## An introduction to topological ideas in computation

**Lecturer:**
Martín Escardó
(University of Birmingham, UK).

About the lecturer | Course Summary | Slides | Assignment

**About the lecturer:**
Martín Escardó's first degree was from UFRGS, Brazil, where he also got an MSc by research. During his studies, he worked in industry. He then joined Imperial College in 1993 for his PhD under the supervision of M.B. Smyth. After completing this, he was a postdoc at Imperial, a lecturer at the Universities of Edinburgh and St Andrews in Scotland. He then joined the University of Birmingham in England, and was appointed as a Reader in 2006. He has worked on exact real number computation, semantics, topology, higher-type computability, constructive mathematics, proof theory, intuitionistic type theory and their connections.

**Course summary:**
A branch of mathematics known as topology has had a long lasting influence in computation and constructive mathematics. In these lectures I will motivate and introduce topological ideas via computational notions. Then we will develop this further to get surprising computational applications, such as exhaustively searching some infinite spaces in finite time. More generally, topology explains how finite computers can deal with infinite objects.

**References:**

- A tutorial paper What Sequential Games, the Tychonoff Theorem and the Double-Negation Shift have in Common
- Blog posts:

**Slides:** You can find slides, Haskell programs and other materials related to the course here.

**Assignment:**

You can find the problem set here. Please send your solutions (or questions, should you have any) to Bartosz Klin by **Sunday, June 30**.