相关论文: Problems on Polytopes, Their Groups, and Realizati…

This talk is a write-up on some origins of abstract convexity and afew vexing limitations on the range of abstraction in convexity.

We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.

We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…

This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…

Abstract polytopes are a combinatorial generalization of convex and skeletal polytopes. Counting how many flag orbits a polytope has under its automorphism group is a way of measuring how symmetric it is. Polytopes with one flag orbit are…

In this survey article, we summarize some recent progress and problems on the symplectomorphism groups, with an emphasis on the connection to the space of ball-packings.

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…

On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven…

This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceedings of the Colloquium).

The polymake software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features displayed are enabled by recent changes…

We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…

Some recent progress and a personal selection of open problems in heavy quarkonium physics (spectroscopy, decay and production) inspired by the activity of the Quarkonium Working Group are reviewed.

We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

This is the second of two papers where we study polytopes arising from affine Coxeter arrangements. Our results include a formula for their volumes, and also compatible definitions of hypersimplices, descent numbers and major index for all…

The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…

This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web…