IHES Annual Report 2021 | 1918 | IHES Annual Report 2021

CONFERENCES

Switzerland International Congress on Mathematical Physics (ICMP), ICCP Geneva (August 3) Multiplicative Higgs Bundles (conference)

Vasily PESTUN Theoretical Physics, Permanent Professor since 2014.

In 2021, VASILY PESTUN shifted his research to the problem of automated theorem proving in computer verified formal systems. These systems are rapidly advancing and become sufficiently expressive in principle to formalize most modern mathematical theories. For example, the proof of the foundational lemmas in Peter Scholze s theory was recently checked in the interactive theorem proving system Lean. However, the interactive theorem proving systems such as Lean still require very laborious input from humans, often the size of the computerized proof is hundred times the size of the proof written in the traditional mathematical notations and in natural language.

The interactive theorem proving systems normally do not search for the proof, they only check the proofs entered by a human. Vasily Pestun has also assembled and is leading a research team at IHES, which is also collaborating with researchers from IBM, whose effort is to combine the advances in modern techniques of statistical learning, deep neural networks and interactive theorem proving systems to create self-learning semi-automatic theorem proving capabilities.

SCIENTIFIC ACTIVITY

DISTINCTIONS

Gold Medal, 28th International Physics Olympiads (1997) Centennial Fellowship, Princeton University (2003-2008) Porter Ogden Jacobus Fellowship, Princeton University (2007-2008) Junior Fellow, Harvard Society of Fellows (2008-2011) ERC Starting Grant Quantum Algebraic Structures in Field Theories (QUASIFT) (2015) Hermann Weyl Prize (2016)

Editor of: Letters in Mathematical Physics Communications in Mathematical Physics

PUBLICATIONS

With N. Fulton, A. Shinnar, B. Targer and K. Vajjha CertRL: Formalizing Convergence Proofs for Value and Policy Iteration in Coq CPP 21: Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs.

Slava RYCHKOV Theoretical Physics, Permanent Professor since 2017.

DISTINCTIONS

New Horizons Prize in Physics (2014) Institut Universitaire de France, junior member (2012-2017) Grand prix Mergier Bourdeix, Académie des sciences de Paris (2019)

Editor of: SciPost Physics

SLAVA RYCHKOV continued collaboration with his former postdocs Apratim Kaviraj and Emilio Trevisani on the Parisi-Sourlas supersymmetry. A long paper prepared in 2020 resolved a long-standing puzzle concerning the phase transition in lattice models with magnetic impurities (Random Field Ising Model). That work explained from the renormalization group theory point of view why an old and famous conjecture by Giorgio Parisi and Nicolas Sourlas according to which this transition must exhibit a form of supersymmetry and the same critical...

SCIENTIFIC ACTIVITY

PUBLICATIONS

With A. Kaviraj and E. Trevisani Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group J. High Energ. Phys. 03 (2021) 219, pre publication arXiv:2009.10087.

With A. Giuliani and V. Mastropietro Gentle Introduction to Rigorous Renormalization Group: a Worked Fermionic Example J. High Energ. Phys. 01 (2021) 026, pre publication arXiv:2008.04361.

With P. Kravchuk and J. Qiao Distributions in CFT II. Minkowski Space J. High Energ. Phys. 08 (2021) 094, pre publication arXiv:2104.02090.

With M. Reehorst, D. Simmons Duffin, B. Sirois, N. Su and B. van Rees Navigator Function for the Conformal Bootstrap SciPost Physics 11, 072 (2021), pre publication arXiv:2104.09518.

With T. Kennedy Tensor RG Approach to High-temperature Fixed Point Prepublication arXiv:2107.11464.

With A. Kaviraj and E. Trevisani The Fate of Parisi-Sourlas Supersymmetry in Random Field Models Prepublication arXiv:2112.06942.

CONFERENCES

France International Network on Quantum Fields and Strings Kickoff Meeting, Fédération Denis Poisson, Tours (June 9) Conformal Bootstrap: Recent Numerical and Analytical Developments (video conference)

Germany Theory Seminar, Mathematisches Institut - Universität Bonn (April 23) Deligne Categories in Quantum Field Theory and Lattice Model (video seminar)

Condensed Matter Theory Group Seminar, Technische Universität München (November 3) Tensor RG Approach to High temperature Fixed Point (video seminar)

Italy Exact Quantisation and Applications to Condensed Matter Physics, SISSA, Trieste (September 27) Tensor RG Approach to High temperature Fixed Point (conference)

Switzerland Theory Colloquium, Department of Theoretical Physics, CERN, Geneva (September 15) The Dream of Non perturbative Precision RG (colloquium, video recording)

United Kingdom Paths to Quantum Field Theory, Durham University (August 23) Renormalization Group Transformations without Truncations (video conference)

United States Theory Seminar, Stanford University (February 2) Replicas and RG: Case Study of Random Field Ising Model (video seminar)

Quantum Field Theory Seminar, Oxford University (March 2) Some Mathematical Problems Posed by the Conformal Bootstrap Program (video seminar)

Mathematical Physics Seminar, Rutgers University (June 2) Long range Ising Model and Relatives: a Renormalization group Laboratory (video seminar)

2021 Ph.D. School of the Simons Bootstrap Collaboration, Simons Foundation, New York (July 9) Lorentzian CFT and QFT Axioms, Lecture 1 (video lecture) - (July 12) Lorentzian CFT and QFT Axioms, Lecture 2 (video lecture) - (July 14) Lorentzian CFT and QFT Axioms, Lecture 3 (video lecture)