Related papers: Lectures on infinity categories
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
Four lectures on invertible field theories at the Park City Mathematics Institute 2019. Cobordism categories are introduced both as plain categories and topologically enriched. We then discuss localization of categories and its relationship…
We give a review of some recent developments in the theory of tensor categories. The topics include realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory,…
We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very…
These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate…
This is a written version of lectures that I would have given myself about aspects of the differential operator that is obtained from the linearized Kapustin-Witten equations on the product of the half-line with a compact, oriented,…
These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…
Lecture notes for an introductory course in elementary particles.
This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference 'Groups and Geometries', held at the Indian Statistical Institute in Bangalore in December 2012. The aim of this paper is to…
This is an extended version of my 2018 Heinemann prize lecture describing the work for which I got the prize. The citation is very broad so this describes virtually all my work prior to 1995 and some afterwards. It discusses work in…
We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.
These are the (somewhat extended) lecture notes for four lectures delivered at the spring school during the thematic programme "Mathematical Perspectives of Gravitation beyond the Vacuum Regime" at ESI Vienna in February 2022.
In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.