Topological Quantum Field Theories - mini-course
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Collection Number
C23048
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.
Displaying 1 - 12 of 726
Format results
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QFT for Mathematicians 2022
28 talks-Collection Number C22011Talk
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Welcome and Opening Remarks
Kevin Costello Perimeter Institute for Theoretical Physics
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3d Theories and Twists I
Kevin Costello Perimeter Institute for Theoretical Physics
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3d Gauge Theory and Elliptic Stable Envelopes I
Andrei Okounkov Columbia University
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Classical BV Formalism and Topological Quantum Field Theory
Philsang Yoo Seoul National University
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A and B models in 3d and 4d I
Justin Hilburn Perimeter Institute for Theoretical Physics
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3d B Models and Knot Homology I
Lev Rozansky University of North Carolina - Chapel Hll
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On Boundary VOA's
Davide Gaiotto Perimeter Institute for Theoretical Physics
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3d Gauge Theory and Elliptic Stable Envelopes II
Mykola Dedushenko Stony Brook University
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Global Categorical Symmetries
34 talks-Collection Number C22008Talk
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Welcome and Opening Remarks
Theo Johnson-Freyd Dalhousie University
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Non-Invertible Symmetries in d>2
Justin Kaidi Stony Brook University
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Monodromy and derived equivalences
Andrei Okounkov Columbia University
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Lessons from SU(N) Seiberg-Witten Geometry
Emily Nardoni University of Tokyo
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Vertex algebras and self-dual Yang-Mills theory
Kevin Costello Perimeter Institute for Theoretical Physics
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Non-invertible Global Symmetries in the Standard Model
Shu-Heng Shao Stony Brook University
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Analytic Langlands correspondence over C and R
Pavel Etingof Massachusetts Institute of Technology (MIT)
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A (kind of) monoidal localization theorem for the small quantum group
Cris Negron University of Southern California
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Women at the Intersection of Mathematics and Theoretical Physics
16 talks-Collection Number C21002Talk
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Welcome and Opening Remarks
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Bianca Dittrich Perimeter Institute for Theoretical Physics
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Theo Johnson-Freyd Dalhousie University
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Sylvie Paycha Universität Potsdam
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Katarzyna Rejzner University of York
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Anne Taormina Durham Academy
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Reiko Toriumi Okinawa Institute of Science and Technology (OIST)
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Division algebraic symmetry breaking
Cohl Furey Humboldt University of Berlin
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State sum models with defects
Catherine Meusburger University of Erlangen-Nuremberg
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Quantum information and black holes
Johanna Erdmenger University of Würzburg
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Researcher Presentations
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Karen Yeats University of Waterloo
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Sabine Harribey Nordita - Nordic Institute for Theoretical Physics
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Philine van Vliet Deutsches Elektronen-Synchrotron (DESY)
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Maria Elena Tejeda-Yeomans University of Colima
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Maryam Khaqan Emory University
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Mathematical Puzzles from Causal Set Quantum Gravity
Sumati Surya Raman Research Institute
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On generalized hyperpolygons
Laura Schaposnik University of Illinois at Chicago
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Exploring spacetime beyond classicality
Renate Loll Radboud Universiteit Nijmegen
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Octonions and the Standard Model
16 talks-Collection Number C21001Talk
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Welcome and Opening Remarks
Kirill Krasnov University of Nottingham
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Finite quantum geometry, octonions and the theory of fundamental particles.
Michel Dubois-Violette University of Paris-Saclay
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Supersymmetry and RCHO revisited
Paul Townsend University of Cambridge
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Spin (8,9,10), Octonions and the Standard Model
Kirill Krasnov University of Nottingham
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Gravity as the square of gauge theory
Leron Borsten Imperial College London
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A Magic Pyramid of Supergravity Theories from Yang-Mills Squared
Mia Hughes Imperial College London
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Division algebraic symmetry breaking
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Cohl Furey Humboldt University of Berlin
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Mia Hughes Imperial College London
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Clifford algebra of the Standard Model
Ivan Todorov Bulgarian Academy of Sciences
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Geometric Representation Theory
24 talks-Collection Number C20030Talk
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Singularities of Schubert varieties within a right cell
Martina Lanini Università degli Studi di Roma Tor Vergata
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Yangians and cohomological Hall algebras of Higgs sheaves on curves
Olivier Schiffmann University of Paris-Saclay
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Tate's thesis in the de Rham setting
Sam Raskin The University of Texas at Austin
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Fundamental local equivalences in quantum geometric Langlands
Gurbir Dhillon Stanford University
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Z-algebras from Coulomb branches
Oscar Kivinen California Institute of Technology
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Cotangent complexes of moduli spaces and Ginzburg dg algebras
Sarah Scherotzke University of Luxembourg
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Elliptic Cohomology and Physics
11 talks-Collection Number C20029Talk
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Projective elliptic genera and applications
Fei Han National University of Singapore
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Topological Modular Forms and Quantum Field Theory
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Equivariant elliptic cohomology with integral coefficients
Lennart Meier Utrecht University
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The de Rham model for elliptic cohomology from physics
Arnav Tripathy Harvard University
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Quasisymmetric characteristic numbers for Hamiltonian toric manifolds
Jack Morava Johns Hopkins University
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Codes, vertex algebras and topological modular forms
Gerd Laures Ruhr-Universität Bochum
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Elliptic characteristic classes, bow varieties, 3d mirror duality
Richard Rimanyi University of North Carolina - Chapel Hll
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PSI 2019/2020 - Statistical Physics (Kubiznak)
3 talks-Collection Number C19036Talk
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PSI 2019/2020 - Statistical Physics - Lecture 1
David Kubiznak Charles University
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PSI 2019/2020 - Statistical Physics - Lecture 2
David Kubiznak Charles University
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PSI 2019/2020 - Statistical Physics - Lecture 3
David Kubiznak Charles University
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PSI 2019/2020 - Mathematica (Xu)
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QFT for Mathematicians
25 talks-Collection Number C19023Talk
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Lecture 1: Factorization Algebras and the General Structure of QFT
Philsang Yoo Seoul National University
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Lecture 1: Supersymmetric Quantum Mechanics and All That
Mathew Bullimore Durham University
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TA Session: 0d QFT and Feynman diagrams
Theo Johnson-Freyd Dalhousie University
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Lecture 1: Boundary Conditions and Extended Defects
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Lecture 2: Factorization Algebras and the General Structure of QFT
Kevin Costello Perimeter Institute for Theoretical Physics
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TA Session: Supersummetry Algebras
Chris Elliott University of Massachusetts Amherst
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Lecture 3: Factorization Algebras and the General Structure of QFT
Philsang Yoo Seoul National University
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Lecture 2: Supersymmetric Quantum Mechanics and All That
Mathew Bullimore Durham University
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Cohomological Hall Algebras in Mathematics and Physics
19 talks-Collection Number C19018Talk
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An introduction to Cohomological Hall algebras and their representations
Yan Soibelman Kansas State University
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Gauge theory, vertex algebras and COHA
Davide Gaiotto Perimeter Institute for Theoretical Physics
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Networks of intertwiners, 3d theories and superalgebras
Yegor Zenkevich Institute for Theoretical and Experimental Physics
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COHA of surfaces and factorization algebras
Mikhail Kapranov Kavli Institute for Theoretical Physics (KITP)
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Yangians from cohomological Hall algebras
Ben Davison University of Edinburgh
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Algebraic structures of T[M3] and T[M4]
Sergei Gukov California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
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Categorification of 2d cohomological Hall algebras
Francesco Sala University of Tokyo
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Short star-products for filtered quantizations
Pavel Etingof Massachusetts Institute of Technology (MIT)
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Topological Holography Course (Costello)
8 talks-Collection Number C19017Talk
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Topological Holography Course - Lecture 1
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 2
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 3
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 5
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 6
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 7
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 8
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Holography Course - Lecture 9
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Quantum Field Theories - mini-course
-Collection Number C23048A 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. -
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Women at the Intersection of Mathematics and Theoretical Physics
16 talks-Collection Number C21002 -
Octonions and the Standard Model
16 talks-Collection Number C21001Over 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.
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Geometric Representation Theory
24 talks-Collection Number C20030 -
Elliptic Cohomology and Physics
11 talks-Collection Number C20029 -
PSI 2019/2020 - Statistical Physics (Kubiznak)
3 talks-Collection Number C19036PSI 2019/2020 - Statistical Physics (Kubiznak) -
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Cohomological Hall Algebras in Mathematics and Physics
19 talks-Collection Number C19018This 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.
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Topological Holography Course (Costello)
8 talks-Collection Number C19017Topological Holography Course (Costello)