Related papers: Introduction to staggered sheaves
We present a general introduction to continued fractions, with special consideration to the function fields case. These notes were prepared for a summer class given this year in Beijing at Beihang university.
These lecture notes are based on a master course given at University Hassan II - Agdal in spring 2012.
These are notes for my Takagi lecture at the University of Tokyo in November, 2016. I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p>0 and Lusztig's character formula. I explain…
This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it…
These notes provide a brief introduction to modern cosmology, focusing primarily on theoretical issues. Some attention is paid to aspects of potential interest to students of string theory, on both sides of the two-way street of…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show…
This is a survey on stated skein algebras and their representations.
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
It has been well known for some time that for strictly stationary Markov chains that are ``reversible'', that special symmetry provides special extra features in the mathematical theory. This paper here is primarily a purely expository…
The note complements topological aspects of the theory of chiral algebras.
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
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 provide an introduction to the theory of Wishart distributions and Wishart processes, particularly what concerns their existence and their realizations as solutions of Wishart SDEs. The material is based on recent…
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…