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.
Format results

3 talksCollection Number C19036
Talk

PSI 2019/2020  Statistical Physics  Lecture 1
David Kubiznak Charles University

PSI 2019/2020  Statistical Physics  Lecture 2
David Kubiznak Charles University

PSI 2019/2020  Statistical Physics  Lecture 3
David Kubiznak Charles University


PSI 2019/2020  Mathematica (Xu)
Collection Number C19031 
QFT for Mathematicians
25 talksCollection Number C19023Talk

Lecture 1: Factorization Algebras and the General Structure of QFT
Philsang Yoo Seoul National University

Lecture 1: Supersymmetric Quantum Mechanics and All That
Mathew Bullimore Durham University

TA Session: 0d QFT and Feynman diagrams
Theo JohnsonFreyd Dalhousie University

Lecture 1: Boundary Conditions and Extended Defects
Davide Gaiotto Perimeter Institute for Theoretical Physics

Lecture 2: Factorization Algebras and the General Structure of QFT
Kevin Costello Perimeter Institute for Theoretical Physics

TA Session: Supersummetry Algebras
Chris Elliott University of Massachusetts Amherst

Lecture 3: Factorization Algebras and the General Structure of QFT
Philsang Yoo Seoul National University

Lecture 2: Supersymmetric Quantum Mechanics and All That
Mathew Bullimore Durham University


Cohomological Hall Algebras in Mathematics and Physics
19 talksCollection Number C19018Talk

An introduction to Cohomological Hall algebras and their representations
Yan Soibelman Kansas State University

Gauge theory, vertex algebras and COHA
Davide Gaiotto Perimeter Institute for Theoretical Physics

Networks of intertwiners, 3d theories and superalgebras
Yegor Zenkevich University of California, Berkeley

COHA of surfaces and factorization algebras
Mikhail Kapranov Kavli Institute for Theoretical Physics (KITP)

Yangians from cohomological Hall algebras
Ben Davison University of Edinburgh

Algebraic structures of T[M3] and T[M4]
Sergei Gukov California Institute of Technology (Caltech)  Division of Physics Mathematics & Astronomy

Categorification of 2d cohomological Hall algebras
Francesco Sala University of Tokyo

Short starproducts for filtered quantizations
Pavel Etingof Massachusetts Institute of Technology (MIT)


Topological Holography Course (Costello)
8 talksCollection Number C19017Talk

Topological Holography Course  Lecture 1
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 2
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 3
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 5
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 6
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 7
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 8
Kevin Costello Perimeter Institute for Theoretical Physics

Topological Holography Course  Lecture 9
Kevin Costello Perimeter Institute for Theoretical Physics


Higher Algebra and Mathematical Physics
21 talksCollection Number C18024Talk

Welcome and Opening Remarks

Theo JohnsonFreyd Dalhousie University

Andre Henriques University of Oxford
PIRSA:18080042 

N=1 supersymmetric vertex algebras of small index
Davide Gaiotto Perimeter Institute for Theoretical Physics

Geometric Langlands: Comparing the views from CFT and TQFT
Joerg Teschner Deutsches ElektronenSynchrotron, DESY  Theory Group

Cutting and gluing branes
David Nadler University of California, Berkeley

The lowenergy TQFT of the generalized double semion model
Arun Debray University of Texas  Austin


Moduli of connexions on open varieties
Bertrand Toen Paul Sabatier University

The Duistermaat–Heckman distribution for the based loop group
Lisa Jeffrey University of Toronto


Gauge Theory, Geometric Langlands and Vertex Operator Algebras
11 talksCollection Number C18004Talk

Gauge Theory, Geometric Langlands, and All That
Edward Witten Institute for Advanced Study (IAS)  School of Natural Sciences (SNS)

Overview of the global Langlands correspondence
Dima Arinkin University of WisconsinMilwaukee

Gauge theory, vertex algebras and quantum Geometric Langland dualities
Davide Gaiotto Perimeter Institute for Theoretical Physics


Introduction to local geometric Langlands
Sam Raskin The University of Texas at Austin





Talk

Semisimple Hopf algebras and fusion categories
Cesar Galindo Universidad de los Andes

The Hopf C*algebraic quantum double models  symmetries beyond group theory
Andreas Bauer Freie Universität Berlin

Modular categories and the Witt group
Michael Mueger Radboud Universiteit Nijmegen

Topological Quantum Computation
Eric Rowell Texas A&M University

Gapped phases of matter vs. Topological field theories
Davide Gaiotto Perimeter Institute for Theoretical Physics

An Introduction to Hopf Algebra Gauge Theory
Derek Wise University of ErlangenNuremberg

Kitaev lattice models as a Hopf algebra gauge theory
Catherine Meusburger University of ErlangenNuremberg

Topological defects and highercategorical structures
Jurgen Fuchs Karlstad University


Quantum Field Theory on Manifolds with Boundary and the BV Formalism
12 talksCollection Number C17013Talk

Perturbative BVBFV theories on manifolds with boundary
Alberto Cattaneo University of Zurich

Gactions in quantum mechanics (and spectral sequences and the cosmological constant)
Tudor Dimofte University of Edinburgh

Perturbative BVBFV theories on manifolds with boundary Part 2
Alberto Cattaneo University of Zurich

Degenerate Field Theories and Boundary Theories
Philsang Yoo Seoul National University

Bulkboundary BV quantization for 21 theories
Brian Williams Boston University

A link between AdS/CFT and Koszul duality
Kevin Costello Perimeter Institute for Theoretical Physics

Poisson Sigma Model with symplectic target
Francesco Bonechi National Institute for Nuclear Physics

Vertex algebras and BV master equation
Si Li Tsinghua University


String Theory for Mathematicians  Kevin Costello
4 talksCollection Number C17014Talk

String Theory for Mathematicians  Lecture 1
Kevin Costello Perimeter Institute for Theoretical Physics

String Theory for Mathematicians  Lecture 2
Kevin Costello Perimeter Institute for Theoretical Physics

String Theory for Mathematicians  Lecture 3
Kevin Costello Perimeter Institute for Theoretical Physics

String Theory for Mathematicians  Lecture 7
Kevin Costello Perimeter Institute for Theoretical Physics


Hitchin Systems in Mathematics and Physics
18 talksCollection Number C17001Talk

Critical points and spectral curves
Nigel Hitchin University of Oxford

Generalizing Quivers: Bows, Slings, Monowalls
Sergey Cherkis University of Arizona


Nahm transformation for parabolic harmonic bundles on the projective line with regular residues
Szilard Szabo Budapest University of Technology and Economics

A mathematical definition of 3d indices
Tudor Dimofte University of Edinburgh

Perverse Hirzebruch ygenus of Higgs moduli spaces
Tamas Hausel Institute of Science and Technology Austria

Motivic Classes for Moduli of Connections
Alexander Soibelman University of Southern California

BPS algebras and twisted character varieties
Ben Davison University of Edinburgh


Exact Operator Algebras in Superconformal Field Theories
Collection Number C16038

PSI 2019/2020  Statistical Physics (Kubiznak)
3 talksCollection Number C19036PSI 2019/2020  Statistical Physics (Kubiznak) 


Cohomological Hall Algebras in Mathematics and Physics
19 talksCollection 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.

Topological Holography Course (Costello)
8 talksCollection Number C19017Topological Holography Course (Costello) 
Higher Algebra and Mathematical Physics
21 talksCollection Number C18024Higher algebra has become important throughout mathematics physics and mathematical physics and this conference will bring together leading experts in higher algebra and its mathematical physics applications. In physics the term algebra is used quite broadly any time you can take two operators or fields multiply them and write the answer in some standard form a physicist will be happy to call this an algebra. Higher algebra is characterized by the appearance of a hierarchy of multilinear operations (e.g. A_infty and L_infty algebras). These structures can be higher categorical in nature (e.g. derived categories cosmology theories) and can involve mixtures of operations and cooperations (Hopf algebras Frobenius algebras etc.). Some of these notions are purely algebraic (e.g. algebra objects in a category) while others are quite geometric (e.g. shifted symplectic structures). An early manifestation of higher algebra in highenergy physics was supersymmetry. Supersymmetry makes quantum field theory richer and thus more complicated but at the same time many aspects become more tractable and many problems become exactly solvable. Since then higher algebra has made numerous appearances in mathematical physics both high and lowenergy. A telltale sign of the occurrence of higher structures is when classification results involve cohomology. Group cohomology appeared in the classification of condensed matter systems by the results of Wen and collaborators. Altland and Zirnbauer s "tenfold way" was explained by Kitaev using Ktheory. And Kitaev's 16 types of vortexfermion statistics were classified by spin modular categories. All these results were recently enhanced by the work of Freed and Hopkins based on cobordism theory. In high energy physics cohomology appears most visibly in the form of "anomalies". The ChernSimons anomaly comes from the fourth cohomology class of a compact Lie group and the 5brane anomaly is related to a certain cohomology class of the Spin group. The classification of conformal field theories involves the computation of all algebras objects in certain monoidal categories which is a type of nonabelian cohomology. Yet another important role for higher algebra in mathematical physics has been in the famous Langlands duality. Langlands duality began in number theory and then became geometry. It turned into physics when Kapustin and Witten realized geometric Langlands as an electromagnetic duality in cN=4 super YangMills theory. Derived algebra higher categories shifted symplectic geometry cohomology and supersymmetry all appear in Langlands duality. The conference speakers and participants drawn from both sides of the Atlantic and connected by live video streams will explore these myriad aspects of higher algebra in mathematical physics.

Gauge Theory, Geometric Langlands and Vertex Operator Algebras
11 talksCollection Number C18004The workshop will explore the relation between boundary conditions in fourdimensional gauge theory the Geometric Langlands program and Vertex Operator Algebras.

Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics
18 talksCollection Number C17029The Kitaev quantum double models are a family of topologically ordered spin models originally proposed to exploit the novel condensed matter phenomenology of topological phases for faulttolerant quantum computation. Their physics is inherited from topological quantum field theories, while their underlying mathematical structure is based on a class of Hopf algebras. This structure is also seen across diverse fields of physics, and so allows connections to be made between the Kitaev models and topics as varied as quantum gauge theory and modified strong complementarity. This workshop will explore this shared mathematical structure and in so doing develop the connections between the fields of mathematical physics, quantum gravity, quantum information, condensed matter and quantum foundations.

Quantum Field Theory on Manifolds with Boundary and the BV Formalism
12 talksCollection Number C17013In the past five years their have a been number of significant advances in the mathematics of QFT on manifolds with boundary. The work of Cattaneo, Mnev, and Reshitihkinbeyond setting rigorous foundationshas led to many computable and salient examples. Similarly, the work of Costello (specifically projects joint with Gwilliam and Si Li) provides a framework (and deformation/obstruction) for the observable theory of such theories with boundary/defects. There are related mathematical advances: constructible factorization algebras and higher category theory as pioneered by Lurie and the collaboration of Ayala, Francis, and Tanaka. The goal of the workshop is to bring together the leading experts in this multifaceted subject.The structure of the workshop will be such as to maximize the exchange of knowledge and collaboration. More specifically, the morning sessions will consist of several lecture series, while the afternoons will be reserved for research working groups. The mornings will communicate the essential ideas and techniques surrounding bulkboundary correspondences and perturbative AKSZ theories on manifolds with boundary/corners. The afternoons will be research driven and focus on specific problems within the following realms: the interaction of renormalization with cutting/pasting, aspects of the AdS/CFT correspondence, cohomological approaches to gravity, and the observable/defect theory of AKSZ type theories.

String Theory for Mathematicians  Kevin Costello
4 talksCollection Number C17014String Theory for Mathematicians  Kevin Costello 
Hitchin Systems in Mathematics and Physics
18 talksCollection Number C17001Hitchin Systems in Mathematics and Physics

Exact Operator Algebras in Superconformal Field Theories
Collection Number C16038Exact Operator Algebras in Superconformal Field Theories