Related papers: Restricted Overpartitions and concave compositions…

Our main result is the martingale representations for Markov additive processes where the modulator is a Levy process. These processes have three parts: the modulator, the jumps of the ordinate triggered by the modulator, and the…

We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta…

In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an…

In this note, we explicitly construct mock modular forms with integral Fourier coefficients by evaluating regularized Petersson inner products involving their shadows, which are unary theta functions of weights 1/2 and 3/2 . In addition, we…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

Slack and margin rescaling are variants of the structured output SVM, which is frequently applied to problems in computer vision such as image segmentation, object localization, and learning parts based object models. They define convex…

We give a short overview over recent work on finding constraints on partition functions of 2d CFTs from modular invariance. We summarize the constraints on the spectrum and their connection to Calabi-Yau compactifications.

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic…

In this paper we study the branching functions of tensor products of N=3 superconformal modules.

We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…

This doctoral thesis undertakes an in-depth exploration of limiting shape theorems across diverse mathematical structures, with a specific focus on subadditive processes within finitely generated groups exhibiting polynomial growth rates,…

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The non-holomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We…

We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…

We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes.…

We show the modular properties of the multiple 'elliptic' gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's…

Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…

In this paper, we use theta integrals to give a different construction of mock Maass forms studied by Sander Zwegers. With this method, we construct new real-analytic modular forms, whose Fourier coefficients are logarithms of algebraic…

Families of quasimodular forms arise naturally in many situations such as curve counting on Abelian surfaces and counting ramified covers of orbifolds. In many cases the family of quasimodular forms naturally arises as the coefficients of a…

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…