Related papers: Modular Invariance and Characteristic Numbers

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

In this series of papers, we propose a theory of enumerative invariants counting self-dual objects in self-dual categories. Ordinary enumerative invariants in abelian categories can be seen as invariants for the structure group $\mathrm{GL}…

We prove that only finitely many $j$-invariants of elliptic curves with complex multiplication are algebraic units. A rephrased and generalized version of this result resembles Siegel's Theorem on integral points of algebraic curves.

Let F be the cubic field of discriminant -23 and let O be its ring of integers. By explicitly computing cohomology of congruence subgroups of GL(2,O), we computationally investigate modularity of elliptic curves over F.

Using $E_8$ bundles, we construct some modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$. By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…

We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…

We establish large deviation type estimates for i.i.d. products of two dimensional random matrices with finitely supported probability distribution. The estimates are stable under perturbations and require no irreducibility assumptions. In…

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…

We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…

Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G.…

We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…

We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…

We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…

The space of Lam\'e functions of order m is isomorphic to the space of pairs (elliptic curve, Abelian differential) where the differential has a single zero of order 2m at the origin and m double poles with vanishing residues. We describe…

In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…

We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…