Reshetikhin Nicolai

Professor of Mathematics
Department of Mathematics, Evans Hall 917,
University of California, Berkeley, CA 94720-3840
email: reshetik at-sign
phone number: 510- 642-6550
Royal Danish Academy of Sciences and Letters .


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.

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.

Chern-Simons Research Lectures: The lectures series in Berkeley are representing modern developments in mathematical physics.

Spring 2015 Representation theory, and mathematical physics. 891 Evans, Wedensdays, 4:00-5:30pm. In Fall 2020 the seminar will be run online.

Most of my publications after 1994 can be found on the . Here is a 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Here are two unpublished preprints on invariants of knots and quantum groups which were written in 1987, were circulated by mail, but were never published: Invariants of tangles 1 and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 loosely organized collection of references on various 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.


2020, Fall Math 121A: Mathematical Tools for the Physical Sciences , Math 277: Poisson geometry, Lie groups and Hamiltonian integrable systems .
2020, Spring Calculus Math 1B .

Some previously taught courses:

2016, Fall Calculus Math 1B , Freshmen seminar on probability theory, math 24
2015, Spring Calculus Math 1B .
2013, Fall Complex Analysis Math 185 , section 001, Quantum Integrable Systems .
2012, Fall Quantum Field Theory.
2010, Spring Differential Geometry Math 140


Current graduate students:Mostafa Adnane, Aaron Brookner, David Keating, Calvin McPhail-Snyder, Meredith Shea, Antonio Villafranka .

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 .

Current master students: Tristan Kuen (UvA)

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), Dima Solovyev (St. Petersburg University)


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.