Related papers: The Tate conjecture over finite fields (AIM talk)
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.
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
This book was intended to serve as supporting material for a mini-course on web geometry delivered at the 27th Brazilian Mathematical Colloquium which took place at IMPA in the last week of July 2009.
These are the post-proceedings of the second ARCADE workshop, which took place on the 26th August 2019 in Natal, Brazil, colocated with CADE-27. ARCADE stands for Automated Reasoning: Challenges, Applications, Directions, Exemplary…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.
These notes are an expanded version of the author's lectures at the graduate workshop "Noncommutative Algebraic Geometry" at the Mathematical Sciences Research Institute in June 2012. The main topics discussed are Artin-Schelter regular…
The biannual TARK conferences bring together researchers from a wide variety of fields sharing a common interest in reasoning about rationality and knowledge. The impact of this tradition, going back to 1986, is apparent in many of today's…
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
In this article a few of the qualitative spatio-temporal knowledge representation techniques developed by the constraint reasoning community within artificial intelligence are reviewed. The objective is to provide a broad exposure to any…
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.
This is a colloquium style pedagogical introduction to the paradigm of large extra dimensions. To be published in the Proceedings of the Workshop "Crossing the boundaries: Gauge dynamics at strong coupling," (May 14 - 17, 2009,…
Talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…
A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…
The Fourth International Conference on Applied Category Theory took place at the Computer Laboratory of the University of Cambridge on 12--16 July 2021. It was a hybrid event, with physical attendees present in Cambridge and other…
Lecture notes for the proceedings of the workshop "Algebraic Combinatorics related to Young diagram and statistical physics", Aug. 6-10 2012, I.I.A.S., Nara, Japan.
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.