相关论文: Degenerations of surface scrolls and the Gromov-Wi…
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1…
We give a recursive formula for purely real Welschinger invariants of real Del Pezzo surfaces of degree $K^2\ge 3$, where in the case of surfaces of degree $3$ with two real components we introduce a certain modification of Welschinger…
We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
We present an algorithm to compute the Brauer group of involution surface bundles over rational surfaces.
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be…
In \cite{TY18}, higher genus Gromov--Witten invariants of the stack of $r$-th roots of a smooth projective variety $X$ along a smooth divisor $D$ are shown to be polynomials in $r$. In this paper we study the degrees and coefficients of…
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the distinguished vertices. Generalizing previously known…
We determine the Gromov-Witten invariants of the local Enriques surfaces for all genera and curve classes and prove the Klemm-Mari\~{n}o formula. In particular, we show that the generating series of genus $1$ invariants of the Enriques…
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference…
We propose a novel evolutionary algorithm for optimizing real-valued objective functions defined on the Grassmann manifold Gr}(k,n), the space of all k-dimensional linear subspaces of R^n. While existing optimization techniques on Gr}(k,n)…
We consider closed subschemes in the affine grassmannian obtained by degenerating $e$-fold products of flag varieties, embedded via a tuple of dominant cocharacters. For $G= \operatorname{GL}_2$, and cocharacters small relative to the…
We use simple geometric arguments to calculate the dimension zero local Gromov-Witten invariants of elliptic multiple fibers. This completes the calculation of all dimension zero GW invariants of elliptic surfaces with $p_g>0$.
We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the…
Gromov-Witten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from K. Behrend, B. Fantechi: The intrinsic normal cone.
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
We argue relations between the Aharonov invariants and Tamanoi's Schwarzian derivatives of higher order and give a recursion formula for Tamanoi's Schwarzians. Then we propose a definition of invariant Schwarzian derivatives of a…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point…
Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through use of integer spin weighted spherical harmonics we present a method which allows for the implementation of arbitrary…