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

This expository article is based on a lecture from the Stanford Symposium on Algebraic Topology: Application and New Directions, held in honor of Gunnar Carlsson, Ralph Cohen, and Ib Madsen.

This is an expanded version of the notes of our lectures given at the conference "Current Developments in Mathematics 2003" held at Harvard University on November 21--22, 2003. We present an overview of the main definitions, results and…

The article contains a few questions and speculations related to the moduli spaces of curves, K3 surfaces, maps, and sheaves presented in the problem session of the AGNES conference in Amherst (April 2010).

These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.

We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric…

This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…

The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International…

The note complements topological aspects of the theory of chiral algebras.

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…

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to "String Topology" and…

Mini-proceedings of the ECT* Workshop, Hadronic Atoms and Kaonic Nuclei - Solved Puzzles, Open Problems and Future Challenges in Theory and Experiment, 12-16 October 2009

This paper has excessive overlap with the following papers also written by the authors or their collaborators: hep-th/0505013 and 0705.2930.

This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's…

This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.

We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…

A list of problems prepared for the proceedings of the Workshop on Exotic Homology Manifolds, Oberwolfach June 29-July 5 2003.

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…

This paper, in French, is a celebration of Max Dehn, and an essay of describing some of his results published in the beginning of the 1910's, and their offspring. It has been written up for a winter school in Les Diablerets, March 7-12,…