Conference: Young Homotopy-theorist Meeting 2025

ABSTRACT:

The Young Homotopy-theorist Meeting will be held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh, Scotland, October 6 - 10, 2025. The workshop will bring together 35 early-career mathematicians to facilitate collaborative research and training. The workshop will provide an unparalleled opportunity for young researchers who use the tools of homotopy theory to develop long-lasting and meaningful international collaborations.

The award will allow US-based researchers to be involved in this unique opportunity. The organizers have secured funding for the conference through the ICMS covering most conference costs and this National Science Foundation grant will specifically fund travel to the conference for US-based mathematicians. Participation of US-based mathematicians will be beneficial to the progress of not only homotopy theory research in the US, but also to mathematical progress in many adjacent disciplines.

Homotopical techniques originated in algebraic topology and homological algebra, but in recent years more broad applications of homotopy theory abound. For example, homotopical tools and ideas play a major work in the influential work of Bhatt--Morrow--Scholze on integral p-adic Hodge theory; work of Scholze–Clausen on condensed mathematics; work of Hill--Hopkins--Ravenel on the Kervaire invariant one problem; and a resolution of a conjecture of Grothendieck by Carlson–Haine–Wolf.

These examples highlight the timeliness and importance of promoting research collaborations amongst young homotopy theorists. With this in mind, the conference will be organized to provide a research collaboration launching pad for participants. The conference will feature thirteen talks by participants, providing an opportunity for participants to share and discuss their work to their peers.

Amongst the speakers are the four invited early-career speakers: Robert Burklund (Copenhagen), Peter Haine (Berkeley), Alice Hedenlund (Uppsala), and Lucy Yang (Columbia).

The conference will also include two mini-courses by Clark Barwick and Piotr Pstrągowski. The mini-course topics will bring participants to the forefront of these active research areas, creating a pathway to engage new scholars. There will be two evening lightning sessions, where participants can give ten- to fifteen-minute talks showcasing their research, and there will be a poster session on Monday.

The conference schedule will also allow ample time for informal discussion. Information about the conference may be found at https://www.icms.org.uk/YoungHomotopyTheorists

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.