Related papers: Lectures on algebraic stacks
We study fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. Then use this additional structure to analyze geometric/ topological properties of stacks.…
These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and…
This survey article is a much extended version of a lecture given at a Clay Institute workshop in October 2006. It describes all known results on the existence of stable coherent systems on algebraic curves.
This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.
This is a collection of notes based on lectures given at IIT Madras in September 2019 and at IFT Madrid in November 2019. It is supposed to be a concise (and therefore not comprehensive) and pragmatic course on applied holography and…
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…
This volume contains the proceedings of the 19th International Conference on Quantum Physics and Logic (QPL 2022), which was held June 27-July 1, 2022 at Wolfson College, University of Oxford, UK. QPL is an annual conference that brings…
This is a sequel to the author's "Truth and Knowledge", College Publications, 2022, and contains some problems and results in connection with a possible representation for Yablo like structures.
This is a note on MacPherson's Chern class for algebraic stacks, based on a previous paper of the author [arXiv:math/0407348]. We also discuss other additive characteristic classes in the same manner.
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
This volume constitutes the informal proceedings of the 32nd International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2022), held on 21-23rd September 2022 as a hybrid (blended) meeting, both in-person (at the…
New cases of the multiplicity conjecture are considered.
These are lecture notes from a course given at the summer school "Heat kernels and spectral geometry: from manifolds to graphs" in Bregenz, Austria, 2022. They are designed to be accessible to doctoral level students, and include background…
This is a preliminary draft of Chapters 4-5 of our forthcoming textbook "Introduction to Cluster Algebras." Chapters 1-3 have been posted as arXiv:1608.05735. This installment contains: Chapter 4. New patterns from old Chapter 5. Finite…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
These notes on creative telescoping are based on a series of lectures at the Institut Henri Poincare in November and December 2023.
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
This is the writeup of lectures delivered in Asian Pacific introductory school on superstring and the related topics in Beijing (2006) and the expanded version of these lectures in the 3rd summer school on strings, fields and holography in…