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We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic…

This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…

This volume contains the post-proceedings of the Fourteenth and the Fifteenth International Workshops on Graph Computation Models (GCM 2023 and 2024). The workshops took place in Leicester, UK on 18th July 2023 and Enschede, the Netherlands…

Computation models and specification methods seem to be worlds apart. The project on abstract state machines (in short ASMs, also known as evolving algebras) started as an attempt to bridge the gap by improving on Turing's thesis. We sought…

A carefully constructed explanation of my connection of the real normed division algebras to the particles, charges and fields of the Standard Model of quarks and leptons provided to an interested group of attendees of the 2nd Mile High…

These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…

Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

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…

This is the arXiv index for the electronic proceedings of GD 2023, which contains the peer-reviewed and revised accepted papers with an optional appendix. Proceedings (without appendices) are also to be published by Springer in the Lecture…

These are the notes for the lectures that I was giving during Fall 2020 at the Moscow Institute of Physics and Technology (MIPT) and at the Yandex School of Data Analysis (YSDA). The notes cover some aspects of initialization, loss…

We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states that the lattice of all boolean algebras of regular languages…

This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical legacy of Bill Thurston, held in June…

Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…

This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups…

These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…

This paper is based on the author's talk at the Grothendieck conference at Chapman university on 26-05-2022. It is not a survey of anabelian geometry but rather exposes some of the personal views and experiences of the author with the…

This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.

These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…