IHES Annual Report 2021 | 4342 | IHES Annual Report 2021

ANTON KAPUSTIN studied general properties of thermoelectric transport in quantum systems. In a joint work with Michael Levin and Lev Spodyneiko, he showed that all components of the thermoelectric tensor must vanish at zero temperature thanks to the 3rd law of thermodynamics. This is in stark contrast to the Hall conductance which can tend to a nonzero value at zero temperatur. This result implies that the only topological invariants of gapped two-dimensional systems arising from transport are the Hall conductance and the thermal Hall conductance, in agreement with expectations from field theory.

In a separate paper with L. Spodyneiko, he derived microscopic formulas for thermoelectric transport coefficients for general lattice systems. These formulas generalize the textbook Kubo formulas which apply only in special circumstances. The new derivation highlights the importance of edge effects for defining the skew-symmetric parts of the transport coefficients. A. Kapustin also studied how the equivalence principle constrains the coupling of nonrelativistic systems to gravity. He showed that the action must be invariant under a gauge symmetry which transforms both the Ehresmann connection and the Newtonian potential. This gauge symmetry is a nonrelavistic limit of the time reparameterization symmetry of general relativity theory.

ACTIVITÃ‰ SCIENTIFIQUE

Louis Michel Chair

Anton KAPUSTIN Physics, Professor, California Institute of Technology.

DISTINCTIONS

Simons Investigator (since 2016)

Editor of: Selecta Mathematica (new series)

PUBLICATIONS

With M. Touraev Nonrelativistic Geometry and the Equivalence Principle Classical and Quantum Gravity 38, 135003 (2021).

With L. Spodyneiko Microscopic Formulas for Thermoelectric Transport Coefficients in Lattice Systems Phys. Rev. B104, 035150 (2021).

With M. Levin and L. Spodyneiko Nernst and Ettingshausen Effects in Gapped Quantum Materials Phys. Rev. B103, 235101 (2021).

CONFERENCES

United States QMAP Seminar, University of California, Davis (September 24) Local Noether Theorem for Quantum Lattice Systems and Applications (seminar)

Simons Collaboration on Global Categorical Symmetries, Simons Center for Geometry and Physics, Stony Brook (October 11) A local Noether Theorem for Quantum Lattice Systems and Topological Invariants of Gapped States (video conference)

Portugal QM3 Seminars: Quantum Matter Meets Maths, Instituto Superior Tecnico, Lisbon (December 13) Higher Berry Classes for Many body Quantum Lattice Systems (video seminar)

Switzerland Topological Phase of Matter, a satellite workshop of the International Congress on Mathematical Physics 2021, Leysin (July 27) Zero temperature Hall Conductance as a Topological Invariant of Gapped 2d Lattice Systems (conference)

Dennis GAITSGORY Mathematics, Professor, Harvard University.

DENNIS GAITSGORY continued to apply the newly discovered connection between the classical theory of automorphic functions and the geometric theory of automorphic sheaves with nilpotent singular support via the categorical trace of Frobenius endomorphism in order to understand the phenomenon of Arthur parameters.

SCIENTIFIC ACTIVITY

Israel Gelfand Chair in Mathematics

PUBLICATIONS

With D. Arinkin, D. Kazhdan, S. Raskin, N. Rozenblyum and Y. Varshavsky Automorphic Functions as the Trace of Frobenius Prepublication arXiv:2102.07906.

DISTINCTIONS

Chevalley Prize in Lie Theory (2018)

Editor of: Compositio Mathematica, Tunisian Journal of Mathematics, EPIGA

CONFERENCES

China (P.R.) Tsinghua University, Beijing (December 2, 7, 9 and 16) Classical and Geometric Langlands over Function Fields (video mini-courses)

United States Geometric Langlands Office Hours, Harvard University, Cambridge (spring) (organizer)

Infinite Dimensional Algebra Seminar, Massachusetts Institute of Technology, Cambridge (September 10) Factorization of the Minimal Model CFT and Langlands Duality (video seminar)

Mathematical Institute of the Americas, University of Miami (November 8) Geometric Langlands in its Various Contexts (November 10) Restricted Geometric Langlands as a Common Denominator (video lecture)