相关论文: Recent Advances in the Langlands Program
Research Briefs: Cosmic microwave background anisotropy experiments, by Sean Carroll LISA Project Update by Bill Folkner An update on the r-mode instability, by Nils Andersson Laboratory experiments: news from MG9, by Riley Newman Progress…
Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. This article is a brief introduction to the…
GGR News: We hear that... by Jorge Pullin * Research Briefs: Too many coincidences?, by Laura Mersini The Quest for a Realistic Cosmology in String Theory, by Andrew Chamblin SFB/TR 7, by A. Gopakumar and D. Petroff The mock LISA data…
We show that local-global compatibility (at split primes) away from $p$ holds at all points of the $p$-adic eigenvariety of a definite $n$-variable unitary group. The novelty is we allow non-classical points, possibly non-\'{e}tale over…
In exact symplectic manifolds whose Liouville flow is gradientlike for a proper Morse function, one can associate conic microsheaves to eventually conic exact Lagrangians. Here we study how this 'microsheaf quantization' interacts with…
Contents (Part 1): 1.Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory (C D. Froggatt and H. B. Nielsen) 2.Unitary Representations, Noncompact Groups SO(q; d - q)...(N. Mankoc Borstnik, H. B. Nielsen and D.…
We present a gauge-theoretic interpretation of the "analytic" version of the geometric Langlands program, in which Hitchin Hamiltonians and Hecke operators are viewed as concrete operators acting on a Hilbert space of quantum states. The…
We give a parametrization of the simple Bernstein components of inner forms of a general linear group over a local field by invariants constructed from type theory, and explicitly describe its behaviour under the Jacquet-Langlands…
The increasing complexity of software systems has driven significant advancements in program analysis, as traditional methods unable to meet the demands of modern software development. To address these limitations, deep learning techniques,…
GGR News: - The View from the NSF, by Beverly Berger - GGR Program at the APS meeting in Jacksonville we hear that..., by David Garfinkle - 100 years ago, by David Garfinkle Research Briefs: - The Double Pulsar, by Michael Kramer -…
GGR News: o GGR program at the APS meeting in Denver, by David Garfinkle o we hear that ..., by David Garfinkle o 400 years ago, by David Garfinkle Conference reports: o The 24th Texas Symposium on Relativistic Astrophysics, by Scott Hughes…
In this set of notes, we present some recent developments on the fractional Allen-Cahn equation $$ (-\Delta)^s u = u-u^3,$$ with special attention to $\Gamma$-convergence results, energy and density estimates, convergence of level sets,…
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
We propose a global Jacquet-Langlands correspondence for the modules over the von Neumann algebras of $S$-arithmetic subgroups of $\rm{GL}(2)$ and of a quaternion algebra $D$, which are both defined over a totally real number field $F$. If…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
The third ML4H symposium was held in person on December 10, 2023, in New Orleans, Louisiana, USA. The symposium included research roundtable sessions to foster discussions between participants and senior researchers on timely and relevant…
GGR News: -we hear that..., by David Garfinkle -News from the GRG Society, by Abhay Ashtekar -LIGO/GEO/Virgo work together, by Peter Saulson -GWIC Ten Years on, by Stan Whitcomb Research Briefs: -Quasi-local energy, by Bjoern S. Schmekel…
An overview of minimum bias and underlying event studies at the LHC with the ATLAS and CMS detectors is presented. Current uncertainties in the modeling of soft pp inelastic interactions at the LHC energy scale are discussed. Triggers used…
We extend the Langlands program in various subprograms with certain different generalizations: (1) Mixed-parity functorial perturbation of the usual Langlands program after Fargues-Scholze in all characteristics; (2) Robba-Frobenius…