Universität Wien FIND

250100 VO Topics in Integrable Models (2010W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Thursday 07.10. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 14.10. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 21.10. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 28.10. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 04.11. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 11.11. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 18.11. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 25.11. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 02.12. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 09.12. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 16.12. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 13.01. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 20.01. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14
Thursday 27.01. 13:00 - 15:00 Seminarraum S1 Vienna Micro-CT Lab, Althanstraße 12-14

Information

Aims, contents and method of the course

Integrable Models is a very broad topic that can be divided into two major
sub-topics: Classical Integrable Models, the starting point of which is
nonlinear partial differential equations that typically have soliton
solutions, and Quantum Integrable Models, the starting point of which is
exactly solvable models in statistical mechanics and in quantum field
theory.

In this course, we discuss only Classical Integrable Models which by itself
is a very broad subject with many complementary approaches to it, and we
choose to concentrate on an algebraic approach (also known as Sato's Theory)
which plays a central role in modern mathematical physics, particularly
mathematical aspects of string theory.

The course has three parts:

1. The Lax formulation of integrable models: Integrable nonlinear PDE's are
understood as consistency conditions of systems of linear PDE's (we will see
what this means exactly in due course). This part requires 4 to 5 sets of
2-hour lectures.

2. The Fermionic formulation of integrable models: Solutions of integrable
nonlinear PDE's are re-written in terms of expectation values (to be
defined) of fermion (Clifford) operators (also to be defined). This part
requires 4 to 5 sets of 2-hour lectures.

In the third part, we can discuss either

3A. The Geometric formulation of integrable models: Solutions of integrable
nonlinear PDE's are points on a Grassmannian (to be defined) embedded in a
suitable projective space (also to be defined), or
3B. Applications of the Fermionic formulation to algebraic combinatorial
aspects of problems in modern mathematical physics.

Parts 1, 2 and 3A would be based on the textbook

Solitons, by Miwa, Jimbo and Date, Cambridge U Press, 2000

Part 3B would be based on recent works by various authors, including
Nekrasov, Okounkov, Orlov and collaborators.

Prerequisites of the course are basic undergraduate courses, particularly
Calculus, Complex Analysis and Differential Equations.

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

Examination topics

Reading list

Solitons, by Miwa, Jimbo and Date, Cambridge U Press, 2000

Association in the course directory

MANV, MALV

Last modified: Fr 01.10.2021 00:23