Related papers: La correspondance de Langlands sur les corps de fo…
In \cite{lafforgue2012chtoucas}, Vicent Lafforgue attaches a semisimple Langlands parameter (or, what amounts to the same thing, a $\hat{G}$-pseudocharacter) to every cuspidal automorphic representation of a reductive group $G$ over the…
This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.
Much of what I have to say in the following (not all) is contained in my Informal History published in 2010 in the Intl Journ of Mod Phys and available as arXiv:1011.2736 [cond-mat]. But because the literature on the subject continues to…
These lectures provide an introduction to effective theories concentrating on the basic ideas and providing some simple applications
The process of debating is essential in our daily lives, whether in studying, work activities, simple everyday discussions, political debates on TV, or online discussions on social networks. The range of uses for debates is broad. Due to…
This is a survey article written for a workshop on L-functions and random matrix theory at the Newton Institute in July, 2004. The goal is to give some insight into how well-distributed sets of matrices in classical groups arise from…
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical…
$L$-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of $\textrm{GL}(n)$, as first described by Langlands. Conjecturally these two…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…
This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.
For $E/F$ quadratic extension of local fields and $G$ a reductive algebraic group over $F$, the paper formulates a conjecture classifying irreducible admissible representations of $G(E)$ which carry a $G(F)$ invariant linear form, and the…
In the first part of this paper I will describe my work together with Lars and in the second part I will give a look at some of Lars's oldest papers.
This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book "The Genesis of Langlands' Program," edited by Dr. Julia Mueller and Dr. Freydoon…
In this, the eighth article in my Derived Langlands series, I describe the construction of a 2-variable L-function for two representations of general linear groups of a $p$-adic local field. Due to extenuating health circumstances, many of…
We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.
This is an expository article based on my lectures on eigenfunctions of the Laplacian for the 2013 IAS/Park City Mathematics Institute (PCMI) summer school in geometric analysis. Many of the results are based on joint work with H.…
Public lecture given at The Fields Institute, June 2, 2005.
Following earlier work by Michel Bitbol and Laura de La Tremblaye which examines QBism from the perspective of phenomenology, this short paper explores points of contact between QBism and Maurice Merleau-Ponty's essay The intertwining--the…
This is a translation of an inaugural speech given originally in Dutch in 1998. The topic of that speech, intended for a general audience, was what is now called "The Anthropic Landscape of String Theory".
We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.