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

Convex polytopes are convex hulls of point sets in the $n$-dimensional space $\E^n$ that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in $\E^n$ called…

These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…

This paper proposes a novel and simple algorithm of facet enumeration for convex polytopes. The complexity of the algorithm is discussed. The algorithm is implemented in Matlab. Some simple polytopes with known H-representations and…

It is shown how the Beneath-and-Beyond algorithm can be used to yield another proof of the equivalence of V- and H-representations of convex polytopes. In this sense this paper serves as the sketch of an introduction to polytope theory with…

Summary of a talk given at the International Seminar "Analysis of spectral invariants and related operator theory", Tokyo University of Science, Unga Campus, 5-6 Oct. 2009

This paper presents a summary of the theoretical presentations to the international workshop "Diffraction 2006". The range of topics covered during the workshop was quite broad and this summary is therefore somewhat selective covering…

Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures,…

The work contained herein constitutes a report of the "Beyond the Standard Model'' working group for the Workshop "Physics at TeV Colliders", Les Houches, France, 2-20 May, 2005. We present reviews of current topics as well as original…

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…

I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…

The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

These conferences proceedings summarize the experimental findings obtained in small collision systems at the LHC, as presented in the special session on "QGP in small systems?" at the Quark Matter 2015 conference. (The arXiv version is…

The polytope containment problem is deciding whether a polytope is a contained within another polytope. This problem is rooted in computational convexity, and arises in applications such as verification and control of dynamical systems. The…

These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.

We present five open problems in the theory of vertex rings. They cover a variety of different areas of research where vertex rings have been, or are threatening to be, relevant. They have also been chosen because I personally find them…

In this paper, we improve Polyak's local convexity result for quadratic transformations. Extension and open problems are also presented.

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in (Kaibel and Pfetsch, 2008). These polytopes are the convex hulls of all 0/1-matrices with…

The 12th annual workshop, Descriptional Complexity of Formal Systems 2010, is taking place in Saskatoon, Canada, on August 8-10, 2010. It is jointly organized by the IFIP Working Group 1.2 on Descriptional Complexity and by the Department…