Related papers: A survey of Gersten's conjecture
This is a continuation of my work on Arithmetic Teichmuller Spaces developed in the present series of papers. In this paper, I show that the Theory of Arithmetic Teichmuller Spaces leads, using Shinichi Mochizuki's rubric, to a proof of the…
The Hanna Neumann conjecture gives a bound on the intersection of finitely generated subgroups of free groups. We explore a natural extension of this result, which turns out to be true only in the finite index case, and provide…
In this short note, we shall prove some observations regarding the connection between indestructible $\omega_1$-guessing models and the $\omega_1$-approximation property of forcing notions.
Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…
This is an expanded version of talks given by the author at the Trieste Spring School on Supergravity and Superstrings in April of 1997 and at the accompanying workshop. The manuscript is intended to be a mini-review of Matrix Theory. The…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews…
These notes overlap with lectures given at the TASI summer schools in 2014 and 2011, as well as at the European School of High Energy Physics in 2013. This is primarily an attempt at transcribing my hand-written notes, with emphasis on…
The CREST 2018 workshop is the third in a series of workshops addressing formal approaches to reasoning about causation in systems engineering. The topic of formally identifying the cause(s) of specific events - usually some form of…
These are the notes from Asger T\"ornquist's Appalachian Set Theory lectures at Carnegie Mellon University. They form a chapter in the LMS lecture notes series 406.
This paper comprises the written version of the lectures on string theory delivered at the 31st British Universities Summer School on Theoretical Elementary Particle Physics which was held in Manchester, England, August 28 - September 12…
We give an expanded treatment of our lecture series at the 2017 Groups St Andrews conference in Birmingham on local-global conjectures and the block theory of finite reductive groups.
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
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…
We prove the Gersten conjecture for $p$-adic \'etale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic \'etale Tate twists are not $\mathbb A^1$-invariant,…
In this lecture, I review some of the perspectives on the Higgs boson discussed at the Higgs Hunting 2012 Worshop and discuss the short- and long-term aspects of Higgs physics.
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…
We develop the idea for a new string field theory of ours that was proposed earlier in a very rudimentary form in a talk in the Symposium of Tohwa University [1]. The main point is to describe the system of strings in the Universe by means…
In this brief note we draw attention to examples of quantum field theories which may hold interesting lessons for attempts to devise a precise formulation of the Bekenstein bound. Our comments mirror the recent results of Bousso…