Reshetikhin Nicolai

Professor of Mathematics
Chern-Simons Chair in Mathematical Physics
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
My website at the University of Amsterdam (UvA) .
My website at the Center for Quantum Geometry of Moduli Spaces (QGM) .
Royal Danish Academy of Sciences and Letters .



Research:

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 (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 representing modern developments in mathematical physics.

Seminars:
Fall 2011 Representation theory, combinatorics and geometry 891 Evans, Tuesdays, 4:00-5:30pm.
Fall 2010 Representation theory, combinatorics and geometry 736 Evans, Tuesdays, 4:00-5:30pm.
Fall 2010 Dimer models in statistical mechanics891 Evans, Wednesdays, 12:30-2:00pm


Publications:
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Here are two unpublished preprints on invariants of knots and quantum groups which were written in 1987, were circulated by mail, but were never published: Invariants of tangles 1 and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 285339. World Sci. Publishing, Teaneck, NJ, 1989] but this volume is difficult to obtain.

Teaching:

2014, Spring Calculus Math 1B
2013, Fall Complex Analysis Math 185 , section 001, Quantum Integrable Systems
2013, Spring Calculus Math 1B
2012, Fall Calculus Math 1B , Quantum Field Theory.
2011, Fall Calculus Math 1B , Complex Analysis Math 185, section 001 , Complex Analysis Math 185, section 002
2010, Summer The Master-Class "Geometry of gauge theories" at University of Amsterdam.
2010, Spring Calculus Math 1B Differential Geometry Math 140
2009, Summer Complex Analysis Math 185
2009, Spring Sophomore Seminar Math 24 , Quantum Groups Math 261B
2008, Spring Topological Quantum Field Theory.

Current graduate students: Shamil Shakirov , Gus Schrader , Alexander Shapiro , Ananth Sridhar , Mohammad Safdari, Ammar Husain , Keiren Scott James-Lubin, Kevin Wray.
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.
Former master students: Alex Kogan, Wicher Malten (UvA), Robert Noest (UvA), Eddie Nijholt (UvA), Anton Quelle (UvA),


Other:

Photos from 198(1-3?) 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.