Related papers: Problem list on Foliations and Diffeomorphism grou…

These are lecture notes prepared for a minicourse given at the Cimpa Research School "Algebraic and geometric aspects of representation theory", held in Curitiba, Brazil in March 2013. The purpose of the course is to provide an introduction…

This is an informal and approximate transcription of a talk presented at the DESY workshop, September 27--29, 1995. The basic message is that real and long overdue progress is taking place on the problem of regulating non--perturbatively…

We study Lie foliations on compact manifolds whose transverse group is \emph{metabelian} (a natural generalization of the affine group $\GA$ considered in earlier work). We establish a complete classification of $\GA$-Lie foliations in…

The Folium of Descartes in $\mathbb{K}\times\mathbb{K}$ carries group laws, defined entirely in terms of algebraic operations over the field $\mathbb{K}$. The problems discussed in this paper include: normalization of Descartes Folium,…

This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…

The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…

Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify harmonic $\mathfrak{A}$-covers of a tropical curve $\Gamma$ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined…

In January 2020, a workshop was held at EMBL-EBI (Hinxton, UK) to discuss data requirements for deposition and validation of cryoEM structures, with a focus on single-particle analysis. The meeting was attended by 45 experts in data…

This chapter summarizes several approaches combining theory, simulation and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane mediated…

This paper is a discussion of relations between some free-boundary problems and infinite dimensional Lie groups; particularly a version of Nahm's equations for the group of Hamiltonian diffeomorphisms in two dimensions.

Respecting deformational constraints and predeformations poses a substantial challenge in the description of nonlinear elasticity. We here outline how group theory can play a beneficial role to overcome this challenge. Specifically, group…

We introduce invariant rings for forms (homogeneous polynomials) and for d points on the projective space, from the point of view of representation theory. We discuss several examples, addressing some computational issues. We introduce the…

Cell formation problem is among the first obstacles the designer of cellular production systems must overcome. This paper presents a critical analysis of the various criteria and constraints considered in the literature. The objective is to…

This is an extensive survey of the techniques used to formulate generalizations of the Mittag-Leffler Theorem from complex analysis. With the techniques of the theory of differential forms, sheaves and cohomology, we are able to define the…

This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…

These notes are a summary of the problem session discussions at various CANT (Combinatorial and Additive Number Theory Conferences). Currently they include all years from 2009 through 2019 (inclusive); the goal is to supplement this file…

This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We…

The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses,…

These are introductory notes on word growth of groups, and include a gentle presentation of wreath products as well as recent results on construction of groups of with given growth function. They are are an expanded version of a mini-course…

The Hecke category is at the heart of several fundamental questions in modular representation theory. We emphasise the role of the "philosophy of deformations" both as a conceptual and computational tool, and suggest possible connections to…