

Mathematical physics, including mathematics, is a research area where novel mathematical techniques are invented to tackle problems in physics, and where novel mathematical ideas find an elegant physical realization. Historically, it would have been impossible to distinguish between theoretical physics and pure mathematics. Often spectacular advances were seen with the concurrent development of new ideas and fields in both mathematics and physics. Here one might note Newton's invention of modern calculus to advance the understanding of mechanics and gravitation. In the twentieth century, quantum theory was developed almost simultaneously with a variety of mathematical fields, including linear algebra, the spectral theory of operators and functional analysis. This fruitful partnership continues today with, for example, the discovery of remarkable connections between gauge theories and string theories from physics and geometry and topology in mathematics.
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Andrei Okounkov Columbia University
Philsang Yoo Seoul National University
Justin Hilburn Perimeter Institute for Theoretical Physics
Lev Rozansky University of North Carolina - Chapel Hll
Davide Gaiotto Perimeter Institute for Theoretical Physics
Mykola Dedushenko Stony Brook University
Theo Johnson-Freyd Dalhousie University
Justin Kaidi Stony Brook University
Andrei Okounkov Columbia University
Emily Nardoni University of Tokyo
Kevin Costello Perimeter Institute for Theoretical Physics
Shu-Heng Shao Stony Brook University
Pavel Etingof Massachusetts Institute of Technology (MIT)
Cris Negron University of Southern California
Bianca Dittrich Perimeter Institute for Theoretical Physics
Theo Johnson-Freyd Dalhousie University
Sylvie Paycha Universität Potsdam
Katarzyna Rejzner University of York
Anne Taormina Durham Academy
Reiko Toriumi Okinawa Institute of Science and Technology (OIST)
Cohl Furey Humboldt University of Berlin
Catherine Meusburger University of Erlangen-Nuremberg
Johanna Erdmenger University of Würzburg
Karen Yeats University of Waterloo
Sabine Harribey Nordita - Nordic Institute for Theoretical Physics
Philine van Vliet Deutsches Elektronen-Synchrotron (DESY)
Maria Elena Tejeda-Yeomans University of Colima
Maryam Khaqan Emory University
Sumati Surya Raman Research Institute
Laura Schaposnik University of Illinois at Chicago
Renate Loll Radboud Universiteit Nijmegen
Kirill Krasnov University of Nottingham
Michel Dubois-Violette University of Paris-Saclay
Paul Townsend University of Cambridge
Kirill Krasnov University of Nottingham
Leron Borsten Imperial College London
Mia Hughes Imperial College London
Cohl Furey Humboldt University of Berlin
Mia Hughes Imperial College London
Ivan Todorov Bulgarian Academy of Sciences
Martina Lanini Università degli Studi di Roma Tor Vergata
Olivier Schiffmann University of Paris-Saclay
Sam Raskin The University of Texas at Austin
Gurbir Dhillon Stanford University
Oscar Kivinen California Institute of Technology
Sarah Scherotzke University of Luxembourg
Fei Han National University of Singapore
Davide Gaiotto Perimeter Institute for Theoretical Physics
Lennart Meier Utrecht University
Arnav Tripathy Harvard University
Jack Morava Johns Hopkins University
Gerd Laures Ruhr-Universität Bochum
Richard Rimanyi University of North Carolina - Chapel Hll
David Kubiznak Charles University
David Kubiznak Charles University
David Kubiznak Charles University
Philsang Yoo Seoul National University
Mathew Bullimore Durham University
Theo Johnson-Freyd Dalhousie University
Davide Gaiotto Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Chris Elliott University of Massachusetts Amherst
Philsang Yoo Seoul National University
Mathew Bullimore Durham University
Yan Soibelman Kansas State University
Davide Gaiotto Perimeter Institute for Theoretical Physics
Yegor Zenkevich Institute for Theoretical and Experimental Physics
Mikhail Kapranov Kavli Institute for Theoretical Physics (KITP)
Ben Davison University of Edinburgh
Sergei Gukov California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
Francesco Sala University of Tokyo
Pavel Etingof Massachusetts Institute of Technology (MIT)
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
Kevin Costello Perimeter Institute for Theoretical Physics
A quantum field theory is deemed topological if it exhibits the remarkable property of being independent of any background metric. In contrast to most other types of quantum field theories, topological quantum field theories possess a well-defined mathematical framework, tracing its roots back to the pioneering work of Atiyah in 1988. The mathematical tools employed to define and study topological quantum field theories encompass concepts from category theory, homotopy theory, topology, and algebra.
In this course, we will delve into the mathematical foundations of this field, explore examples and classification results, especially in lower dimensions. Subsequently, we will explore more advanced aspects, such as invertible theories, defects, the cobordism hypothesis, or state sum models in dimensions 3 and 4 (including Turaev-Viro and Douglas-Reutter models), depending on the interests of the audience.
Today, the mathematics of topological quantum field theories has found numerous applications in physics. Recent applications include the study of anomalies, non-invertible symmetries, the classification of topological phases of matter, and lattice models. The course aims to provide the necessary background for understanding these applications.
Over the years, various researchers have suggested connections between the octonions and the standard model of particle physics. The past few years, in particular, have been marked by an upsurge of activity on this subject, stimulated by the recent observation that the standard model gauge group and fermion representation can be elegantly characterized in terms of the octonions. This workshop, which will be the first ever on this topic, is intended to bring this new community together in an attempt to better understand these ideas, establish a common language, and stimulate further progress.
The workshop will consist of an hour-long talk every Monday at noon (EST), with the first talk on Monday February 8, and the final talk on Monday May 17.
This workshop will bring together leading mathematicians and physicists interested in the Cohomological Hall algebra as it appears in the study of moduli spaces and in gauge and string theory.