Ein Überblick über die Förderarbeit der Udo Keller Stiftung Forum Humanum anhand der Ereignisse eines Jahres.
Montag, 30. Mai 2022
International meeting from 30 May to 2 June 2022 at Cohaus Schlehdorf in Bavaria
Proofs in mathematical practice serve to warrant the truth of mathematical theorems. Proof theory arose with Hilbert's programme to put abstract mathematics on a firm basis by proving consistency in the meta-mathematics and by finite methods only. Gödel's incompleteness theorems have allegedly dashed Hilbert's programme as such but thus have stood at the beginning of a seminal paradigm shift in proof theory: to see mathematical proofs also as a rich source of computational information such as certified algorithms and effective bounds. Contemporary research in this fertile area is known under terms such as dynamical methods, program extraction and proof mining.
Incidentally, today's quest for safety and reliability of data and algorithms is very similar to the debate on foundations of mathematics about a century ago which culminated in Hilbert's and Gödel's advances---today, however, with grave consequences for technology and economy. The key to solving these problems of the digital society up to artificial intelligence is to be found in the logical grounding of mathematics and computer science themselves, the current development of which leads to new joint research methods and perspectives in mathematics and computer science.
In this vein, an international meeting will be held from 30 May to 2 June 2022 at Cohaus Schlehdorf in Bavaria. The aim of this meeting is to bring together eminent scholars and young researchers active in the foundations of mathematics and computer science. There will be ample opportunity to form ad-hoc groups working on specific projects, but also to discuss in more general terms the vision of extracting computational information from proofs. The participants' expertise will include ordinal analysis, predicative foundations, constructive mathematics, type theory, computation in higher types, proof mining and program extraction from proofs
Programme
Monday, 30 May
9:15 - 10:00
Welcome / Klaus Mainzer (TUM, EASA): Proof and Computation. Perspectives for Mathematics, Computer Science, and Philosophy
10:00 - 10:30
Arndt Bode (BAdW)
Benedikt Löwe (DVMLG)
Hajime Ishihara (JAIST)
Franz Merkl (LMU)
10:30 - 11:00
Coffee break
11:00 - 11:45
Stan Wainer (University of Leeds): Functions and Ordinals
11:45 - 12:30
Anton Freund (TU Darmstadt): On a uniform Kruskal-Friedman theorem
Lunch break
14:30 - 14:45
Martin Wirsing (LMU)
14:45 - 15:30
Gerhard Jäger (University of Bern): Gentzen in the 3- and 4-Valued Jungle
15:30 - 16:00
Coffee break
16:00 - 16:45
Dag Normann (University of Oslo): A recent development in the computability theory for functionals of type 3
16:45 - 17:30
Hideki Tsuiki (Kyoto University): Induction / coinduction and projections of fractals
19:00
Dinner at Hotel Klosterbräu
Tuesday, 31 May
9:00 - 9:45
Michael Rathjen (University of Leeds): Paralipomena zur Beweistheorie
9:45 - 10:30
Ulrich Kohlenbach (TU Darmstadt): The Computational Content of Proofs: Applications in Optimization and Ergodic Theory
10:30 - 11:00
Coffee break
11:00 - 11:45
Isabel Oitavem (NOVA University Lisbon): Relativized Classes in Implicit Complexity
11:45 - 12:30
Matthias Baaz (TU Wien): Cut-elimination for prenex cuts in intuitionistic logic without v is elementary
Lunch break
14:00 - 14:45
Laura Crosilla (University of Oslo): On Weyl's predicative concept of set
14:45 - 15:30
Fredrik Forsberg (University of Strathclyde): Constructive Ordinal Theory in Homotopy Type Theory
15:30 - 16:00
Coffee break
Social programme (optional)
16:30
Boat trip (alternatively hike) to Seehotel Grauer Bär
19:00
Dinner at Seehotel Grauer Bär
Wednesday, 1 June
9:00 - 9:45
Henk Barendregt (Radboud University): A lambda calculus satellite
9:45 - 10:30
Anton Setzer (Swansea University): Formalising Martin-Löf's Meaning Explanations for Type Theory in Agda
10:30 - 11:00
Coffee break
11:00 - 11:45
Hans Leiß (LMU Munich): Fixed-point closure of *-continuous Kleene algebras
11:45 - 12:30
Matthias Eberl (ind.): Don't forget the universal quantifier
Lunch break
Working groups
15:30 - 16:00
Coffee break
Working groups
Thursday, 2 June
9:00 - 9:45
Thorsten Altenkirch (University of Nottingham): Normalisation by Evaluation
9:45 - 10:30
Ingo Blechschmidt (University of Padua): Reifying dynamical algebra: maximal ideals for arbitrary rings, constructively
10:30 - 11:00
Coffee break
11:00 - 11:30
Holger Thies (Kyoto University): From Coq Proofs to Efficient Certified Exact Real Computation
11:30 - 12:00
Nils Köpp (LMU Munich): Tree representation of continuous functions on (pre-)Gray-code
12:00 - 12:30
Franziskus Wiesnet (TU Wien): Par means Parallel: Multiplicative Linear Logic as Concurrent Functional Programs
Lunch break
14:00 - 14:30
Olga Petrovska (Swansea University): Operational Semantics for Prawf
14:30 - 15:00
Reinhard Kahle (University of Tübingen): surprise
15:00: - 15:30
Helmut Schwichtenberg (LMU Muenchen): tba