Related papers: Lectures on algebraic stacks
Hilbert series are a standard tool in algebraic geometry, and more recently are finding many uses in theoretical physics. This summary reviews work applying machine learning to databases of them; and was prepared for the proceedings of the…
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The goal of this note is to spell out the (apparently well-known and intuitively clear) notion of abelian category over an algebraic stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category…
Opening Lecture at the Hong Kong University of Science and Technology Jockey Club Institute for Advanced Study Program on High Energy Physics Conference, January 18--21, 2016.
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
This is a set of notes on automorphic forms and theta correspondence, based on my lectures at the 2022 Arizona Winter School.
This paper is based on author's lectures at Kyoto University in 2010 Summer, and in the 6th MSJ-SI `Development of Moduli Theory' at RIMS in June 2013. The purpose of lectures was to review several results on Hilbert schemes of points which…
This is an expanded version of the author's talk at the third annual meeting of International Consortium of Chinese Mathematicians held at USTC in December 2020. In this expository article, we give a survey on joint works with Hosono, Lian,…
These are lecture notes for a minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.
These lecture notes have been developed for the course Computational Social Choice of the Artificial Intelligence MSc programme at the University of Groningen. They cover mathematical and algorithmic aspects of voting theory.
In the last six years remarkable developments have taken place concerning the representation theory of N=2 superconformal algebras. Here we present the highlights of such developments.
In these notes, we describe several geometric interpretations of $H^2(X)$ when $X$ is a trisected 4-manifold. The main insight is that, by analogy with Hodge theory and sheaf cohomology in algebraic geometry, classes in $H^2(X)$ can be…
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…
This is the list of the full papers accepted for presentation at the 32nd International Conference on Logic Programming, New York City, USA, October 18-21, 2016. In addition to the main conference itself, ICLP hosted four pre-conference…
These notes are based on the lecture courses given at the Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul Sabatier (Toulouse, 08-12.01.1996).
These are notes of my lecture courses given in the summer of 2024 in the School on Number Theory and Physics at ICTP in Trieste and in the 27th Brazilian Algebra Meeting at IME-USP in S\~ao Paulo. We give an elementary account of $p$-adic…
Reproducing my talk at Algebra Symposium held at Hiroshima University, August 26--29, 2013, I review recent results on super algebraic groups, emphasizing results obtained by myself and my coauthors using Hopf algebraic techniques. The…
These are notes on Zhang's work and subsequent developments produced in preparation for 5 hours of talks for a general mathematical audience given in Cambridge, Edinburgh and Auckland over the last year. Being for colloquium-style talks,…