Related papers: Problems on Polytopes, Their Groups, and Realizati…
This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of Chevalley groups; constructing p-groups…
In this paper we discuss a couple of observations related to polynomial convexity. More precisely, (i) We observe that the union of finitely many disjoint closed balls with centres in $\cup_{\theta\in[0,\pi/2]}e^{i\theta}V$ is polynomially…
This report is a combined version of two talks presented by the authors at the Edinburgh $b$-physics Workshop, December 1991. It presents the ideas of heavy quark symmetry and gives an introduction to some applications. The references…
Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.
We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on $n$ vertices.
We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…
This paper is a write-up of the ideas that were presented, developed and discussed at the fourth International Workshop on QCD Challenges from pp to AA, which took place in February 2023 in Padua, Italy. The goal of the workshop was to…
Notes for the upcoming Workshop on Symplectic Field Theory IX, Polyfolds for SFT. These notes are essentially the first few chapters of a forthcoming book entitled "Polyfold Constructions: Tools, Techniques, and Functors"
The conference Unexpected Phenomena in Energy Minimization and Polarization, held in Sofia, Bulgaria in 2024, provided a platform for researchers to discuss and propose challenging open questions across various fields, such as potential…
To appear in proceedings of Solitons, A CRM-Fields-CAP Summer Workshop in Theoretical Physics, July 20-26, Kingston, Ontario, Canada 1997. (Talk delivered by M. Rocek.)
Each point of a simplex is expressed as a unique convex combination of the vertices. The coefficients in the combination are the barycentric coordinates of the point. For each point in a general convex polytope, there may be multiple…
This text is the extended version of a talk given at the conference Geometry, Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the Observatoire de Paris. We explore the notion of solder (or soldering form) in differential…
This paper is extended and broadly generalized version of earlier published rapid communication, Phys.Rev.E, Vol.58, R 5213 (1998). It also elaborates on some problems which were left unsolved or just mentioned in Physics Reports Vol.298,…
This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…
These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…
Based on comments made at the 23rd Solvay Conference, December 2005, Brussels.
Quantum groups have been studied within several areas of mathematics and mathematical physics. This has led to different approaches, each of them with their own techniques and conventions. Starting with Hopf algebras, where there is a…
We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…
A short informal survey on the topics listed in the title. For the proceedings of the International Conference on Rings and Algebras X.
We study the maximum weight convex polytope problem, in which the goal is to find a convex polytope maximizing the total weight of enclosed points. Prior to this work, the only known result for this problem was an $O(n^3)$ algorithm for the…