Related papers: Some topological genera and Jacobi forms

The abelian and monoidal structure of the category of smooth weight modules over a non-integrable affine vertex algebra of rank greater than one is an interesting, difficult and essentially wide open problem. Even conjectures are lacking.…

Let (W, S) be a Coxeter system. A W-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W-graph corresponding to the action of the Iwahori-Hecke algebra on the…

We give a detailed path integral derivation of the elliptic genus of a supersymmetric coset conformal field theory, further twisted by a global U(1) symmetry. It gives rise to a Jacobi form in three variables, which is the modular…

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…

We prove two conjectures regarding the representation growth of groups of type $A_2$. The first, conjectured by Avni, Klopsch, Onn and Voll, regards the uniformity of representation zeta functions over local complete discrete valuation…

Let $A$ and $B$ be abelian varieties defined over the function field $k(S)$ of a smooth algebraic variety $S/k.$ We establish criteria, in terms of restriction maps to subvarieties of $S,$ for existence of various important classes of…

Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $M\xi$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for…

For each compact almost Kahler manifold $(X,\om,J)$ and an element A of $H_2(X;Z)$, we describe a closed subspace $\ov{\frak M}_{1,k}^0(X,A;J)$ of the moduli space $\ov{\frak M}_{1,k}(X,A;J)$ of stable J-holomorphic genus-one maps such that…

Eisenstein series play an important role in the theory of modular forms and have profound connections with $q$-series identities, partition theory, and special functions. Likewise, Ramanujan's mock theta functions, originally introduced in…

For a class of generalized holomorphic Eisenstein series, we establish complete asymptotic expansions (Theorems~1~and~2), which together with the explicit expression of the latter remainder (Theorem~3), naturally transfer to several new…

Given an involutive automorphism $\theta$ of a Coxeter system $(W,S)$, let $\mathfrak{I}(\theta) \subseteq W$ denote the set of twisted involutions. We provide a minimal set of moves that can be added to the braid moves, in order to connect…

Let $Z$ be the quotient of the Siegel modular threefold $\mathcal{A}^{{\rm sa}}(2,4,8)$ which has been studied by van Geemen and Nygaard. They gave an implication that some 6-tuple $F_Z$ of theta constants which is in turn known to be a…

Lichnerowicz-Jacobi cohomology and homology of Jacobi manifolds are reviewed. We present both in a unified approach using the representation of the Lie algebra of functions on itself by means of the hamiltonian vector fields. The use of the…

For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given…

We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To…

The J-function in Gromov-Witten theory is a generating function for one-point genus zero Gromov-Witten invariants with descendants. Here we give formulas for the quantum K-theoretic J-functions of type A flag manifolds and conjectural…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold…

A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the lowest non-vanishing derivatives of theta functions with…

We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, in terms of its lambda-structure. More explicitly, we will see that if L* is the torus of invertible elements in the n-dimensional separable…