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Graduate level courses, mathematics, 2010-2011

Fall 2010

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

Course webpage

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.

Course webpage

Topological combinatorics

KTH, Jakob Jonsson

Course webpage

Algebraic geometry (surfaces, étale cohomology)

SU, Torsten Ekedahl

Course webpage

Algebraic geometry: computations and applications

KTH, Dickestein/Sturmfels

Course webpage

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:

Lecture Notes

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.

Survey by Borcea and Brändén

Several complex variables

Room 22, House 5, Kräftriket. Thursdays 10-12. Course start: February 24

Course information

Tillhör: Institutionen för matematik
Senast ändrad: 2015-05-27