Related papers: From Heun to Painlev\'e on Sasaki-Einstein Spaces …

The multisymplectic formalism of field theories developed by many mathematicians over the last fifty years is extended in this work to deal with manifolds that have boundaries. In particular, we develop a multisymplectic framework for first…

We construct an explicit diffeomorphism between the Sasaki-Einstein spaces Y^{p,q} and the product space S^3 \times S^2 in the cases q \le 2. When q=1 we express the K\"ahler quotient coordinates as an SU(2) bundle over S^2 which we…

We establish abstract horizontal norm relations involving the unramified Hecke-Frobenius polynomials that correspond under the Satake isomorhpism to the degree eight spinor $L$-factors of $ \mathrm{GSp}_{6} $. These relations apply to…

We discuss in detail the different analogues of Dolbeault cohomology groups on Sasaki-Einstein manifolds and prove a new vanishing result for the transverse Dolbeault cohomology groups $H_{\bar\partial}^{(p,0)}(k)$ graded by their charge…

We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…

In this paper we study the relativistic scalar particle described by the Klein-Gordon interacts with the uniform magnetic field in the context of the Som-Raychaudhuri space-time. Based on the property of the biconfluent Heun function…

We study several connected problems of holomorphic function spaces on homogeneous Siegel domains. The main object of our study concerns weighted mixed norm Bergman spaces on homogeneous Siegel domains of type II. These problems include:…

Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single…

We generate new 11-dimensional supergravity solutions from deformations based on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of…

We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construction of the $q$-difference Painlev\'e equations, showing…

Given a compact segment, $\beta$, of a cuspidal geodesic on the modular surface, we study the number of sign changes of cusp forms and Eisenstein series along $\beta$. We prove unconditionally a sharp lower bound for Eisenstein series along…

We perform the Hamiltonian constraint analysis for a wide class of gravity theories that are invariant under spatial diffeomorphism. With very general setup, we show that different from the general relativity, the primary and secondary…

Let $\mathcal{K}(n, V)$ be the set of $n$-dimensional compact Kahler-Einstein manifolds $(X, g)$ satisfying $Ric(g)= - g$ with volume bounded above by $V$. We prove that after passing to a subsequence, any sequence $\{ (X_j,…

These are notes for the Aisenstadt lectures given in may/june 2002 at CRM, Montreal, enlarged and updated in 2014 by taking into account the recent results of Elias and Williamson on Soergel bimodules. The main object is the study of…

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of…

We investigate the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime with a fixed time-flow vector. For existence of a well-defined Hamiltonian variational principle taking into…

In this paper, we will give a complete geometric background for the geometry of Painlev\'e $VI$ and Garnier equations. By geometric invariant theory, we will construct a smooth coarse moduli space $M_n^{\balpha}(\bt, \blambda, L) $ of…

On the hyperbolic space, we study a semilinear equation with non-autonomous nonlinearity having a critical Sobolev exponent. The Poincar\'e-Sobolev equation on the hyperbolic space explored by Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa…

We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein…

In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…