Conference: "Integrability, Anomalies and Quantum Field Theory" - IHES

Conference: “Integrability, Anomalies and Quantum Field Theory”

From February 10 to 14, 2020, the Institut des Hautes Études Scientifiques hosted the conference “Integrability, Anomalies and Quantum Field Theory“. Organised by Anton Alekseev (University of Geneva) and Maxim Kontsevich (IHES), this conference honoured Professor Samson Shatashvili on his 60th birthday.

The interactions of Mathematics and Physics have greatly intensified during the last three decades, and it led to a number of very significant breakthroughs in Mathematics. Among other things, these breakthroughs include new invariants of 3 and 4-dimensional manifolds, the discovery of mirror symmetry in Algebraic Geometry, and the theory of deformation quantization.
This progress became possible due to close interactions between Mathematics and theoretical Physics and due to the dialogue between mathematicians and physicists working on similar problems but using very different methods.

The conference touched upon two important aspects of interaction between Mathematics and Quantum Field Theory.

Quantum Integrability is a very interesting theory which was first discovered on the Physics side. It was soon realized that it is related to Algebra through the theory of Vertex Operator Algebras (VOA) and to Complex Analysis (through the study of various Riemann-Hilbert problems). The problem of Bethe Ansatz completeness became an important mathematical problem and a driving force in Combinatorics and Representation Theory. Recently, relations between quantum integrability and Geometric Representation Theory (on the Mathematics side) and Quantum Gauge Theory (on the Physics side) attracted a lot of attention of the research community. These links will be one of the major topics of the conference.

Anomalies were discovered in Physics as the phenomenon when symmetry of a system changes under quantization. Famously, it occurs in gauge theories and in string theory, and it serves as one of the key criteria for choosing realistic models of field theory. Anomalies also became one of the important topics in Mathematics. They are related to the behaviour of determinant bundles of Dirac operators on manifolds, to the index theory and to K-theory. In many cases, anomalies represent the part of Quantum Field Theory which can be defined and computed mathematically. Anomalies will be one of the key topics of the meeting.

Professor Samson Shatashvili made deep contributions in the theory of anomalies and in quantum integrability. In particular, in collaboration with Ludwig Faddeev he discovered the interpretation of gauge theory anomalies in terms of abelian extensions of gauge groups on manifolds of odd dimension. In the theory of quantum integrability, together with a number of collaborators he discovered a deep link between Bethe equations and supersymmetric quantum gauge theory.
Professor at the Trinity College, Dublin and at the Simons Center for Geometry and Physics, Stony Brook, he served as a Louis Michel Chair and then as an Israel Gelfand Chair at IHES. He contributed in a significant way in the development of ideas and in the unique research atmosphere of IHES.

Invited speakers were:
Costas Bachas (ENS-Paris), Jean-Michel Bismut (Université Paris-Sud Orsay), Gregory Gabadadze (New York University), Sergei Gukov (Caltech), Simeon Hellerman (IPMU), Chris Hull (Imperial College London), Vladimir Kazakov (ENS-Paris), Zohar Komargodski (SCGP), Vladimir Korepin (Stony Brook University), Manuela Kulaxizi (Trinity College Dublin), Sergei Lukyanov (Rutgers University), Ruben Minasian (IPhT & CEA Saclay), Vasily Pestun (IHES), Alexey Rosly (ITEP, Skoltech, HSE, IITP, Moscow), Sinead Ryan (Trinity College Dublin), Ivo Sachs (LMU Munich), Nana Shatashvili (Tbilisi State University, Georgia), Fedor Smirnov (LPTHE Sorbonne-Université), Leon Takhtajan (Stony Brook University), Anne Taormina (Durham University), Cumrun Vafa (Harvard University), Pierre Vanhove (IPhT & CEA Saclay), Erik Verlinde (Universiteit van Amsterdam), Alexander Zamolodchikov (Stony Brook University).

Programme and registration on the conference web page.

Video playlist of the conference: