Courses
in Mathematics and its Applications

for advanced graduate and PhD students

Dept. of Mathematics, LTH as part of the Center of Mathematical Sciences is going to organize a series of advanced courses devoted to different topics in modern mathematics and its applications in natural sciences. These courses provide a possibility for all interested individuals to study important and hot areas by attending lectures given by our experts. Students from other departments and faculties as well as active researchers who want to learn more math re also welcome.

For each course 7 lectures will be given, but it is expected that essential time will also be allocated for self-studies allowing students to go through additional chapters. Every standard course will give 5 university points.

Academic year 2010-2011

  1. "General concepts in ergodic theory FMA070F "
    Jörg Schmeling (lp1: weeks 1-5, August-October 2010, first meeting Monday 30/8 at 15-17 in MH:333 )
    Ergodic theory provides some of the most profound tools of analyzing ''chaotic systems'' with statistical properties. While it is impossible to understand the behavior of the complete system, ergodic theory tells you to make predictions for ''typical'' initial conditions. Ergodic theory might be considered as a mixture of probability theory, measure theory, dynamical system theory, Hamiltonian dynamics or functional analysis. However the very essence is to provide new methods and tools to understand these fields in a better way. In the lectures we will explain and prove the main ergodic theorems due to von Neumann, Birkhoff, Hopf, Kingman, Oseledets and their generalizations and implications in dynamical system theory. To avoid more advanced algebraic knowledge we will restrict to one-dimensional discrete or continuous time dynamical systems.
    More information:
    http://www2.lth.se/forskarutbildning/fukurser/KursList.asp?id=588
  2. "Quantum graphs: spectral theory and inverse problems FMA075F "
    Pavel Kurasov (lp1: weeks 6-7, October 2010, first meeting: October 5, 13.15 i MH:309A)
    Quantum graphs denote a wide class of models used to describe systems where the dynamics is confined to a neighborhood of graph-like structures. Such models have natural applications in nanosystems, but related methods are useful in other fields such as microwave networks, chemistry, and even medicine. This course will give an introduction into the theory of quantum graphs considered as ordinary differential equations on metric graphs. Their spectral and scattering properties will be investigated. In particular we are going to discuss how geometric properties of graphs are reflected by the spectrum of the corresponding differential operators. The corresponding inverse problems will be discussed in details.
    More information on the web-pages
    http://www.maths.lth.se/matematiklth/personal/kurasov/Kursgraph.html
    http://www2.lth.se/forskarutbildning/fukurser/KursList.asp?id=502
  3. "Numerical methods for deterministic and stochastic differential equations"
    Carmen Arevalo and Gustaf Söderlind CANCELED !
    More information on the web-page
    http://www2.lth.se/forskarutbildning/fukurser/KursList.asp?id=503
  4. "Discrete Optimization FMA060F "
    Fredrik Kahl (lp3: January-February 2011)
    Discrete optimization is a branch of optimization in applied mathematics. As opposed to continuous optimization, the variables used in the mathematical program (or some of them) are restricted to assume only discrete values, such as the integers. The course will focus on recent methods for solving large discrete optimization problems. Content: Pseudo boolean optimization, minimization of submodular functions, graph cuts, relaxation techniques (linear programming and semidefinite programming). Applications include markov random fields and standard graph problems (vertex cover, set cover, matching and more).
    More information on the web-pages
    http://www.maths.lth.se/matematiklth/personal/fredrik/discreteoptimization/
    http://www2.lth.se/forskarutbildning/fukurser/KursList.asp?id=504
  5. "Symmetric operators FMA065F "
    Annemarie Luger (lp4: March-May 2011)
    Symmetric and self-adjoint linear operators, such as Schrödinger operators, play an inportant role in mathematical physics. The course will give an introduction to the classical extension theory. This amounts to describing all self-adjoint extensions of a symmetric operator and studying their (spectral) properties. Note that for symmetric matrices (that are symmetric operators in a finite dimensional space) this question is void, whereas e.g. in connection with differential operators (in spaces of functions) a rich structure waits to be explored. We will illustrate the results by examples from different areas.
    More information on the web-page
    http://www2.lth.se/forskarutbildning/fukurser/KursList.asp?id=505


During the academic year 2009-2010 the following research courses were given:
  1. "Population Dynamics" Mario Natiello (lp2: 2009-10-26--12-11)
  2. "Complex Analysis I"
  3. "Quantum Computing" Sergei Silvestrov (lp4: 2010-03-15--05-21)
More information concerning these courses can be found " here " .

Our regular courses at the department are:
  1. "Functional analysis" Pavel Kurasov (lp1-2 2010-08-30--12-10)
  2. "Partial Differential Equations and Distribution Theory" Pelle Pettersson (lp2-3 2010-10-25--2011-03-04)
Our far sighted plans include the following courses: Some of these courses are going to form chains giving a possibility to learn the corresponding subjects much deeper. The other courses are designed to provide an introduction into their subject leaving large parts for own studies (corresponding courses for own studies will also be announced here).

If you are interested in the courses listed above, please contact the coordinator Pavel Kurasov (kurasov@maths.lth.se) and your wishes will be taken into account when planning courses for the next academic year.
If you are a representative for a department from Lund university and think that several of your students/colleagues might be interested in one of our courses or any other mathematical course contact us to discuss possible collaborations.