Elliptic Cohomology and Physics
Elliptic Cohomology and Physics
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Thursday May 28, 2020Speaker(s):
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.
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Thursday May 28, 2020Speaker(s):
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.
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Thursday May 28, 2020Speaker(s):
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.Collection/Series:Scientific Areas:
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Wednesday May 27, 2020Speaker(s):
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.
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Wednesday May 27, 2020Speaker(s):
(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.
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Wednesday May 27, 2020Speaker(s):
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.
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Tuesday May 26, 2020Speaker(s):
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
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Tuesday May 26, 2020Speaker(s):
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.
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Tuesday May 26, 2020Speaker(s):
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.
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Monday May 25, 2020Speaker(s):Collection/Series:Scientific Areas:
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