dynamical Systems

Seminar starting at 17.15. Topics are related but not the same.)

**Abstract:**

The talk is aimed at discussing the theory of nonlinear

superposition principles for nonlinear differential equations on Lie

algebras. The problem of identifying all systems of first-order ordinary

differential equations whose general solution can be expressed

as a function of a finite number of particular solutions

(they are termed a fundamental system of solutions)

was considered by E. Vessiot, A. Guldberg
and S. Lie in 1893,

and I call the underlying Lie algebra the Vessiot-Guldberg-Lie
algebra.

In the first lecture, we will discuss definitions and the main theorem

due to Lie and illustrate it by several examples.

A new application will be considered in Lecture 2.

Different criterias for existence of weak solutions
and three different

existence theorems will be discussed.

**Titel på svenska:**

**Sammanfattning på svenska:**

**Time:** Wednesday, February 13, 14.00-15.00
(OBS! time)

**Place:** MH:333, Matematikcentrum,

**Speaker:** **Daniel Bundzik** (Malmö Högskola)

**Title:**"Quantum physics, Quantum mechanics and Applications"

**Abstract:**

A historical review of quantum physics

will be presented. The fundament

of quantum mechanics is discussed with Schrödinger equation as

reference. If time admits, modern quantum

mechanical applications are
illustrated.

**Titel på
svenska: **"Kvantfysik,
Kvantmekanik och Tillämpningar"

**Sammanfattning på svenska:**

En historisk
överblick av kvantfysikens frågeställningar och fenomen

presenteras. Kvantmekanikens fundament diskuteras med Schrödingers

ekvation som utgångpunkt. I mån av tid illustreras
moderna

kvantmekaniska tilläpningar.

**Time:** Monday, January 21, 13.15-14.15

**Place: **MH: 332A, Centre for Mathematical Sciences

**Speaker: Oskar Hagberg **(Mathematical
Statistics, Centre for Mathematical Sciences, Lund)

**Title:**"Hilbert space techniques for
discrete time series"

**Abstract: **(This talk is my examination of the course Spectral Theory for
Hilbert Spaces.)

The
spectral representation theorems for unitary operators in Hilbert spaces will

be shown to have the spectral representation theorems of random processes as

special cases. For simplicity and brevity, I confine myself to the case of

discrete time, as described e.g. in chapter VI of Shiryaev's
``Probability''.

(The theory for the continuous case is analoguous.) I
will make a short

summary of the needed theory of random processes, so no previous

knowledge of this subject will be necessary to understand the talk.

**Titel på svenska:Hilbertrumsteknik** for diskreta tidsserier

**Sammanfattning
på svenska:**

(Detta föredrag är min examination av kursen Spektralteori för hilbertrum.)

Spektralrepresentationssatserna
for unitära operatorer i hilbertrum kommer att visas

ha satserna om spektralrepresentation av stokastiska processer som

specialfall. För enkelhels skull kommer jag att
begränsa mig till fallet med

diskret tid, som det beskriv i t.ex. kapitel VI i Shirjaevs
"Probability". (Fallet

med kontinuerlig tid är analogt) Jag kommer helt kort att gå igenom den

nödvändiga teorin för stokastiska processer; därför behövs inga speciella

förkunskaper i sannolikhetsteori för att förstå det som sägs.

AUTUMN 2001

**Time:** Thursday, October 18,
16.00--17.00

**Place: **MH: 333, Centre for Mathematical Sciences

**Speaker: Tomas Persson **(Centre for
Mathematical Sciences, Lund)

**Title:**" Operator Monotone functions and Löwner's
theorem"

**Abstract: **The notion and some basic properties

of operator monotone functions will be discussed.

The famous Löwner theorem with two different proofs

by Gunnar Sparr and by A. Koranyi will be presented.

**Titel på
svenska:** Operatormonotona
funktioner och Löwners sats

**Sammanfattning
på svenska:** Begrepp och
några grundläggande egenskaper

av operatormonotona funktioner och Löwners sats

kommer att diskuteras. Den berömda satsen av Löwner
med två olika bevis

av Gunnar Sparr och A. Koranyi kommer att
presenteras.

**Time:** Thursday, October 25, 14.00-15.00

**Place: **MH: 309B, Centre for Mathematical Sciences

**Speaker: Mattias Nilsson **(Centre for
Mathematical Sciences, Lund)

**Title:**"Non-commutative operators of
wavelet analysis"

**Abstract: **Introduction to non-commutative operator methods

in wavelet analysis will be given.

It will be
shown that Wavelet analysis is based on properties

of several important non-commuting operators.

The significance of these operators in Wavelet theory

originates in the fact that they satisfy some commutation relations

(Cuntz relations) and consequently generate operator
representations

of the so called Cuntz C^{*}-algebras.

Some basic
constructions describing this interplay will be presented.

Background
on wavelets will be given.

The lecture
will be of introductory nature, and no special knowledge will be needed.

**Titel på
svenska:** Icke-kommutativa
operatorer inom waveletanalys.

**Sammanfattning
på svenska:**

En introduktion till icke-kommutativa operatormetoder

inom waveletanalysen kommer att ges.

Det visar sig att
waveletanalysen grundas på flera viktiga egenskaper
hos vissa icke-kommuterande operatorer. Betydelsen för dessa operatorer i waveletteorin

härstammar från det faktum att de uppfyller vissa kommuteringsrelationer

(Cuntz-relationer) som således genererar
operatorrepresentationer

av så kallade Cuntz C*-algebror.

Grundläggande
konstruktioner som beskriver dessa samband kommer att presenteras.

En bakgrund till waveletanalysen kommer även att ges.

Det här kommer
att vara en introducerande föreläsning.

Inga särskilda förkunskaper krävs !!!

**Time:** Wednesday, October 31, 14.00-15.00

**Place: **MH: 333, Centre for Mathematical Sciences

**Speaker: **Anders Dahlner** **(Centre for Mathematical Sciences,

**Title:**"Commutative Banach
algebras, The Gelfand Transform and Wiener's
Lemma"

**Abstract: ** We give a brief introduction to commutative Banach algebras and to

the Gelfand transform (a generalization of Fourier
transform and other transforms).

Applications to certain problems in classical analysis will also be discussed.

**Titel på svenska:"Kommutativa** Banachalgebror,
Gelfandtransformen och Wieners Lemma"

**Sammanfattning
på svenska:**

Vi ger en kortfattad introduktion till kommutativa Banachalgebror

och till Gelfandtransformen (en generalisering av Fouriertransformen och andra
transformer). Tillämpningar till vissa problem inom klassisk analys kommer
också att diskuteras.

**Time:** Wednesday, November 14, 15.30-16.30

**Place: **MH: 333, Centre for Mathematical Sciences

**Speaker: **Serguei Shimorin (Centre for Mathematical Sciences,

**Title:** Completely bounded maps and similarity to a contraction

**Abstract:**

We shall discuss the concepts of completely bounded

and completely positive maps between operator algebras.

As an application of the theory of completely bounded maps,

we shall consider Paulsen's criterion:

an operator in a Hilbert space is similar to a contraction if and only if

it is completely polynomially bounded.

**Titel på
svenska:**
"Fullständigt begränsade avbildningar och likformighet med en kontraktion."

**Sammanfattning
på svenska:**

Vi kommer att
diskutera begreppen fullständigt begränsade

och fullständigt positiva avbildningar mellan operator algebror.

Som en tillämpning av teorin kommer vi att studera Paulsens kriterium:

En operator i ett Hilbert rum är likformig med en kontraktion om och

endast om den är fullständigt polynomiellt begränsad.

**Time:** Tuesday, December 4 at 14.00-15.00

**Place: **MH: 331, Centre for Mathematical Sciences

**Speaker: Per Östborn **(Mathematical Physics,
Lund)

**Title:**"Introduction to quantum computing
- an application

of the theory of linear operators in Hilbert
space"

**Abstract:**

At this seminar you will learn what a quantum computer is,

how it works, and what makes it different from an ordinary, classical computer.

Properties of quantum mechanics make it possible for

the quantum computer to solve some problems more efficiently

than an ordinary computer. We will describe some of this properties.

We finish by describing a quantum algorithm which factorizes

large integers more efficiently than any known classical algorithm.

The seminar
will stay at a basic level. No previous knowledge

of the subject is required.

**Titel på svenska:"Inledning** till kvantberäkningar -- en tillämpning

av teorin för operatorer på Hilbertrum."

**Sammanfattning
på svenska:**

På detta
seminarium får du lära dig vad en kvantdator är,

principerna för hur den fungerar, och vad som skiljer

den från en vanlig, klassisk dator.

Egenskaper hos kvantmekaniken gör att kvantdatorn kan lösa vissa problem

effektivare än en vanlig dator.

Vi kommer att beskriva vilka egenskaper det rör sig om.

Vi avslutar med att beskriva en kvantalgoritm som faktoriserar
stora heltal

effektivare än alla kända klassiska algoritmer.

Seminariet kommer
att hållas på en grundläggande nivå.

Inga förkunskaper i ämnet krävs.

**Time:** Tuesday, December 21 at 14.00-15.00

**Place: **MH: 332A, Centre for Mathematical Sciences

**Speaker: Kristian Sandberg**

(Dept. of Applied Mathematics, University of Colorado at Boulder, USA)

**Title:**"Representations of dynamical systems via commutation relations."

**Abstract:**

Operator
algebras are of fundamental importance in quantum mechanics.

An observable is represented by a self-adjoint
operator A and

according to the Heisenberg picture the time evolution F_{t} of a

physical system is related to a unitary transformation U such that

F_{t}(A)=U^{*}AU.

The
mathematical framework for the dynamics of operators is based on

so-called C*-dynamical systems. The representations of such systems

are closely connected to commutations relations of operators. However,

such representations are often limited to cases where the underlying maps of
the

dynamical system are homeomorphisms.

In this
talk we will study the matrix equation AB=BF(A) where F is a

polynomial and see how the pair of matrices (A,B) contain significant

information about the dynamical system generated by the polynomial map

acting on the complex plane. Our study is not limited to self-adjoint

matrices A and we present solutions for maps that are not bijective.
We

will also see how the solutions include information about the

stablity of the dynamics.

**Titel på svenska:"Representationer** of dynamiska system via
kommuteringsrelationer."

**Sammanfattning
på svenska:**

Operator algebror
är av fundemental betydelse i kvantmekanik.

Ett observerbart objekt representeras av en sjalv-adjungerande
operator A

och enligt Heisenbergs formulering är systemts tidsberoende F_{t} relaterat

till en unitar transformation U så att F_{t}(A)=U^{*}AU.

Matematiken bakom
dynamik av operatorer kan studeras med C*-dynamiska

system. Representationerna av sådana system är nära relaterat till

kommuteringsrelationer av operatorer. Sådana representationer är dock

ofta begränsade till fall då den underliggande avbildningen för den dynamiska

systemet ar en homeomorfi.

I detta föredrag
studerar vi matrisekvationen AB=BF(A) dar F är ett

polynom och ser hur matrisparet (A,B) innehåller
viktig information of

det dynamiska systemet genererat av polynomet F i det komplexa

talplanet. Våra studier är inte begränsade till själv-adjungerade matriser A

och vi presenterar lösningar for avbildningar som inte är bijektiva.

Vi kommer också att se hur lösningarna innehåller information om det

dynamiska systemets stabilitet.

*Principles of the NANG seminar*

**NANG seminar has a broad scope thanks to universal
appearance and important role of ****non-commutativity****.**

**We hope that the activities of the seminar will be
useful for researchers, teachers and especially**

**for graduate and undergraduate students.**

**One of the main goals of NANG seminar is to highlight
fundamental and unifying**

**role of non-commutativity in exploration of
the borders (and bridges) between different parts of mathematics and** **its various
applications in Physics, Chemistry, Engineering, Economics, Computer Science,
Informatics, Biology,**
**Medicine and other subjects.**

**Analysis, algebra, geometry, operator algebras and
operator theory, algebraic geometry,**

**combinatorics**** and
graph theory, stochastic processes, probability theory and statistics,**

**dynamical systems and ergodic theory,
numerical analysis,**

**and other areas of Mathematics are connected in many ways via non-commutativity**

**to its applications outside mathematics.**

**Thus the NANG seminar is important member of seminars in Lund.**

**Please note the
following principles which are followed by the NANG seminar: **

**1. Talks at
the NANG seminar should have some direct or indirect relation to non-commutativity.
There
is NO other restrictions on the subjects or directions of the
talks. The seminar has equally high
respect to all research directions and cherishes scientific freedom. **

**in other departments and institutions in Lund**

This page
is created and maintained by Sergei Silvestrov