First Workshop on Proof Mining (WPM24)
TU Darmstadt, 4–6 September 2024
An international workshop on proof mining will be held in Darmstadt, Germany on 4–6 of September 2024.
The event is supported by the Department of Mathematics at TU Darmstadt, the DFG, the ASL and the DVMLG.
With this meeting, we want to initiate a series of workshops dedicated to providing opportunities for people from the diverse areas connected to proof mining to meet, present work in progress and have an interdisciplinary exchange of ideas and knowledge. As such, the topics of interest in particular include logical aspects of proof interpretations as well as applied aspects from in particular nonlinear analysis and optimization.
Proof theory started in the school of David Hilbert in Göttingen in the beginning of the 20th century with what is today known as Hilbert's program, a project in mathematical logic which aimed to show that the use of so-called ideal (i.e. non-constructive, set-theoretic or infinitary) principles in proofs of concrete so-called real statements could be (at least in principle) eliminated. In a modern view, this program is often subsumed under the goal of proving the consistency of powerful theories containing such ideal principles in certain finitistic theories. As is well-known, Gödel's second incompleteness theorem already rules out the provability of the consistency of many theories in themself.
While Hilbert's program in this specific sense is therefore impossible to achieve globally, Georg Kreisel's work starting in the 1950's under the name of "unwinding proofs" marks the beginning of a seminal paradigm shift in proof theory, namely to use proof-theoretic devices developed in the course of Hilbert's program to extract computational information from specific given mathematical proofs, showing that Hilbert's program is actually largely achievable as far as most proofs from the literature are concerned. This field gained maturity in the 1990's through the work of Ulrich Kohlenbach, since then known as Proof Mining, and by now comprises over 200 works with many case studies situated within numerical mathematics and many branches of modern analysis.
Current research in this fast-growing area is concerned both with the development of new logical tools designed for facilitating a firm theoretical basis of this enterprise as well as with advancing the range of case studies into new territories relevant also for the mathematicians working in these fields in question.
Scope
proof mining in all its facets, in particular comprising the following:
- proof interpretations and, in particular, functional interpretations
- applications to mainstream mathematics in various areas: fixed point theory, monotone operator theory, ergodic theory, number theory, probability theory, etc.
Participation
The meeting has now concluded. Participants include:
M. Bacak, University of Leipzig (DE)
R.I. Bot, University of Vienna (AT)
H. Cheval, University of Bucharest (RO)
B. Dinis, University of Evora (PT)
N. Dumitru, University of Bucharest (RO)
P. Engracia, ISCTE Lisbon (PT)
F. Ferreira, University of Lisbon (PT)
P. Firmino, University of Lisbon (PT)
A. Freund, University of Würzburg (DE)
J. Garcia-Falset, University of Valencia (ES)
S.-M. Grad, ENSTA Paris (FR)
U. Kohlenbach, TU Darmstadt (DE)
M. Neri, University of Bath (GB)
A. Nicolae, Babes-Bolyai University (RO)
P. Oliva, Queen Mary University of London (GB)
P. Pinto, TU Darmstadt (DE)
N. Pischke, TU Darmstadt (DE)
T. Powell, University of Bath (GB)
S. Saeidi, University of Kurdistan (IR)
S. Sanders, Ruhr University Bochum (DE)
L. Sauras-Altuzarra, CUNEF University (ES)
A. Sipos, University of Bucharest (RO)
A. Wan, University of Bath (GB)
J. Wei, University of Pennsylvania (US)
If you are interested in participating in the workshop, please contact Nicholas Pischke or Pedro Pinto for registration. The deadline for registration for the workshop is the 1st of August 2024. The meeting will take place in person. Please note that talks are by invitation only.
We are an ASL sponsored workshop which means that graduate students who are members of the ASL are eligible to apply for modest student travel awards to attend the meetings. Please read this webpage and/or contact Nicholas Pischke or Pedro Pinto for more information.
Programme
Below, you find the schedule for the workshop. You can find the book of abstracts here.
Venue
Universitäts- und Landesbibliothek Darmstadt
Vortragssaal (S1|20, R.01)
Magdalenenstr. 8
64289 Darmstadt
Reaching Darmstadt and the Venue:
Darmstadt is easily accessible by various modes of transportation. For those traveling by train, the city's main station, Darmstadt Hauptbahnhof, is a key hub. If you are arriving by air, the nearest airport is Frankfurt Airport, from which you can reach Darmstadt via regional trains or, more conveniently, the Airliner Bus service. This direct bus connects Frankfurt Airport Terminal 1 with Darmstadt in approximately 30 minutes. Tickets can be purchased onboard using card only; for more details, visit the dedicated website.
Once in Darmstadt, the city's efficient public transportation system, comprising buses and trams, ensures quick and reliable travel. Key stations near the Technical University of Darmstadt and the event venue include 'Schloss,' 'Luisenplatz,' 'Willy-Brandt-Platz,' and 'Alexanderstraße/TU.' For up-to-date schedules, check the local public transport website. Please note that due to ongoing construction in Darmstadt, it's advisable to recheck your itinerary shortly before your arrival.
Place for the dinner:
On Thursday, we plan to all go to dinner together. For that, we have reserved tables for 19:45 German time at Ristorante Sardegna which is located at Kahlertstraße 1, 64293 Darmstadt.
Organisers
Poster
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