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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：P-adic Simpson correspondence via exponential twisting
指数扭曲 P—adic—Simpson对应 p-adic-Simpson对应关系
2023/12/11
In this talk, I shall explain the work of G. Faltings on a p-adic Simpson correspondence, using exponential twisting. This reinterpretation of the correspondence makes clearer analogy between the p-ad...
THE GEOMETRIC THETA CORRESPONDENCE FOR HILBERT MODULAR SURFACES
GEOMETRIC THETA CORRESPONDENCE；HILBERT MODULAR SURFACES
2015/10/14
In a series of papers [11, 12, 13, 14] we have been studying the geometric theta correspondence (see below) for non-compact arithmetic quotients of symmetric spaces associated to orthogonal groups. It...
Unipotent Representations and the Dual Pairs Correspondence
Dual Pairs Correspondence Unipotent Representations
2015/8/17
Much of the material in this talk was presented at the conference in honor
of Roger Howe. The slides are available at
http://math.mit.edu/conferences/howe/program.php
The theme of the talk is to n...
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann’s zeta function
Statistical tests random unitary matrix Riemann zeta function data set
2015/7/14
This paper presents some new statistical tests and new conjectures regarding
the correspondence between the eigenvalues of random unitary matrices and
the zeros of Riemann’s zeta function. Global fe...
ARITHMETIC PROPERTIES OF THE SHIMURA-SHINTANI-WALDSPURGER CORRESPONDENCE
ARITHMETIC PROPERTIE CORRESPONDENCE
2015/7/6
We prove that the theta correspondence for the dual pair (SLg2; P B￡), for B an indeˉnite
quaternion algebra over Q, acting on modular forms of odd square-free level, preserves
rationality and p-int...
Conformal Triality and AdS/CFT 3 Correspondence
Conformal Triality AdS/CFT 3 Correspondence
2015/3/19
Conformal Triality and AdS/CFT 3 Correspondence.
Conservation relations for local theta correspondence
conservation relation theta correspondence oscillator representation degenerate principal series
2012/4/16
We prove Kudla-Rallis's conjecture on first occurrences of orthogonal-symplectic dual pair correspondence, for a local field of characteristic zero.
Quadro-quadric cremona transformations in low dimensions via the JC-correspondence
Quadro-quadric cremona transformations low dimensions JC-correspondence Algebraic Geometry
2012/4/18
We apply the results of arXiv:1109.3573 to study quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps...
Genericity and contragredience in the local Langlands correspondence
Genericity contragredience local Langlands correspondence Representation Theory Number Theory
2012/4/17
Recently Adams and Vogan made a conjecture about the behavior of the local Langlands correspondence with respect to taking the contragredient of a representation. We prove this conjecture for the temp...
Motivic Donaldson-Thomas invariants and McKay correspondence
Motivic Donaldson-Thomas invariants McKay correspondence Algebraic Geometry
2011/9/29
Abstract: Let $G\subset SL_2(C)\subset SL_3(C)$ be a finite group. We compute motivic Pandharipande-Thomas and Donaldson-Thomas invariants of the crepant resolution $Hilb^G(C^3)$ of $C^3/G$ generalizi...
Three Applications to Rational Relations of the High Undecidability of the Infinite Post Correspondence Problem in a Regular omega-Language
Decision problems infinite Post Correspondence Problem analytical hierarchy high undecidability infinitary rational relations
2011/10/10
Abstract: It was noticed by Harel in [Har86] that "one can define $\Sigma_1^1$-complete versions of the well-known Post Correspondence Problem". We first give a complete proof of this result, showing ...
The Geometrical Satake Correspondence for Ramified Groups
Geometrical Satake Correspondence Ramified Groups Number Theory
2011/9/22
Abstract: We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cy...
A congruence property of the local Langlands correspondence
Simple type modular local Langlands correspondence effective local Langlands correspondence Number Theory
2011/9/2
Abstract: Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensio...
Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
Shimura curves p-adic Jacquet-Langlands correspondence Number Theory
2011/8/25
Abstract: We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. ...
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
Quantum-to-Classical Correspondence Hubbard-Stratonovich Dynamical Systems
2011/3/2
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-St...