photo of mhe

Martín Hötzel Escardó

Also known as Martin Escardo.

Reader in Theoretical Computer Science
School of Computer Science, University of Birmingham
Birmingham B15 2TT, UK

Publications, talks, cv, timetable, teaching
Research interests: Topology in higher-type computation, constructive mathematics, dependent type theory, univalent type theory, domain theory, locale theory, game theory.
The only difference between reality and fiction is that fiction needs to be credible.
Mark Twain.

In mathematics and the theory of computation, what is interesting is what is incredible but true, defying our intuitions, giving new light to our understanding. This is of course the case for all sciences, and even (more?) for engineering, with "true" replaced by "doable".

In the theory of higher-type computation, in the sense of Kleene and Kreisel, my favourite example is the characterization of the sets that can be exhaustively searched by an algorithm, in the sense of Turing, in finite time, as those which are topologically compact.

In particular, this understanding gives examples of infinite sets that can be completely inspected in finite time in an algorithmic way, which perhaps defies intuition.

I am also interested in constructive mathematics, which I see as a generalization, rather than as a restriction, of classical mathematics. In constructive mathematics, in the way I conceive it, computability is a side-effect, rather than its foundation.

What distinguishes classical and constructive mathematics is that the latter is better equipped to explicitly indicate the amount of information given by its definitions, theorems and proofs. This is particularly the case for Martin-Loef type theory, and even more for its univalent extensions.

The above is a (probably misleading) hint of what my research is about.

I joined Birmingham University in September 2000. My first degree was from the Universidade Federal do Rio Grande Sul, where I also obtained an MSc degree by research. During my undergraduate and MSc studies, I worked in industry. I then went to Imperial College of the University of London in October 1993 for my PhD under the supervision of Mike B. Smyth. After completing this in April 1997, I was a postdoc for one year at Imperial, a lecturer at the University of Edinburgh for two years, and then at the University of St Andrews for one year, after which I came here and have happily been part of a vibrant theory research group.
email: office: 212 phone: +44 121 414 2797 fax: +44 121 414 4281

directions: Look for building Y9 in the yellow zone of the Edgbaston campus map. This is about 1 minute walking time from the train station. Turn left when you exit the station, and walk for about 30 meters. Our building is the right-hand one of two red-brick twin buildings facing each other.

Last modified Fri Apr 15.