Fifty years of Mathematics with Masaki Kashiwara

This submission has been withdrawn by arXiv administration.

In this survey we recognize Enrique Arrondo's contributions over the whole of its career, recalling his professional history and collecting the results of his mathematical production.

This is an exposition of the results on Geometric crystals and the associated Kashiwara crystal bases (presented by the first author in RIMS, August 2004)

We give a brief survey on aspects of the local index theory as developed from the mathematical works of V. K. Patodi. It is dedicated to the 70th anniversary of Patodi.

This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].

This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent results illustrating the interplay between noncommutative geometry and arithmetic geometry/number theory.

This paper has been withdrawn by the author due a few mistakes in the paper.

Cem Tezer was a fastidious, meticulous, highly idiosyncratic and versatile scientist. Without him Turkish community of mathematics would be incomplete. Our sense of gratitude for his work in various areas of mathematics, history of sciences, literature, music and his encouragement to do mathematics for only its beauty was hardly unique and even unusual. After he passed away on 27 February 2020, while working actively at Middle East Technical University, the number of colleagu...

This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in algebraic geometry and representation theory relevant for GCT are presented.

This is a survey article about some of the work of Peter Scholze for the Jahresbericht der DMV. No originality is claimed. It is hoped that it can serve as a guideline to an exciting and increasingly large edifice of theory.