Related papers: The Tate conjecture over finite fields (AIM talk)
These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.
The notion of $\tau$-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite dimensional algebras. The…
This note is an extended version of my presentation at the "Focused Research Workshop on Exterior Di{\S}erential Systems and Lie Theory" held at the Fields Institute in Toronto, December 9-13, 2013. Some ideas and constructions of this note…
Presentation for a talk "Two betting strategies that predict all compressible sequences" given at Seventh International Conference on Computability, Complexity and Randomness (CCR 2012)…
We give here the contents pages for the Proceedings of the Lattice 2001 conference (19th International Symposium on Lattice Field Theory) that took place in August 2001 in Berlin, Germany. The contents are in HTML form with clickable links…
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
This paper, which is a summary (in which considerable creative license has been taken) of the author's talk at the sixth international conference on $p$-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017),…
We present detailed summaries of the talks that were given during a week-long workshop on Arithmetic Groups at the Banff International Research Station in April 2013. The vast majority of these reports are based on abstracts that were…
These informal notes, initially prepared a few years ago, look at various questions related to infinite processes in several parts of mathematics, with emphasis on examples.
This is a summary of a talk given at the "Conference on Pure and Applied Topology", Isle of Skye, June 24, 2005. It contains an announcement and sketch of proof of the classification of 2-compact groups.
The sixth assessment of the international panel on climate change (IPCC) states that "cumulative net CO2 emissions over the last decade (2010-2019) are about the same size as the 11 remaining carbon budget likely to limit warming to 1.5C…
This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with…
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete…
Lecture notes reviewing most recent developments in string/M/brane theory given by C. G. at the CIME Summer International Center of Mathematics at Cetraro. July 1997.
We show that the Tate conjecture for divisors over a finite field $\mathbb F$ is equivalent to an explicit algebraic problem about the third Milnor K-group of the function field $\bar {\mathbb F}(x,y,z)$ in three variables over $\bar…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…
This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture…
We investigate the idea that different interpretations of quantum mechanics can be seen as restrictions of the consistent (or decoherent) histories quantum mechanics of closed systems to particular classes of histories,together with the…
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…
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…