相关论文: On a new proof of the Okuyama--Sakai conjecture

This is the third and the last of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of…

Several examples are given of continuous families of SU(2) vector potentials $A_i^a(x)$ in 3 space dimensions which generate the same magnetic field $B^{ai}(x)$ (with det $B\neq 0$). These Wu-Yang families are obtained from the Einstein…

We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative $K_0$-groups of orders in finite dimensional separable algebras that need not be commutative. By combining this…

Recently, Hong Wang and Joshua Zahl announced a proof of the 3-dimensional Kakeya conjecture. This is a survey article on the proof of Kakeya. We introduce the problem, discuss previous work and some of the difficulties of the problem, and…

For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this we develop in…

In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a…

We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain mixed settings, which in themselves slightly extend the…

We survey recent developments on generalizing the Gross--Zagier formula to high dimensional Shimura varieties, with an emphasis on the Arithmetic Gan--Gross--Prasad conjecture and the relative trace formula approach.

In this work we present a number of generalizations of Wick's theorems on integrals with Gaussian weight to a larger class of weights which we call subgaussian. Examples of subgaussian contractions are that of Kac-Moody or Virasoro type,…

In this paper we prove that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is constructed in the framework of the…

As the first step of proving the Hodge-FVH correspondence recently proposed in [19], we derive the Virasoro constraints and the Dubrovin--Zhang loop equation for special cubic Hodge integrals. We show that this loop equation has a unique…

We review the theory of Co-Gorenstein algebras, which was introduced by Beligiannis in the article "The Homological Theory of Contravariantly Finite Subcategories: Gorenstein Categories, Auslander-Buchweitz Contexts and (Co-)Stabilization".…

In this paper, the generalized Bloch Conjecture on zero cycles for the quotient of certain complete intersections with trivial canonical bundle is proved to hold. As an application of Bloch-Srinivas method on the decomposition of the…

We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving…

In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them…

We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equivariant one for a set of gauge theories. Second, we suggest…

In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for the case of C^3 has been finished.

This is the second of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace…

We study open topological gravity in two dimensions, or, the intersection theory on the moduli space of open Riemann surfaces initiated by Pandharipande, Solomon and Tessler. The open free energy, the generating function for the open…

A theorem proved by Dobrinskaya in 2006 shows that there is a strong connection between the $K(\pi,1)$ conjecture for Artin groups and the classifying space of Artin monoids. More recently Ozornova obtained a different proof of…