Related papers: Lectures on Noncommutative Resolutions
Multiplier ideals, and the vanishing theorems they satisfy, have found many applications in recent years. In the global setting they have been used to study pluricanonical and other linear series on a projective variety. More recently, they…
These are lecture notes for a minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
These notes accompany a series of three lectures on automorphic loops to be delivered by the author at Workshops Loops '15 (Ohrid, Macedonia, 2015). Automorphic loops are loops in which all inner mappings are automorphisms. The first paper…
This is mostly* a non-technical exposition of the joint work arXiv:1212.0373 with Caporaso and Payne. Topics include: Moduli of Riemann surfaces / algebraic curves; Deligne-Mumford compactification; Dual graphs and the combinatorics of the…
Application of the noncommutative geometry to several physical models is considered.
Poisson algebras have become an essential topic in mathematics with a rich structure and wide applicability. Despite numerous resources available on Poisson structures, the algebraic side of the story remains relatively less explored. This…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
The paper is withdrawn by the author. This was an embryon of the book which has now been published with World Scientific under the title "Lectures on Quantum Chromodynamics". See http://www.wspc.com.sg/books/physics/4443.html, where the…
This is an exposition of the results on Geometric crystals and the associated Kashiwara crystal bases (presented by the first author in RIMS, August 2004)
For a general class of contractions of a variety X to a base Y, I discuss recent joint work with M. Wemyss defining a noncommutative enhancement of the locus in Y over which the contraction is not an isomorphism, along with applications to…
Lecture notes of an algebraic geometry graduate course. The topics covered are as follows. Cohomology: ext sheaves and groups, cohomology with support, local cohomology, local duality. Duality: relative duality, Cohen-Macaulay schemes.…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
This chapter is based on a series of lectures that I gave at the National University of Singapore in April 2013. The notes survey the representation theory of the cyclotomic Hecke algebras of type A with an emphasis on understanding the KLR…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…