Related papers: $\mathcal{S}$-categories, $\mathcal{S}$-groupoids,…
The series of three lectures given at Tel-Aviv University in 1992: 1. Tensor categories. 2. Quantum groups. 3. Topological (quantum) field theories. Published as the preprint IAS 897-92 of Tel-Aviv University and The Mortimer and Raymond…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
Algebra objects in $\infty$-categories of spans admit a description in terms of $2$-Segal objects. We introduce a notion of span between $2$-Segal objects and extend this correspondence to an equivalence of $\infty$-categories.…
These lecture notes form an expanded account of a course given at the Summer School on Topology and Field Theories held at the Center for Mathematics at the University of Notre Dame, Indiana during the Summer of 2012. A similar lecture…
These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to "String Topology" and…
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…
These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.
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 notes for three lectures on higher properads given at a program at the mathematical institute MATRIX in Australia in June 2016. The first lecture covers the case of operads, and provides a brief introduction to the Moerdijk-Weiss…
These are lecture notes from Clay Summer School in Goettingen, in 2006; the lectures were an attempt at an elementary introduction to math.KT/0611623.
This survey stems from Amnon Neeman's lecture series at Ohakawa's memorial workshop. Starting with Ohakawa's theorem, this survey intends to supply enough motivation, background and technical details to read Neeman's recent papers on his…
Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if…
These are the lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute. I give an introduction to Higgs bundles and their application to the study of character varieties for surface group…
These are the extended notes of a talk I gave at the Geometric Topology Seminar of the Max Planck Institute for Mathematics in Bonn on January 30th, 2012. My goal was to familiarize the topologists with the basics of arithmetic hyperbolic…
This article presents a novel approach to construct a model category structure designed to model the homotopy theory of spaces equipped with an action by the group $C_2$, where morphisms are considered to be isovariant. Our methodology…
Four pedagogical Lectures at the NATO-ASI on "Quantum Geometry" in Akureyri, Iceland, August 1999. Contents: 1. O(N) Vector Models, 2. Large-N QCD, 3. QCD in Loop Space, 4. Large-N Reduction
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…
I review recent developments of "non-semisimple" modular tensor categories in the sense of Lyubashenko and the categorical Verlinde formula for such categories (this is a proceedings article for Meeting for Study of Number theory, Hopf…