Related papers: Wall-crossings for Hassett descendant potentials
We have solved a number of holonomic PDEs derived from the Bessel modules which are related to the generating functions of classical Bessel functions and the difference Bessel functions recently discovered by Bohner and Cuchta. This…
We propose an intersection-theoretic method to reduce questions in genus zero logarithmic Gromov-Witten theory to questions in the Gromov-Witten theory of smooth pairs, in the presence of positivity. The method is applied to the enumerative…
Hurwitz numbers count ramified covers of a Riemann surface with prescribed monodromy. As such, they are purely combinatorial objects. Tautological classes, on the other hand, are distinguished classes in the intersection ring of the moduli…
We analyse the intersection of positively and negatively sectional-hyperbolic sets for flows on compact manifolds. First we prove that such an intersection is hyperbolic if the intersecting sets are both transitive (this is false without…
Particular solutions of the Poisson equation can be constructed via Newtonian potentials, integrals involving the corresponding Green's function which in two-dimensions has a logarithmic singularity. The singularity represents a significant…
One-dimensional potentials defined by $V^{(S)}(x) =S(S+1) \hbar^2 \pi^2 /[2ma^2\sin^2(\pi x/a)]$ (for integer $S$) arise in the repeated supersymmetrization of the infinite square well, here defined over the region $(0,a)$. We review the…
Gromov-Witten (GW) theory produces Chow and cohomology classes on the moduli of curves, and there are several conjectures/speculations about their relation to the tautological ring. We develop new degeneration techniques to address these.…
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating functions in the natural way and compute their product,…
The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential…
We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting…
We use techniques from Gromov-Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane…
The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…
We analyse a supersymmetric mechanical model derived from (1+1)-dimensional field theory with Yukawa interaction, assuming that all physical variables take their values in a Grassmann algebra B. Utilizing the symmetries of the model we…
The matrix model of topological field theory for the moduli space of p-th spin curves is extended to the case of the Lie algebra of the orthogonal group. We derive a new duality relation for the expectation values of characteristic…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
Recently, S. Li and A. Pott\cite{LP} proposed a new concept of intersection distribution concerning the interaction between the graph $\{(x,f(x))~|~x\in\F_{q}\}$ of $f$ and the lines in the classical affine plane $AG(2,q)$. Later, G.…
It is a classical result due to Jacobi in algebraic combinatorics that the generating function of closed walks at a vertex $u$ in a graph $G$ is determined by the rational function \[ \frac{\phi_{G-u}(t)}{\phi_G(t)} \] where $\phi_G(t)$ is…
The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…