Related papers: Algebraic Topology (Hanoi, August 2004): The probl…

We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.

This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems.

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…

We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods,…

Consider the restricted Hanoi graphs which correspond to the variants of the famous Tower of Hanoi problem with multiple pegs where moves of the discs are restricted throughout the arcs of a movement digraph whose vertices represent the…

These notes contain everything necessary to run a flipped course on "The Atmosphere" at an introductory undergraduate level. There are notes for the students to read before each course meeting and problems for them to work on in small…

Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.

The following is an extended version of a talk given at the Kinosaki Symposium on Algebraic Geometry in October 2011. The aim is to give an overview of product-quotient surfaces, the results that have been proven so far in collaboration…

Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…

The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…

We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…

A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

These notes deal with algebras equipped with an involution and related matters.

These remarks summarize some of the discussion at the NOW 2004; in addition some topics not touched on at the meeting are reviewed briefly.

A compendium of thirty previously published open problems in computational geometry is presented.

revision posted November 1996

This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…