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
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11 talks-Collection NumberC20029
Talk
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Projective elliptic genera and applications
National University of Singapore -
Topological Modular Forms and Quantum Field Theory
Perimeter Institute for Theoretical Physics -
Equivariant elliptic cohomology with integral coefficients
Utrecht University -
The de Rham model for elliptic cohomology from physics
Harvard University -
Quasisymmetric characteristic numbers for Hamiltonian toric manifolds
Johns Hopkins University -
Codes, vertex algebras and topological modular forms
Ruhr University Bochum -
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Elliptic characteristic classes, bow varieties, 3d mirror duality
University of North Carolina - Chapel Hll
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PSI 2019/2020 - Statistical Physics (Kubiznak)
3 talks-Collection NumberC19036Talk
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PSI 2019/2020 - Statistical Physics - Lecture 1
Charles University -
PSI 2019/2020 - Statistical Physics - Lecture 2
Charles University -
PSI 2019/2020 - Statistical Physics - Lecture 3
Charles University
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QFT for Mathematicians
25 talks-Collection NumberC19023Talk
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Lecture 1: Factorization Algebras and the General Structure of QFT
Seoul National University -
Lecture 1: Supersymmetric Quantum Mechanics and All That
Durham University -
TA Session: 0d QFT and Feynman diagrams
Dalhousie University -
Lecture 1: Boundary Conditions and Extended Defects
Perimeter Institute for Theoretical Physics -
Lecture 2: Factorization Algebras and the General Structure of QFT
Perimeter Institute for Theoretical Physics -
TA Session: Supersummetry Algebras
University of Massachusetts Amherst -
Lecture 3: Factorization Algebras and the General Structure of QFT
Seoul National University -
Lecture 2: Supersymmetric Quantum Mechanics and All That
Durham University
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Cohomological Hall Algebras in Mathematics and Physics
19 talks-Collection NumberC19018Talk
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An introduction to Cohomological Hall algebras and their representations
Kansas State University -
Gauge theory, vertex algebras and COHA
Perimeter Institute for Theoretical Physics -
Networks of intertwiners, 3d theories and superalgebras
University of Edinburgh -
COHA of surfaces and factorization algebras
University of Tokyo -
Yangians from cohomological Hall algebras
University of Edinburgh -
Algebraic structures of T[M3] and T[M4]
California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy -
Categorification of 2d cohomological Hall algebras
University of Tokyo -
Short star-products for filtered quantizations
Massachusetts Institute of Technology (MIT)
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Topological Holography Course (Costello)
8 talks-Collection NumberC19017Talk
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Topological Holography Course - Lecture 1
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 2
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 3
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 5
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 6
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 7
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 8
Perimeter Institute for Theoretical Physics -
Topological Holography Course - Lecture 9
Perimeter Institute for Theoretical Physics
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Higher Algebra and Mathematical Physics
21 talks-Collection NumberC18024Talk
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N=1 supersymmetric vertex algebras of small index
Perimeter Institute for Theoretical Physics -
Geometric Langlands: Comparing the views from CFT and TQFT
Deutsches Elektronen-Synchrotron DESY -
Cutting and gluing branes
University of California, Berkeley -
The low-energy TQFT of the generalized double semion model
University of Texas - Austin -
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Moduli of connexions on open varieties
Paul Sabatier University -
The Duistermaat–Heckman distribution for the based loop group
University of Toronto
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Gauge Theory, Geometric Langlands and Vertex Operator Algebras
11 talks-Collection NumberC18004Talk
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Gauge Theory, Geometric Langlands, and All That
Institute for Advanced Study (IAS) - School of Natural Sciences (SNS) -
Overview of the global Langlands correspondence
University of Wisconsin-Milwaukee -
Gauge theory, vertex algebras and quantum Geometric Langland dualities
Perimeter Institute for Theoretical Physics -
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Introduction to local geometric Langlands
The University of Texas at Austin -
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Talk
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Semisimple Hopf algebras and fusion categories
Universidad de los Andes -
The Hopf C*-algebraic quantum double models - symmetries beyond group theory
Freie Universität Berlin -
Modular categories and the Witt group
Radboud Universiteit Nijmegen -
Topological Quantum Computation
Texas A&M University -
Gapped phases of matter vs. Topological field theories
Perimeter Institute for Theoretical Physics -
An Introduction to Hopf Algebra Gauge Theory
University of Erlangen-Nuremberg -
Kitaev lattice models as a Hopf algebra gauge theory
University of Erlangen-Nuremberg -
Topological defects and higher-categorical structures
Karlstad University
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Quantum Field Theory on Manifolds with Boundary and the BV Formalism
12 talks-Collection NumberC17013Talk
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Perturbative BV-BFV theories on manifolds with boundary
University of Zurich -
G-actions in quantum mechanics (and spectral sequences and the cosmological constant)
University of Edinburgh -
Perturbative BV-BFV theories on manifolds with boundary Part 2
University of Zurich -
Degenerate Field Theories and Boundary Theories
Seoul National University -
Bulk-boundary BV quantization for 2-1 theories
Boston University -
A link between AdS/CFT and Koszul duality
Perimeter Institute for Theoretical Physics -
Poisson Sigma Model with symplectic target
National Institute for Nuclear Physics -
Vertex algebras and BV master equation
Tsinghua University
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String Theory for Mathematicians - Kevin Costello
4 talks-Collection NumberC17014Talk
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String Theory for Mathematicians - Lecture 1
Perimeter Institute for Theoretical Physics -
String Theory for Mathematicians - Lecture 2
Perimeter Institute for Theoretical Physics -
String Theory for Mathematicians - Lecture 3
Perimeter Institute for Theoretical Physics -
String Theory for Mathematicians - Lecture 7
Perimeter Institute for Theoretical Physics
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Hitchin Systems in Mathematics and Physics
18 talks-Collection NumberC17001Talk
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Critical points and spectral curves
University of Oxford -
Generalizing Quivers: Bows, Slings, Monowalls
University of Arizona -
Holomorphic symplectic Morita equivalence and the generalized Kahler potential
University of Toronto -
Nahm transformation for parabolic harmonic bundles on the projective line with regular residues
Budapest University of Technology and Economics -
A mathematical definition of 3d indices
University of Edinburgh -
Perverse Hirzebruch y-genus of Higgs moduli spaces
Institute of Science and Technology Austria -
Motivic Classes for Moduli of Connections
University of Southern California -
BPS algebras and twisted character varieties
University of Edinburgh
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Deformation Quantization of Shifted Poisson Structures
17 talks-Collection NumberC16005Talk
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Formal derived stack and Formal localization
Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier -
An overview of derived analytic geometry
Institut de Mathématiques de Jussieu -
Categorification of shifted symplectic geometry using perverse sheaves
University of Oxford -
Shifted structures and quantization
University of Pennsylvania -
What is the Todd class of an orbifold?
University of Wisconsin–Madison -
Singular support of categories
University of Wisconsin-Milwaukee -
Symplectic and Lagrangian structures on mapping stacks
Universität Wien -
The Maslov cycle and the J-homomorphism
Boston College
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Elliptic Cohomology and Physics
11 talks-Collection NumberC20029 -
PSI 2019/2020 - Statistical Physics (Kubiznak)
3 talks-Collection NumberC19036PSI 2019/2020 - Statistical Physics (Kubiznak) -
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Cohomological Hall Algebras in Mathematics and Physics
19 talks-Collection NumberC19018This 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 NumberC19017Topological Holography Course (Costello) -
Higher Algebra and Mathematical Physics
21 talks-Collection NumberC18024Higher 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 co-operations (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 high-energy 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 low-energy. A tell-tale 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 "ten-fold way" was explained by Kitaev using K-theory. And Kitaev's 16 types of vortex-fermion 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 Chern--Simons anomaly comes from the fourth cohomology class of a compact Lie group and the 5-brane 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 non-abelian 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 Yang--Mills 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.
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Gauge Theory, Geometric Langlands and Vertex Operator Algebras
11 talks-Collection NumberC18004The workshop will explore the relation between boundary conditions in four-dimensional gauge theory the Geometric Langlands program and Vertex Operator Algebras.
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Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics
18 talks-Collection NumberC17029The 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 fault-tolerant 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.
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Quantum Field Theory on Manifolds with Boundary and the BV Formalism
12 talks-Collection NumberC17013In 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 Reshitihkin--beyond setting rigorous foundations--has 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 multi-faceted 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 bulk-boundary 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.
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String Theory for Mathematicians - Kevin Costello
4 talks-Collection NumberC17014String Theory for Mathematicians - Kevin Costello -
Hitchin Systems in Mathematics and Physics
18 talks-Collection NumberC17001Hitchin Systems in Mathematics and Physics
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Deformation Quantization of Shifted Poisson Structures
17 talks-Collection NumberC16005Deformation Quantization of Shifted Poisson Structures