# Colloquium in commemoration of Felix Hausdorff

## The Hausdorff Center is holding a colloquium in commemoration of Felix Hausdorff. This year, we are celebrating his 150^{th} birthday.

## An Overview of Homotopy Type Theory

Date: June 15, 2018 - 16:45 (coffee and cake will be served at 16:15)

Location: Lipschitz lecture hall

Speaker: Steve Awodey, Introduction by Peter Koepke

Steve Awodey is a professor of Philosophy and Mathematics at Carnegie Mellon University and one of the inventors of homotopy type theory.

Abstract

Homotopy type theory is a new approach to the foundations of mathematics which draws simultaneously on ideas from constructive type theory and abstract homotopy theory. The resulting system has applications ranging from computer formalization and verification of mathematical proofs to the theory of infinity-toposes. The system includes a fascinating new axiom for the foundations of mathematics, proposed by Voevodsky, called the univalence axiom, which allows isomorphic structures to be systematically identified. This principle has been the subject of much recent research, both from a computational standpoint and from a homotopical one. This talk will give an overview of the basics of homotopy type theory, explain the univalence axiom, and mention some current research directions.

Felix Hausdorff

Hausdorff ranks among the preeminent German mathematicians of the early 20th century. He was born on 8 November 1868 in Breslau as the son of a Jewish merchant. He was appointed associate professor in Bonn in 1910 and assumed a full professorship in 1913 in Greifswald. He returned to Bonn in 1921 until his retirement in 1935. With his masterpiece "Grundzüge der Mengenlehre", Hausdorff established topology as an independent discipline in mathematics. During the national socialist regime, he suffered increasing harassment and humiliation until January 26, 1942, when he, his wife, and his sister-in-law chose suicide over imminent deportation to a concentration camp.