Fifty years of Mathematics with Masaki Kashiwara

We give a description of the growth of research on Knot Theory in Japan. We place our report in a general historical context. In particular, we compare the development of research on mathematical topology in Japan with that in Poland and USA, observing several similarities. Toward the end of XIX century and at the beginning of XX century several young mathematicians, educated in Germany, France or England were returning to their native countries and building, almost from scra...

A brief account of K-theory written in honour of Friedrich Hirzebruch

Talk at the International Conference ``G\'eom\'etrie au vingti\`eme ci\`ecle: 1930--2000'', Paris, Institut Henri Poincar\'e, Sept. 2001. The title is a homage to Hans Rademacher and Otto Toeplitz whose book fascinated the author many years ago.

The Midwest Geometry Conference 2007 was devoted to the substantial mathematical legacy of Thomas P. Branson who passed away unexpectedly the previous year. This contribution to the Proceedings briefly introduces this legacy. We also take the opportunity of recording his bibliography. Thomas Branson was on the Editorial Board of SIGMA and we are pleased that SIGMA is able to publish the Proceedings.

This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey contains several open problems and conjectures.

This is a survey on Kawaguchi-Silverman conjecture.

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020).

The 2007 Midwest Geometry Conference included a panel discussion devoted to open problems and the general direction of future research in fields related to the main themes of the conference. This paper summarizes the comments made during the panel discussion.

Mathematical aspects of contemporary classical and quantum gauge theory are sketched.

The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.