Ludwig-Maximilians-Universität München	Mathematisches Institut
Impressum	Datenschutz
Constructive convex analysis	Josef Berger Gregor Svindland

first CORE meeting

7 May 2016 Department of Mathematics, Theresienstraße 39, second floor, room B251

Programme

11:00-11:30	Gregor Svindland	Constructive Operations Research
11:30-12:00	Josef Berger	First results and next steps
12:00-12:45	Douglas S. Bridges	Functional Representations of Partial Orders

13:45-14:30	Hajime Ishihara	The Hahn-Banach theorem and infima of convex functions
14:30-15:15	Horst Osswald	A roundtrip from probability measures to Levy processes and back
15:15-16:00	Sam Sanders	The local constructivity of Nonstandard Analysis

16:30-17:15	Peter M. Schuster	Total Preference Without Choice
17:15-18:00	Helmut Schwichtenberg	Invariance axioms for realizability

Hajime Ishihara, The Hahn-Banach theorem and infima of convex functions
We review results on the Hahn-Banach theorem and infima of convex functions in constructive mathematics.
Sam Sanders, The local constructivity of Nonstandard Analysis
The constructive nature of the praxis of Nonstandard Analysis (NSA) has been observed by many of its practitioners, and is best captured by Osswald’s claim that ‘NSA is locally constructive’. The local constructivity of NSA is the observation that the mathematics performed in the non- standard world of NSA is extremely effective, while jumping between the standard and nonstandard world is extremely non-constructive in general. Following Osswald’s observation, we show how to bring out the effective and constructive content of ‘pure’ NSA, that is theorems of NSA solely formulated with the nonstandard definitions (of continuity, convergence, etc). We will discuss how to obtain effective information from the Loeb measure, inspired by the Lebesgue measure in Reverse Mathematics.

jb 24 may 2016