Related papers: Modular Invariants and Twisted Equivariant K-theor…

The focus of this thesis is on (1) the role of Ka\v c-Moody (KM) algebras in string theory and the development of techniques for systematically building string theory models based on higher level ($K\geq 2$) KM algebras and (2) fractional…

Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction…

The three-manifold topological invariants $\hat Z$ capture the half-index of the three-dimensional theory with ${\mathcal{N}}=2$ supersymmetry obtained by compactifying the M5 brane theory on the closed three-manifold. In 2019, surprising…

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…

Let $G=SU(2)$ and let $\Omega G$ denote the space of based loops in SU(2). We explicitly compute the $R(G)$-module structure of the topological equivariant $K$-theory $K_G^*(\Omega G)$ and in particular show that it is a direct product of…

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new…

We construct three-dimensional non-semisimple topological field theories from the unrolled quantum group of the Lie superalgebra $\mathfrak{osp}(1 \vert 2)$. More precisely, the quantum group depends on a root of unity $q=e^{\frac{2 \pi…

Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group $G$ and the "Verlinde ring" of the loop group of $G$. We call this isomorphism FHT isomorphism. However, it does not hold…

To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new…

In this paper we construct a twisted version of quasi-elliptic cohomology. This theory can be constructed as a K-theory of a loop space. After establishing basic properties of the theory, including restriction, change-of-group and induction…

From a certain induced representation $\mathcal{P}_\ell$ of a double affine Weyl group, we construct a ring $\mathcal{F}_\ell$ that is isomorphic to the fusion ring, or Verlinde algebra, associated to affine Lie algebras at fixed positive…

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary…

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is dis- cussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral…

In this paper, we study contragredient duals and invariant bilinear forms for modular vertex algebras (in characteristic $p$). We first introduce a bialgebra $\mathcal{H}$ and we then introduce a notion of $\mathcal{H}$-module vertex…

In this paper we compute explicit formulas for the holonomy map for a gerbe with connection over an orbifold. We show that the holonomy descends to a transgression map in Deligne cohomology. We prove that this recovers both the inner local…

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is…

We construct and study a bicategory of super 2-line bundles over graded Lie groupoids, providing a unified framework for geometric models of twistings of (Real) K-theory. The core of our work is to exhibit a wide range of models from the…

We consider algebraic varieties canonically associated to any Lie superalgebra, and study them in detail for super-Poincar\'e algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of)…