Related papers: Birational geometry for number theorists
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
These notes are a record of lectures given in the Workshop on Connections Between Algebra and Geometry at the University of Regina, May 29--June 1, 2012. The lectures were meant as an introduction to current research problems related to fat…
We survey our recent papers (some being joint ones) about the relation between the geometry of a compact K\"ahler manifold and the existence of automorphisms of positive entropy on it. We also use the language of log minimal model program…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
This article discusses the design of the Apprenticeship Program at the Fields Institute, held 21 August - 3 September 2016. Six themes from combinatorial algebraic geometry were selected for the two weeks: curves, surfaces, Grassmannians,…
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
In this paper the observational consequence of the cosmological models and the expression for the neoclassical tests, luminosity distance, angular diameter distance and look back time are analyzed in the framework of Lyra geometry. It is…
Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus…
Based on lectures delivered at (1) the AMS meeting at USC, Nov. 1992 (2) Conference on Quantum Aspects of Black Holes, ITP, UC- Santa %Barbara, %%June 1993. (3) 25th Summer Institute, Ecole Normale Superieure, % Paris, Aug. 1992. To appear…
In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed…
These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments discussed include new geometric features of…
This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…
We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual…
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
ICM lecture on minimal models and moduli of varieties.
This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular…
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…