Proof Society Summer School 2019 Swansea, September 8-11, 2019

Proof Society Summer School 2019

Swansea, September 8-11, 2019

The 2nd International Summer School on Proof Theory will be hosted by the Department of Computer Science at Swansea University under the auspices of The Proof Society and is sponsored by the London Mathematical Society, the College of Science at Swansea University, and the Institute of Coding in Wales.

The Summer School will be co-located with the 2nd Workshop on Proof Theory and its Applications which will take place on September 11-13. (These events will not overlap, the summer school will end at noon, while the workshop will start in the afternoon of the 11th).

The Proof Society supports the notion of proof in its broadest sense, through a series of suitable activities; to be therefore inclusive in reaching out to all scientific areas which consider proof as an object in their studies; to enable the community to shape its future by identifying, formulating and communicating it most important goals; to actively promote proof to increase its visibility and representation.

It is the aim of the summer school to cover basic and advanced topics in proof theory. The focus of the second edition will be on philosophy of proof theory, proof theory of impredicative theories, structural proof theory, proof mining, reverse mathematics, type theory and bounded arithmetic.

Other areas like proof complexity, program extraction from proofs, and philosophy of constructive mathematics will be covered at the workshop.

The intended audience for the Summer School is advanced master students, PhD students postdocs and experienced researchers new to the field in mathematics, computer science and philosophy.

The objective of the summer school is to enable young scientists in their future careers by

  • inviting renowned speakers from academia
  • providing a firm foundation in central basic and advanced areas of proof theory
  • allowing them to present their (first results) to fellow (PhD) students, postdocs and professors
  • offering them a forum to grow their own (international) network in an informal setting.

The 1st International Summer School on Proof Theory took place in Ghent in 2018.

Scientific Program

The Summer School will consist of 7 courses:

  • Universal Proof Theory by Rosalie Iemhoff (Utrecht University)
  • Ordinal Analysis and Proof Theory of Impredicative Theories by Wolfram Pohlers (University of Münster)
  • Structural Proof Theory by Paola Bruscoli (University of Bath)
  • Proof mining and functional interpretation by Paulo Oliva (Queen Mary University of London)
  • Reverse Mathematics by Takako Nemoto (Japan Advanced Institute of Science and Technology)
  • Proof Theory of Martin-Löf Type Theory by Anton Setzer (Swansea University)
  • Bounded Arithmetic by Arnold Beckmann (Swansea University)


Time Sun, 8/9 Mon, 9/9 Tue, 10/9 Wed, 11/9
09:00 – 10:00 Iemhoff Iemhoff Iemhoff Oliva
10:00 – 11:00 Pohlers Beckmann Pohlers Nemoto
11:00 – 11:15 Coffee Coffee Coffee Coffee
11:15 – 12:15 Beckmann Nemoto Bruscoli Pohlers
12:15 – 13:15 Oliva Oliva Nemoto Discussion/Poster
13:15 – 15:00 Lunch Lunch/Poster session Solution of Excercises Lunch
15:00 – 16:00 Bruscoli Bruscoli Excursion
16:00 – 16:30 Coffee Coffee
16:30 – 17:30 Setzer Setzer
From 17:30 Beach Party


Department of Computer Science
Computational Foundry
Bay Campus
Swansea University
Crymlyn Burrows
Swansea SA1 8EN

Practical Information and Registration

Registration fee: £60
Deadline for registration: July 8, 2019
To register fill in the
registration form and the organisers will get back to you with the confirmation.

Payment Information

Payments for registration and accommodation can be made via a bank transfer or a credit card. Once your payment is arranged, please contact to confirm your registration.

  • For bank transfers, the details are the following:
    Bank Name: LLoyds TSB
    Bank Address: PO Box 66, Swansea, GB
    Branch Sort Code: 30-95-46
    Branch Swift: LOYDGB21101
    IBAN Number: GB64LOYD30954602783215Bank Account Number: 02783215
    Bank Account Name: Swansea University
    VAT Number: 123 8534 77
    Reference: CSZ1000-107
  • If you prefer to pay by a credit card, please contact the central finance cash office +44 1792 604577, quoting the reference number CSZ1000-107.

Travelling to Swansea Bay Campus

Information on how to get to Swansea is available here. (

You can also fly to Bristol airport and take a National Express ( bus to Bay Campus with one change at the Bristol bus station. We do recommend booking bus and train tickets in advance as you will get a better price.

If you travel from Cardiff, you can also take X10 bus and ask the driver to stop by the Bay campus. There is no need to book this service in advance. The schedule for X10 bus is available here. (


A limited number of ensuite on-campus accommodation (GBP 50 per night) has been reserved for the Summer School and the Workshop. To book fill in the event registration form (above) and the organisers will get back to you. In order to secure accommodation we recommend to register as soon as possible.

Student Grants

A limited number of grants for UK PhD and Research Master students is available. The grants are sponsored by the London Mathematical Society and will be awarded on a first-come-first-serve basis. To apply, send an email to together with a recommendation letter from your supervisor (direct email from the supervisor suffices).

Students from outside the UK may be considered for a fee waiver. For more information, contact

Student members of the ASL may also apply for student travel awards (deadline 8 June 2019,


For any question regarding registration and accommodation please contact

If you have any other enquiries, you can contact the organizing committee at or or or

Local organizing committee

  • Arnold Beckmann, Swansea University
  • Ulrich Berger, Swansea University (Co-chair)
  • Olga Petrovska, Swansea University
  • Anton Setzer, Swansea University (Co-chair)
  • Monika Seisenberger, Swansea University

Programme committee

  • Bahareh Afshari, University of Gothenburg
  • Matthias Baaz, TU Wien
  • Arnold Beckmann, Swansea University (Chair)
  • Ulrich Berger, Swansea University
  • Lev Beklemishev, Steklov Mathematical Institute
  • Balthasar Grabmayr, Humboldt University of Berlin
  • Rosalie Iemhoff, Utrecht University
  • Joost Joosten, University of Barcelona
  • Antonina Kolokolova, Memorial University of Newfoundland
  • Norbert Preining, Accelia Inc.
  • Monika Seisenberger, Swansea University
  • Anton Setzer, Swansea University
  • Andreas Weiermann, Ghent University


The summer school and the workshop are sponsored by the London Mathematical Society, the College of Science at Swansea University, and the Institute of Coding in Wales.

Impressions from Swansea

The Computational Foundry at Swansea University