Related papers: Cobordism-valued intersection theory on $\overline…
We analyse the consequences of the Virasoro conjecture of Eguchi, Hori and Xiong for Gromov-Witten invariants, in the case of zero degree maps to the manifolds CP^1 and CP^2 (or more generally, smooth projective curves and smooth…
We establish a formula for the Gromov-Witten-Welschinger invariants of $\mathbb CP^3$ with mixed real and conjugate point constraints. The method is based on a suggestion by J. Koll\'ar that, considering pencils of quadrics, some real and…
We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
A $p$-adic version of Gromov-Witten invariants for counting plane curves of genus $g$ and degree $d$ through a given number of points is discussed. The multiloop version of $p$-adic string theory considered by Chekhov and others motivates…
G\"ottsche-Schroeter invariants are a genus 0 extension of Block-G\"ottsche invariants. They interpolate between Welschinger invariants involving pairs of complex conjugated points and genus 0 descendant Gromov-Witten invariants. They can…
Witten's top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r-spin structures. It plays a key role in Witten's conjecture relating to the intersection theory on these moduli spaces. Our…
We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and…
Extending our method for investigating Real cobordism (which was recently used by Hill, Hopkins and Ravenel in their solution of the Kervaire invariant 1 problem), we investigate the $RO(G)$-graded homotopy groups of a (non-complete)…
Cobordism of virtual string links on $n$ strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group $\mathbb{Z}^{n(n-1)}$. This paper also…
We compute the relative orbifold Gromov-Witten invariants of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$, with respect to vertical fibers. Via a vanishing property of the Hurwitz-Hodge bundle, 2-point rubber invariants are…
We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points Mbar_{0,m}(n,d) as the subring of invariants of a ring B, relative to the action of the group of symmetries of d elements. B is…
We calculate the genus 1 Gromov-Witten theory of the Hilbert scheme $\mathsf{Hilb}^n(\mathbb{C}^2)$ of points in the plane. The fundamental 1-point invariant (with a divisor insertion) is calculated using a correspondence with the families…
We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we…
The natural sum operation for symplectic manifolds is defined by gluing along codimension two submanifolds. Specifically, let X be a symplectic 2n-manifold with a symplectic (2n-2)-submanifold V. Given a similar pair (Y,W) with a symplectic…
The purpose of this paper is to provide a way to compute the intersection cohomology of the GIT quotient of a nonsingular projective variety. We show that the middle perversity intersection cohomology of the GIT quotient $M//G$ is naturally…
We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…
We study K-theoretic Gromov--Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K-theoretic Gromov--Witten invariants of the quintic threefold modulo…