Related papers: Lecture Notes on Relative Gromov-Witten Invariants
The first part of this work constructs positive-genus real Gromov-Witten invariants of real-orientable symplectic manifolds of odd "complex" dimensions; the present part focuses on their properties that are essential for actually working…
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
A compendium for outsiders.
The purpose of this note is to give an overview of our work on defining algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of orbifolds. This work will be described in detail in a subsequent paper. The presentation here…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
We construct Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing…
We compute, by two methods, the genus one degree zero orbifold Gromov-Witten invariants with non-stacky insertions which are exceptional cases of the dilaton and divisor equations. One method involves a detailed analysis of the relevant…
We propose a conjectural explicit formula of generating series of a new type for Gromov--Witten invariants of $\mathbb{P}^1$ of all degrees in full genera.
Log Gromov-Witten invariants have recently been defined separately by Gross and Siebert and Abramovich and Chen. This paper provides a dictionary between log geometry and holomorphic exploded manifolds in order to compare Gromov-Witten…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
In this note, we give item-by-item responses to the criticisms raised in [TZ] by Tehrani ad Zinger on our paper [LR]. We illuminate the main ideas and contributions in [LR] in section 2, itemize the responses to issues raised in [TZ] and…
In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible)…
We explore the theory of connected Gromov-Witten invariants of the symmetric product stack [Sym^n(A_r)]. We derive closed-form expressions for all equivariant invariants with two insertions and reveal a natural correspondence between the…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…
Memoir on the Sigma invariants and their applications, version 2
We introduce invariant rings for forms (homogeneous polynomials) and for d points on the projective space, from the point of view of representation theory. We discuss several examples, addressing some computational issues. We introduce the…