# Some favourite theorems of mine

**Date**: Wednesday 28 June 2017, 16:00 – 17:30**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Pure Mathematics seminars, Seminar series, Logic seminars**Cost**: Free

#### Douglas Bridges, University of Canterbury. Part of the logic seminar series.

Retirement presents an ideal opportunity for reflection on one's professional life. In this talk I shall discuss my work in a number of areas of Bishop-style constructive mathematics (BISH)---that is, mathematics with intuitionistic logic and an appropriate set- or type-theoretic foundation. Every proof in BISH is essentially an algorithm, and the proof itself can be read as proof that the algorithms contained in it meet their specifications. Moreover, several computer-science groups have extracted and implemented those algorithms for parts of analysis.

In this talk, I describe some of my own work that has caused me the most satisfaction, in areas including:

- complex analysis

- approximation theory

- measure and integration

- functional analysis

- topology via apartness

- mathematical (micro)economics---preference, utility, demand

- constructive Morse set theory (an ongoing project).

Note that the talk is not one in logic: it is about analysis using a<br/>different logic, and is presented by one who regards himself as an analyst.

**Douglas Bridges, ***University of Canterbury*