Related papers: Geometric Methods in Representation Theory
These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of poset topology. These notes include introductory material, as well as recent developments and open problems. Some…
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of…
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
Concluding talk, Physics at LHC 2004, Vienna
These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.
This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications.…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric modeling in…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
Summary talk at ICHEP 2002, Amsterdam, July 2002. I have kept very close to the content and style of the talk as it was delivered. You may access the associated PowerPoint presentation through a link at…
These notes give an introduction to the Gabriel-Roiter measure of a finite dimensional algebra. They are based on a series of four lectures at the "Advanced School and Conference on Representation Theory and Related Topics" in Trieste…
The connection between polynomial solutions of finite-difference equations and finite-dimensional representations of the $sl_2$-algebra is established (the talk given at the Wigner Symposium, Guadalajara, Mexico, August 1995, to be…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
At the end of the five years of work in our GeoDiverCity program, we brought together a diversity of authors from different disciplines. Each person was invited to present an important question about the theories and models of urbanization.…
We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses…
In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory. Lectures given at the Institute for…
This is an introductory survey of the theory of $p$-form conservation laws in field theory. It is based upon a series of lectures given at the Second Mexican School on Gravitation and Mathematical Physics held in Tlaxcala, Mexico from…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…