相关论文: Eta-invariants, Torsion forms and Flat vector bund…

In a recent paper, the discrete Gabor transform was connected to a Gabor transform with a time frequency domain given by the flat torus. We show that the corresponding Bargmann spaces can be expressed as theta line bundles on Abelian…

For a real or complex semisimple Lie group $G$ and two nested parabolic subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$. Associated to the group $P$, we introduce a class of relative natural bundles and…

We revisit classical results of Serre, Fr\"ohlich and Saito in the theory of quadratic forms. Given a neutral Tannakian category $(\mathcal{T},\omega)$ over a field $k$ of characteristic $\neq 2$, another fiber functor $\eta$ over a…

Gukov-Pei-Putrov-Vafa constructed $q$-series invariants called homological blocks in a physical way in order to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT…

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions of a system of nonlinear first order elliptic partial differential equations in the ambient symplectic manifold. The symplectic manifold carries a…

The \emph{flat deformation theorem} states that given a semi-Riemannian analytic metric $g$ on a manifold, locally there always exists a two-form $F$, a scalar function $c$, and an arbitrarily prescribed scalar constraint depending on the…

The purpose of this article is to define and study new invariants of topological spaces: the $p$-adic Betti numbers and the $p$-adic torsion. These invariants take values in the $p$-adic numbers and are constructed from a virtual pro-$p$…

Transition form factors of pi^0, eta, eta' mesons are investigated by means of the anomaly sum rule -- an exact nonperturbative relation which follows from the dispersive representation of the axial anomaly. Considering the problem of…

Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. We prove a "quantum Riemann-Roch…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $\Omega_F$ be Drinfeld's upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of elements whose determinant has norm $1$. By working locally on $\Omega_F$, we…

We dicuss functorial consequences of way the eta invariant of Dirac operators behaves under gluing and change of boundary conditions.

A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual representation of Rota-Baxter…

We present a framework for studying transverse knots and symplectic surfaces utilizing the Seiberg-Witten monopole equation. Our primary approach involves investigating an equivariant Seiberg-Witten theory introduced by Baraglia-Hekmati on…

We study analytic torsion and eta like invariants on CR contact manifolds of any dimension admitting a circle transverse action, and equipped with a unitary representation. We show that, when defined using the spectrum of relevant operators…

We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of $P^N$ of small codimensions and of their preimages with respect to proper morphisms…

We compute the Floer homology and Seiberg-Witten Floer homotopy type of Seifert rational homology $3$-spheres which fiber over $\mathbb{RP}^2$. We show that they are all $L$-spaces and their Floer homotopy type is a suspension of $S^0$.…

Using methods of p-adic analysis we give a different proof of Burnside's problem for automorphisms of quasiprojective varieties X defined over a field of characteristic 0. More precisely, we show that any finitely generated torsion subgroup…

We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative $\eta$-invariant. In particular, by solving a Baum-Douglas type index problem, we give a "geometric" proof of a result of Keswani regarding the…

In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace…

We prove some formulas relating the inverse of a Cartan matrix with algebraic and geometric invariants of finite group representations.