Professor of Mathematics,

Emeritus Professor of Graduate School,

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

Professor of Mathematics,

YMSC

Tsinghua University

Beijing, China

Beijing Institure for Mathematical Sciences and Applications
(BIMSA),

Beijing, China

Correspondent Member of the Royal
Danish Academy of Sciences
and Letter .

**My research interests: **

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.

Here is my research
website:Nicolai Reshetikhin Website
.

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 and quantum field theory (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.

**Here is a record of Simons Research Lectures from
2010-2015: Chern-Simons Research Lectures
**. This lectures series in Berkeley were representing modern
developments in mathematical physics and were funded by Cern-Simons
Chair in Mathematical Physics.

**Publications: **

Most
of my publications after 1994 can be found on the arXiv.org
. Here is a not so recently updated list of my publications.

Here are two unpublished preprints on invariants of knots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.

**Topics
in mathematical physics: **

This is a loosely organized
collection of references on some topics in mathematical physics. This
is a developing project.

The
6-vertex model is statistical mechanics.

Dimer
models is statistical mechanics.

Quantization
of gauge theories.

**Current graduate students:**Mostafa Adnane,
Emily Bain, Tianqing Zhu (YMSC, Tsinghua University). Dima
Solovyev (YMSC, Tsinghua University).

**Former graduate
students:** Josef Mattes, Anton
Kast , Eugene
Stern , Michael
Kelber , Peter
Tingley, Susan Harrington, Milen
Yakimov , Gizem
Karaali Ari Nieh,
Konstantin
Palamarchuk, Ben
Webster, Qingtao
Chen , Sevak Mkrtchyan ,
Noah Snyder ,
Magnus Lauridsen (University of Aarhus), Dan
Belthoft (University of Aarhus),Theo
Johnson-Freyd , Harold
Williams ,Alexandru Chirvasitu, Mohammad Safdari, Shamil
Shakirov , Alexander
Shapiro Gus
Schrader , Ananth
Sridhar , Kai-Chieh
Chen, Ammar
Husain , Calvin McPhail-Snyder, David Keating, Meredith
Shea.

**Former master students:** Alex Kogan, Wicher
Malten (UvA), Robert Noest (UvA), Eddie Nijholt (UvA), Anton Quelle
(UvA), Tim Weelinck (UvA), Keiren Scott James-Lubin, Kevin Wray,
Pelle Steffens (UvA), Tristan Kuen (UvA)), Antonio Villafranka, Aaron
Brookner.

Photos from 1979 conference "Quantum
Solitons" . The photos were taken by A. Budagov, and scanned
by M. Semenov-Tian-Shansky .

St.
Petersburg , photos by I. Vinogradova.

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