School on Univalent Mathematics

organised under the auspices of Scuola Matematica Interuniversitaria (SMI)

July 17-23, 2022, Cortona, Italy

Updates

2022-03-30:

• The application form is now open. Application deadline: 15 April 2022
• Join the UniMath Zulip.

Overview

Homotopy Type Theory and Univalent Mathematics are emerging fields of mathematics that study a fruitful relationship between homotopy theory and (dependent) type theory. This relation plays a crucial role in Voevodsky's program of Univalent Foundations, a new approach to foundations of mathematics, based on ideas from homotopy theory, such as the Univalence Principle.

The UniMath library is a large repository of computer-checked mathematics, developed from the univalent viewpoint. It is freely available for everyone, as an open-source project, from the web. The School will give many young researchers an opportunity to familiarize themselves with the UniMath library and become contributors.

Format

Participants will receive an introduction to Univalent Foundations and to Mathematics in those foundations, by leading experts in the field. In the accompanying problem sessions, participants will formalize pieces of Univalent Mathematics in the UniMath library.

Speakers

Lecturers

• Benedikt Ahrens (Delft University of Technology, University of Birmingham)
• Gianluca Amato (Università di Chieti-Pescara)
• Peter LeFanu Lumsdaine (Stockholm University)
• Marco Maggesi (Università di Firenze)
• Ralph Matthes (CNRS, Université de Toulouse) --- remotely via Zulip
• Paige Randall North (University of Pennsylvania)
• Niels van der Weide (Radboud University)

Guest Speakers

• Kevin Buzzard (Imperial College London), Selling computers to mathematicians (slides)
• Thierry Coquand (University of Gothenburg), Sheaf Cohomology and Univalent Type Theory (slides, link to Agda code by Louise Leclerc)
• Daniel R. Grayson (University of Illinois), Voevodsky's contribution to the foundation of mathematics (slides)

Prerequisites

Participants should be interested in mathematics and the use of computers for mathematical reasoning. Participants do not need to have prior knowledge of logic, Coq, or Univalent Foundations.

Application and funding

There is a limited number of places available at the school. To participate, please fill in the application form. The deadline for application is Sunday, April 15, 2022. Applicants will be notified of acceptance to the School within one week after the deadline. The selected participants are requested to confirm their attendance and pay a participation fee of €80. Scuola Matematica Interuniversitaria (SMI) will provide to the participants

• the courses,
• accommodation during the school, and
• breakfast and lunches.

Location

Social

Schedule

• UniMath install party planned for the afternoon of Sunday 17 July 2022.
• School Monday 18 July - Friday 22 July 2022.

Lecture material

Before the event

• Check recommended reading
• Install UniMath on your laptop

Recommended reading

• Coq in a hurry (by Yves Bertot) An introduction to vanilla Coq. It does not cover the univalent point of view, but gives a gentle introduction to Coq, the underlying proof assistant of UniMath.
• Introduction to the Coq proof-assistant for practical software verification (by Christine Paulin-Mohring) Another introduction with Coq, including screenshots. It is a bit outdated, but might still be useful.
• HoTT book Comprehensive overview of univalent foundations.
• An introduction to univalent foundations for mathematicians (by Dan Grayson) An gentle introduction to univalent foundations.
• Introduction to Homotopy Type Theory (by Egbert Rijke) A comprehensive textbook.

Installing UniMath

Organisers

• Benedikt Ahrens
• Marco Maggesi

For further information and clarifications, please contact us at unimath-cortona2022@googlegroups.com.