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Course by D. V. Bykov "Flag manifold sigma models: spin chains and integrable theories"
February 12–April 30, 2021, online via Zoom

I will present various aspects (both physical and mathematical) of the theory of flag manifold sigma models. At the classical level these theories describe generalized harmonic maps of Riemann surfaces into flag manifolds. In recent years at least two interesting applications of such theories have been found: first of all, they describe continuum limits of spin chains, and the discovered relation allows to study the phase structure of such models; besides, it turns out that some of these models are integrable and, moreover, they open a "window" into a wide class of integrable sigma models, related to Nakajima varieties (from the physical viewpoint these models are generalized Gross–Neveu models). I plan to discuss both of these research directions, as well as the interrelations between them and especially the many open questions.

Financial support. The course is supported by the Simons Foundation and the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

RSS: Forthcoming seminars

Lecturer
Bykov Dmitrii Vladimirovich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center


Course by D. V. Bykov "Flag manifold sigma models: spin chains and integrable theories", February 12–April 30, 2021

April 30, 2021 (Fri)
1. Lecture 12. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
April 30, 2021 16:00, online via Zoom
  

April 23, 2021 (Fri)
2. Lecture 11. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
April 23, 2021 16:00, online via Zoom
  

April 16, 2021 (Fri)
3. Lecture 10. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
April 16, 2021 16:00, online via Zoom
  

April 9, 2021 (Fri)
4. Lecture 9. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
April 9, 2021 16:00, online via Zoom
  

April 2, 2021 (Fri)
5. Lecture 8. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
April 2, 2021 16:00, online via Zoom
  

March 26, 2021 (Fri)
6. Lecture 7. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
March 26, 2021 16:00, online via Zoom
  

March 19, 2021 (Fri)
7. Lecture 6. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
March 19, 2021 16:00, online via Zoom

March 12, 2021 (Fri)
8. Lecture 5. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
March 12, 2021 16:00, online via Zoom

March 5, 2021 (Fri)
9. Lecture 4. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
March 5, 2021 16:00, online via Zoom

February 26, 2021 (Fri)
10. Lecture 3. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
February 26, 2021 16:00, online via Zoom
  

February 19, 2021 (Fri)
11. Lecture 2. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
February 19, 2021 16:00, online via Zoom
  

February 12, 2021 (Fri)
12. Lecture 1. Flag manifold sigma models: spin chains and integrable theories
D. V. Bykov
February 12, 2021 15:00, online via Zoom
  
 
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