Department of Mathematics, Evans Hall 917,

University of California, Berkeley, CA 94720-3840

email: reshetik at-sign math.berkeley.edu

phone number: 510- 642-6550

Royal Danish Academy of Sciences and Letters .

My research interests lie at the interface of mathematical physics, geometry and representation theory, more specifically in quantum field theory, statistical mechanics, geometry and low-dimensional topology, and representation theory of quantum groups.

Representation theory of quantum groups and of quantized universal enveloping algebras is the main algebraic structure behind integrability of most known "non-Gaussian" integrable models in classical and quantum mechanics, in field theory, and in statistical mechanics. This direction has many fascinating problems ranging from answering deep questions in statistical mechanics (in solvable examples, where more tools are available) to deep structural results in representation theory which are motivated by physical applications.

Representation theory of quantum groups is also a powerful tool behind constructions of invariants of knots and 3-dimensional manifolds. Invariants of knots and 3-manifolds can also be obtained by quantizing classical topological field theories. Such theories are, as a rule, are gauge invariant (examples are Chern-Simons theory, BF theory, Poisson sigma model and others). Quantization of such theories involve a lot of modern geometry. One of the challenges in this direction is to develop semiclassical quantization of such theories for space time manifolds with boundary.

Spring 2015 Representation theory, and mathematical physics. 891 Evans, Fridays, 4:00-5:30pm.

Most of my publications after 1994 can be found on the arXiv.org..

Here are two unpublished preprints on invariants of knots and quantum groups which were written in 1987, were circulated by mail, but were never published: Invariants of tangles 1 and Invariants of tangles 2

Here is the preprint (with A. N. Kirillov) where quantum 6j-symbols were introduced and studied: q-6j The results were published in [A. N. Kirillov and N. Yu. Reshetikhin. Representations of the algebra Uq(sl(2)), q-orthogonal polynomials and invariants of links. In Infinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988), pages 285-339. World Sci. Publishing, Teaneck, NJ, 1989] but this volume is difficult to obtain.

This is loosely organized collection of references on various topics in mathematical physics.

The 6-vertex model is statistical mechanics.

Dimer models is statistical mechanics.

Quantization of gauge theories.

Some previously taught courses:

St. Petersburg , photos by I. Vinogradova.

Paintings by St. Petersburg artist N. Rosenbaum. See also this online exposition.