相关论文: String$\mathbf{^c}$ Structures and Modular Invaria…

Using Liu's modular invariance method and its odd-dimensional extension by Han and Yu, we establish new Witten rigidity theorems for the generalized Witten genus of twisted Dirac operators on even-dimensional spin$^c$ manifolds and twisted…

It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that…

New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We…

In this paper automorphic motives are constructed and analyzed with a view toward the understanding of the geometry of compactification manifolds in string theory in terms of the modular structure of the worldsheet theory. The results…

Classification of topological insulators and superconductors is manifested in terms of spin cobordism groups for lower dimensions. It is discussed that the periodic table of topological insulators is a result of the possible choices of spin…

In this paper we establish the existence of certain structures on the ordinary and equivariant homology of the free loop space on a manifold or, more generally, a formal Poincar\'e duality space. These structures; namely the loop product,…

In string field theory there is a fundamental object, the algebra of string field states \A, that must be understood better from a mathematical point of view. In particular we are interested in finding, if possible, a C^* structure over it,…

This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research. We begin…

We introduce a common domain of definition for the loop product and the loop coproduct, reduced loop homology, on which they combine to a unital infinitesimal anti-symmetric bialgebra structure. In particular, a relation conjectured by…

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A-infinity relations, which are the higher genus analog of the (classical) A-infinity relations on…

We show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c)…

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main…

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…

We consider moduli spaces of plane quartics marked with various structures such as Cayley octads, Aronhold heptads, Steiner complexes and G\"opel subsets and determine their cohomology. This answers a series of questions of Jesse Wolfson.…

After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. The second part deals with more recently obtained properties. At first, we…

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one…

We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…

We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…

These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…