Related papers: Lectures on Nakajima's Quiver Varieties

This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.

In (Ib\'a\~nez-Cobos et al., 2008), the authors describe the ordinary quiver of a given generalized path algebra, a concept introduced by Coelho and Liu in (Coelho, Liu, 2000). In this short note, we use this result to characterize which…

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories…

These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…

A brief review of the Wigner functions method in curved space-time. Contribution to the 3rd International Wigner Symposium, 5th-11th September 1993, Oxford, UK.

The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…

These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute. They contain an introduction to the subject and a…

This is an expanded version of the notes by the second author of the lectures on Hitchin systems and their quantization given by the first author at the Beijing Summer Workshop in Mathematics and Mathematical Physics ``Integrable Systems…

This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.

We relate the representations of the rational Cherednik algebras associated with the complex reflection group G(m,1,n) to sheaves on Nakajima quiver varieties associated with extended Dynkin gaphs via a Z-algebra construction. As the…

Lecture notes for a minicourse to given in the XVII Brazilian School of Geometry, UFAM (Amazonas), Brazil, July 2012.

This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by…

This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.

We try to clarify the relations between quiver varieties of type A and Kraft-Pocesi proof of normality of nilpotent conjugacy classes closures.

We show that the range of applicability of the change of representation formula derived in J. Math. Phys. \textbf{54}, 033513 (2013) [arXiv:1302.6928] is very narrow and extend it to include all physical applications, particularly,…

These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers, affine Springer fibers and Hitchin…

This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.

We survey several results known on sampling in computational geometry.

In this revised version, we add some expository material and references and make some minor corrections.