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This is the list of open problems in topological algebra posed on the conference dedicated to the 20th anniversary of the Chair of Algebra and Topology of Lviv National University, that was held on 28 September 2001.

We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on "Arithmetic Topology". Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and…

This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional…

This article contains a collection of problems contributed during the course of the conference.

In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…

The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schr\"odinger Institute on July 17-21. These are the problems that were proposed during the Problem Session:…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Finite Fields by J.-P. Serre and organised at Centro de ciencias…

In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.

We present some new and recent algorithmic results concerning polynomial system solving over various rings. In particular, we present some of the best recent bounds on: (a) the complexity of calculating the complex dimension of an algebraic…

In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…

We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…

This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and conjectures and I hope they may…

This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…

This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative…

Open problems from the 15th Annual ACM Symposium on Computational Geometry.

These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled…

This report records a large number of open problems in Affine Algebraic Geometry that were proposed by participants in a Conference on Open Algebraic Varieties at the Centre de Recherches en Mathematiques in Montreal at December 1994.