Through the framework of Conformal Field Theory (i.e. string theory), linear algebra and Lie theory meet up with number theory in fundamental ways. In particular, the graded traces and pseudo-traces of families of linear operators corresponding to the fields (vertex operators) of interacting particles exhibit certain invariance properties with respect to action of the modular group SL(2,Z). We discuss aspects of modular symmetries that appear in graded trace and pseudo-trace functions for various classes of algebras of fields (vertex algebras) and their modules, including for the new notion of strongly interlocked module introduced by Barron, Batistelli, Orosz Hunziker, and Yamskulna. Several examples will be discussed.
Graded (pseudo-)traces and number theory in Lie theory and physics. Sponsored by the Meyer Fund
In this talk, I will explain the recent development in the Segal-Stolz-Teichner (SST) paradigm. The SST paradigm is a set of ideas connecting stable homotopy theory, especially the theory of elliptic cohomology theory, with supersymmetric quantum field theories in physics. Thanks to the recent mathematical development of equivariant elliptic cohomology thoery, we are currently experiencing a great enrichment the SST paradigm. In the talk, I will illustrate this by explaining my work with Y.Lin on Topological Elliptic Genera.
Equivariant elliptic cohomology and supersymmetric quantum field theories Sponsored by the Meyer Fund
In this talk, I will explain the recent development in the Segal-Stolz-Teichner (SST) paradigm. The SST paradigm is a set of ideas connecting stable homotopy theory, especially the theory of elliptic cohomology theory, with supersymmetric quantum field theories in physics. Thanks to the recent mathematical development of equivariant elliptic cohomology thoery, we are currently experiencing a great enrichment the SST paradigm. In the talk, I will illustrate this by explaining my work with Y.Lin on Topological Elliptic Genera.
Equivariant elliptic cohomology and supersymmetric quantum field theories Sponsored by the Meyer Fund
Graded (pseudo-)traces and number theory in Lie theory and physics.