相关论文: Gravitational Descendants and Linearized Contact H…

We study the $(1,q=-1)$ model coupled to topological gravity as a candidate to describing $2d$ string theory at the self-dual radius. We define the model by analytical continuation of $q>1$ topological recursion relations to $q=-1$. We show…

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed…

We define \emph{$0$-shifted} and \emph{$+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie…

Dubrovin establishes the relationship between the GUE partition function and the partition function of Gromov--Witten invariants of the complex projective line. In this paper, we give a direct proof of Dubrovin's result. We also present in…

Given a (not necessarily discrete) proper metric space $M$ with bounded geometry, we define a groupoid $G(M)$. We show that the coarse Baum--Connes conjecture with coefficients, which states that the assembly map with coefficients for G(M)…

This research announcement discusses our results on Gromov-Witten theory of root gerbes. A complete calculation of genus 0 Gromov-Witten theory of $\mu_{r}$-root gerbes over a smooth base scheme is obtained by a direct analysis of virtual…

We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov-Witten theory of root stacks with extremal ages. Exploiting…

We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the…

We work through, in detail, the orbifold quantum cohomology, with gravitational descendants, of the stack BG, the point modulo trivial action of a finite group G. We provide a simple description of algebraic structures on the state space of…

We apply the fermionic description of CFT obtained in our previous work to the computation of the one-point functions of the descendant fields in the sine-Gordon model.

On a stack of stable maps, the psi classes are modified by subtracting certain boundary divisors. These modified psi classes are compatible with forgetful morphisms, and are well-suited to enumerative geometry: tangency conditions allow…

The Virasoro conjecture is a conjectured sequence of relations among the descendent Gromov-Witten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and…

Let $L\subset J^1(M)$ be a Legendrian submanifold of the 1-jet space of a Riemannian $n$-manifold $M$. A correspondence is established between rigid flow trees in $M$ determined by $L$ and boundary punctured rigid pseudo-holomorphic disks…

We build the abstract theory of Gromov-Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal natural (with respect to Gromov-Witten theory) class of varieties). In particular, we consider ``the minimal Gromov-Witten…

In this work we propose a simple algebraic recursion for the complete one-loop integrands of $N$-graviton correlators. This formula automatically yields the correct symmetry factors of individual diagrams, taking into account both the…

We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with…

We perform the asymptotic enumeration of two classes of rooted maps on orientable surfaces of genus g: m-hypermaps and m-constellations. For m=2, they correspond respectively to maps with even face degrees and bipartite maps. We obtain…

A homology class $d \in H_2(X)$ of a complex flag variety $X = G/P$ is called a line degree if the moduli space $\overline{M}_{0,0}(X,d)$ of 0-pointed stable maps to $X$ of degree $d$ is also a flag variety $G/P'$. We prove a quantum equals…

We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that…

Given a smooth target curve $X$, we explore the relationship between Gromov-Witten invariants of $X$ relative to a smooth divisor and orbifold Gromov-Witten invariants of the $r$-th root stack along the divisor. We proved that relative…