Elliptic Cohomology and Physics

Projective vector bundles (or gerbe modules) are generalizations of vector bundles in the presence of a gerbe on manifolds. Given a projective vector bundle, we will first show how to use it to twist the Witten genus to get modular invariants, which we call projective elliptic genera. Then we will…

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…

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.

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…

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.

(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…

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…

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…

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…

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…