School on Univalent Mathematics

organised under the auspices of Scuola Matematica Interuniversitaria (SMI)

July 17-23, 2022, Cortona, Italy




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.


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.



Guest Speakers


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 school/workshop takes place at the Palazzone di Cortona, Cortona, Italy.


Please join our Zulip server for discussion before, during, and after the school.


Lecture material

See the UniMath/Schools Github repository.

Before the event

Recommended reading

You can prepare for the school by studying some of the material listed below.

Installing UniMath

Please install UniMath on your laptop before coming to Cortona. To this end, read the installation instructions. In case of problems or questions, contact the UniMath mailing list. You can also attend the UniMath install party on Sunday afternoon for help with the installation - see Section "Schedule" for more information.


For further information and clarifications, please contact us at