Mathematical physics

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 373 - 384 of 903

Welcome and Opening Remarks

Ben Webster University of Waterloo
June 22, 2020

PIRSA:20060024
Mathematical physics
On the classification of topological phases

Theo Johnson-Freyd Dalhousie University
June 01, 2020

PIRSA:20060018
Mathematical physics
Conformal blocks in genus zero, and Elliptic cohomology

Nitu Kitchloo Johns Hopkins University
May 28, 2020

PIRSA:20050060
Mathematical physics
Quasi-elliptic cohomology theory and the twisted, twisted Real theories

Zhen Huan Huazhong University of Science and Technology
May 28, 2020

PIRSA:20050059
Mathematical physics
Sigma-VOA correspondence

Miranda Cheng Universiteit van Amsterdam
May 28, 2020

PIRSA:20050058
Mathematical physics
Elliptic characteristic classes, bow varieties, 3d mirror duality

Richard Rimanyi University of North Carolina at Chapel Hill
May 27, 2020

PIRSA:20050057
Mathematical physics
Twisted superconformal algebras and representations of higher Virasoro algebras

Brian Williams Boston University
May 27, 2020

PIRSA:20050056
Mathematical physics
Codes, vertex algebras and topological modular forms

Gerd Laures Ruhr University Bochum
May 27, 2020

PIRSA:20050055
Mathematical physics
Quasisymmetric characteristic numbers for Hamiltonian toric manifolds

Jack Morava Johns Hopkins University
May 26, 2020

PIRSA:20050054
Mathematical physics
The de Rham model for elliptic cohomology from physics

Arnav Tripathy Harvard University
May 26, 2020

PIRSA:20050053
Mathematical physics
Equivariant elliptic cohomology with integral coefficients

Lennart Meier Utrecht University
May 26, 2020

PIRSA:20050052
Mathematical physics
Topological Modular Forms and Quantum Field Theory

Davide Gaiotto Perimeter Institute for Theoretical Physics
May 25, 2020

PIRSA:20050051
Mathematical physics

Welcome and Opening Remarks

Ben Webster University of Waterloo
June 22, 2020

PIRSA:20060024
Mathematical physics
On the classification of topological phases

Theo Johnson-Freyd Dalhousie University
June 01, 2020

PIRSA:20060018
Mathematical physics
There is a rich interplay between higher algebra (category theory, algebraic topology) and condensed matter. I will describe recent mathematical results in the classification of gapped topological phases of matter. These results allow powerful techniques from stable homotopy theory and higher categories to be employed in the classification. In one direction, these techniques allow for complete a priori classifications in spacetime dimensions ≤6. In the other direction, they suggest fascinating and surprising statements in mathematics.
Conformal blocks in genus zero, and Elliptic cohomology

Nitu Kitchloo Johns Hopkins University
May 28, 2020

PIRSA:20050060
Mathematical physics
A fundamental theorem in the theory of Vertex algebras (known as Zhu’s theorem) demonstrates that the space generated by the characters of certain Vertex algebras is a representation of the modular group. We will cast this theorem in the language of homotopy theory using the language of conformal blocks. The goal of this talk is to justify the claim that equivariant elliptic cohomology, seen as a derived spectrum, is a homotopical analog of Zhu’s theorem in the special case of the Affine Vacuum vertex algebra at a fixed integral level. The talk will not require knowing the definition of Vertex algebras or conformal blocks.
Quasi-elliptic cohomology theory and the twisted, twisted Real theories

Zhen Huan Huazhong University of Science and Technology
May 28, 2020

PIRSA:20050059
Mathematical physics
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic cohomology theories. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. In addition, we define twisted quasi-elliptic cohomology. They can be related to a twisted equivariant version Devoto’s elliptic cohomology via a Chern character map. Moreover, we construct twisted Real quasi-elliptic cohomology and the Chern character map in this case. This is joint work with Matthew Spong and Matthew Young.
Sigma-VOA correspondence

Miranda Cheng Universiteit van Amsterdam
May 28, 2020

PIRSA:20050058
Mathematical physics
In this talk I will discuss an interesting phenomenon, namely a correspondence between sigma models and vertex operator algebras, with the two related by their symmetry properties and by a reflection procedure, mapping the right-movers of the sigma model at a special point in the moduli space to left-movers. We will discuss the examples of N=(4,4) sigma models on $T^4$ and on $K3$. The talk will be based on joint work with Vassilis Anagiannis, John Duncan and Roberto Volpato.
Elliptic characteristic classes, bow varieties, 3d mirror duality

Richard Rimanyi University of North Carolina at Chapel Hill
May 27, 2020

PIRSA:20050057
Mathematical physics
We study elliptic characteristic classes of natural subvarieties in some ambient spaces, namely in homogeneous spaces and in Nakajima quiver varieties. The elliptic versions of such characteristic classes display an unexpected symmetry: after switching the equivariant and the Kahler parameters, the classes of varieties in one ambient space ``coincide” with the classes of varieties in another ambient space. This duality gets explained as “3d mirror duality” if we regard our ambient spaces as special cases of Cherkis bow varieties. I will report on a work in progress with Y. Shou, based on earlier related works with G. Felder, A. Smirnov, V. Tarasov, A. Varchenko, A. Weber, Z. Zhou.
Twisted superconformal algebras and representations of higher Virasoro algebras

Brian Williams Boston University
May 27, 2020

PIRSA:20050056
Mathematical physics
(Super)conformal algebras on two-dimensional spacetimes play a ubiquitous role in representation theory and conformal field theory. In most cases, however, superconformal algebras are finite dimensional. In this talk, we introduce refinements of certain deformations of superconformal algebras which share many facets with the ordinary (super) Virasoro algebras. Representations of these refinements include the higher dimensional Kac—Moody algebras, and many more motivated by physics. Finally, we will show how these algebras enhance to higher dimensional chiral/factorization algebras which upon ``localization" deform to well-studied chiral algebras on Riemann surfaces.
Codes, vertex algebras and topological modular forms

Gerd Laures Ruhr University Bochum
May 27, 2020

PIRSA:20050055
Mathematical physics
The talk illuminates the role of codes and lattice vertex algebras in algebraic topology. These objects come up naturally in connection with string structures or topological modular forms. The talk tries to unify these different concepts in an introductory manner.
Quasisymmetric characteristic numbers for Hamiltonian toric manifolds

Jack Morava Johns Hopkins University
May 26, 2020

PIRSA:20050054
Mathematical physics
Baker and Richter's $A_\infty$ analog of the complex cobordism spectrum provides characteristic numbers for complex-oriented toric manifolds, which generalize to define similar invariants for Hamiltonian toric dynamical systems: roughly, the `completely integrable' systems of classical mechanics which (by KAM theory) possess remarkable stability properties. arXiv:1910.12609
The de Rham model for elliptic cohomology from physics

Arnav Tripathy Harvard University
May 26, 2020

PIRSA:20050053
Mathematical physics
I'll discuss elliptic cohomology from a physical perspective, indicating the importance of the Segal-Stolz-Teichner conjecture and joint work with D. Berwick-Evans on rigorously proving some of these physical predictions.
Equivariant elliptic cohomology with integral coefficients

Lennart Meier Utrecht University
May 26, 2020

PIRSA:20050052
Mathematical physics
Thirteen years ago, Lurie has sketched a way to obtain equivariant elliptic cohomology and equivariant topological modular forms without the need to restrict to rational or complex coefficients. Recently, David Gepner and I have found one way to flesh out the details and and provide computations in the U(1)-equivariant case. On this work I will report.
Topological Modular Forms and Quantum Field Theory

Davide Gaiotto Perimeter Institute for Theoretical Physics
May 25, 2020

PIRSA:20050051
Mathematical physics

Title	Speaker(s)	Date	Talk Type	Info link
Welcome and Opening Remarks	Ben Webster	2020-06-22	Conference	View details
On the classification of topological phases	Theo Johnson-Freyd	2020-06-01	Scientific Series	View details
Conformal blocks in genus zero, and Elliptic cohomology	Nitu Kitchloo	2020-05-28	Conference	View details
Quasi-elliptic cohomology theory and the twisted, twisted Real theories	Zhen Huan	2020-05-28	Conference	View details
Sigma-VOA correspondence	Miranda Cheng	2020-05-28	Conference	View details
Elliptic characteristic classes, bow varieties, 3d mirror duality	Richard Rimanyi	2020-05-27	Conference	View details
Twisted superconformal algebras and representations of higher Virasoro algebras	Brian Williams	2020-05-27	Conference	View details
Codes, vertex algebras and topological modular forms	Gerd Laures	2020-05-27	Conference	View details
Quasisymmetric characteristic numbers for Hamiltonian toric manifolds	Jack Morava	2020-05-26	Conference	View details
The de Rham model for elliptic cohomology from physics	Arnav Tripathy	2020-05-26	Conference	View details
Equivariant elliptic cohomology with integral coefficients	Lennart Meier	2020-05-26	Conference	View details
Topological Modular Forms and Quantum Field Theory	Davide Gaiotto	2020-05-25	Conference	View details

Mathematical physics

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