## Workshop on "Unstable Homotopy Theory", November 11 - 15, 2024

Unstable homotopy theory is about understanding the detailed structure and properties of topological spaces and morphisms between them. Central to this study is the concept of homotopy types (also known as ∞-groupoids, animas, or spaces), which classify topological spaces up to weak homotopy equivalence. This subject is rich in both computational and structural aspects: On the one hand, it has been a long-term project to compute algebraic invariant of homotopy types, such as homotopy groups and homology groups of a given topological space. On the other hand, it encompasses the ongoing search for algebraic structures within homotopy types.

Recently there have been many fruitful results in understanding homotopy types by using algebraic and higher categorical techniques. Examples include extension of Quillen’s Lie algebra model of rational homotopy types to higher v_n-periodic homotopy types, variants and generalizations of Mandell's results on models of finite type p-complete nilpotent CW-complexes, and significant progress in unstable motivic homotopy theory based on the theory of unstable localisation developed by Bousfield and Farjoun.

With these latest advances one can study homotopy types from an algebraic point of view by using tools from the theory of operadic calculus, Koszul duality, Goodwillie calculus, higher category theory and higher algebra. We hope to gather experts and early-career mathematicians working in unstable homotopy theory and adjacent fields at our workshop, to communicate these important results, to promote the exchange of ideas and to stimulate future research in this area.

**Speakers:**

Benjamin Antieau (Northwestern University / MPIM Bonn)

Gregory Arone (Stockholm University)

Tom Bachmann (Johannes-Gutenberg-Universität Mainz)

William Balderrama (University of Bonn)

Shaul Barkan (Hebrew University Jerusalem)

Mark Behrens (University of Notre Dame)

Thomas Blom (University of Copenhagen / MPIM Bonn)

Robert Burklund (University of Copenhagen)

Xiaowen Dong (Johannes-Gutenberg-Universität Mainz)

Gijs Heuts (Utrecht University)

Geoffroy Horel (Université Sorbonne Paris Nord)

Nikolai Konovalov (University of Chicago / MPIM Bonn)

Josefien Kuijper (Utrecht University)

Adela Zhang (University of Copenhagen)

**Organisers:**

Tobias Barthel (MPIM Bonn)

Yuqing Shi (MPIM Bonn)

**Registration****:**

The registration is closed as of October 1, 2024.

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