Graduate level courses, mathematics, 2010-2011
Fall 2010
| Course code | Course name | Credit |
|---|---|---|
| FSF3625 | Partial differential equations | 7.5 cr |
| FSF3626 | Mathematical analysis för Ph.D. students | 7.5 cr |
| FSF3703 | Topological combinatorics | 7.5 cr |
| MMxxxx | Algebraic geometry (surfaces, étale cohomology) | 7.5 cr |
Spring 2011
| Course code | Course name | Credit |
|---|---|---|
| FSF3601 | Algebraic geometry: computations and applications | 7.5 cr |
| FSF3624 | Random matrices | 7.5 cr |
| - | Differential geometry for algebraists | 7.5 cr |
| - | Geometry of zeros with applications | - |
| - | Several complex variables | 7.5 cr |
Partial differential equations
KTH, Anders Szepessy
Course start: Period 2
Mathematical analysis för Ph. D. students
KTH, Torbjörn Kolsrud
Seminar room 3721 (KTH), Wednesdays 10.15-12.00 (except October 6 and 20). course start: September 15.
Topological combinatorics
KTH, Jakob Jonsson
Algebraic geometry (surfaces, étale cohomology)
SU, Torsten Ekedahl
Algebraic geometry: computations and applications
KTH, Dickestein/Sturmfels
Random matrices
KTH, Kurt Johansson
Course start: Monday, January 24 at 10.15. Room 3733 (KTH).
Course description (pdf 33 kB)
Differential geometry for algebraists
SU, Sergei Merkulov
Room 306, house 6, Kräftriket. Wednesdays 10-12 and certain Fridays 15-17. Course start: January 26
We take a not very usual way to explain basic notions of differential geometry via the theory of sheaves. Its main advantage lies in its potential for deep generalizations of that classical notions. The course is self-contained.
Lecture notes (which include homework exercise) are available for download:
Geometry of zeros with applications
SU, Petter Brändén
Room 306, House 6, Kräftriket. Fridays 13-15. Course start: February 11
Course description: The course is about the geometry of zeros of univariate and multivariate polynomials and transcendental entire functions. We will discuss classical results and new results, as well as several applications to other areas of mathematics such as combinatorics, matrix theory, probability theory and statistical mechanics. The approach is that of Borcea and myself, see (see link below for a survey of some relevant topics).
Syllabus: Linear operators on polynomials and entire functions preserving the property of having all zeros in a specified domain, Lee-Yang theorems in statistical physics (phase transitions), applications to correlation inequalities in probability theory, and to certain models in combinatorics.
Litterature: Hand-outs, papers.
Prerequests: Basic knowledge of complex analysis, probability theory and combinatorics.
Examination: One or two homework assignments and a presentation of a relevant topic.
Several complex variables
SU
Room 22, House 5, Kräftriket. Thursdays 10-12. Course start: February 24