Bykov's lectures

Flag manifolds: representation theory and two-dimensional sigma-models

Dmitri Bykov

Ludwig-Maximilians-Universität München (Germany)

Steklov Mathematical Institute (Moscow, Russia)

Abstract: Flag manifolds are ubiquitous objects in modern theoretical physics. I will discuss how they appear in representation theory (via coherent states), and how these representation-theoretic ideas find natural applications in the theory of spin chains and two-dimensional sigma models.

Dates and place:

12 December 2017, Tuesday 10:00 - 12:00 Istanbul Center for Mathematical Sciences, Bogazici University

14 December 2017, Thursday 10:00 - 12:00 Physics Department, Mimar Sinan Fine Arts University

Papers for further reading:

• Perelomov A., Generalized coherent states and their applications, Texts and Monographs in Physics. Springer-Verlag, Berlin, 1986.
• Alekseevsky D. V., Flag manifolds, 11th Yugoslav Geometrical Seminar (Divčibare, 1996), Zb. Rad. Mat. Inst. Beograd. (N.S.) 6(14) (1997), 3–35.
• Berezin F. A., General concept of quantization, Comm. Math. Phys. 40 (1975), 153–174.
• Kostant B., Sternberg Sh., Symplectic projective orbits, New directions in applied mathematics (Cleveland, Ohio, 1980), pp. 81–84, Springer,1982.
• Bykov D., The geometry of antiferromagnetic spin chains, Comm. Math. Phys. 322 (2013), no. 3, 807–834.