相关论文: Invitation to higher local fields (Introduction)

This talk presents the review of forgotten but attractive formalism proposed by Joos and Weinberg in the sixties for description of high-spin particles. Problems raised in the recent works [Ahluwalia {\it et al.}] are discussed. New results…

We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…

This is a written version of the opening talk at the 6th International Workshop on Chiral Dynamics, at the University of Bern, Switzerland, July 6, 2009, to be published in the proceedings of the Workshop. In it, I reminisce about the early…

In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on $M$. In particular, given the local data for a gerbe with structure 2-group given by a…

The notes were prepared for a series of talks that I gave in Hagen in late June and early July 2003, and, with some changes, in the University of La Lagu\~{n}a, the Canary Islands, in September, 2003. They aim (i) to revisit some oldish…

This is a letter (not intended for publication in a regular journal) written in response to two referees of my preprint "Local duality theorems for commutative algebraic groups". In it, I discuss possible applications of the new theory of…

We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…

This is an edited write-up of lecture notes of the 7-th Appalachian set theory workshop of the same title led by the first named author at the Cornell University on November 22, 2008. A draft version of the notes was prepared by the second…

The aim of this book is to introduce the reader to the beauty of Algebra, through a journey from the natural numbers to prime fields and finite fields, with some detours. Many books are devoted to the construction of these fields from the…

These notes give an introduction to the Gabriel-Roiter measure of a finite dimensional algebra. They are based on a series of four lectures at the "Advanced School and Conference on Representation Theory and Related Topics" in Trieste…

These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to…

In this note I provide an extended version of the talk given at BW2011 workshop. The concise introduction to the non-local SFT motivated models is given with an emphasis on the non-local generalization of gravity. A number of open questions…

This volume contains the papers presented at the 1st workshop on Quantitative Formal Methods: Theory and Applications, which was held in Eindhoven on 3 November 2009 as part of the International Symposium on Formal Methods 2009. This volume…

This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…

This is a sequel to the author's book "Derived Langlands" which introduced an embedding of the category of admissible representations of a locally p-adic group in to the derived category of the monomial category of the group. This article…

This thesis presents some mathematical results related to quantum field theory. The first chapter is dedicated to TRAPs and how they could be used to rigorously define Feynman rules. The second introduces generalisations of MZVs and study…

This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…

This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…