Operadic Methods in Geometry II

This meeting will take place in Paris (both at Université Sorbonne Paris Nord and at the École Normale Supérieure de Paris) from October 8th (3pm) to October 10th (1pm)
The goal of this meeting is to discuss some recent developments in the use of operadic methods in various flavours of geometry (complex, symplectic, algebraic, derived algebraic,...). The 1st edition of OMG took place in Barcelona in 2023.

Organizers

Registration is free but mandatory. Please use this form to register (before 1st October 2024).

Speakers

Schedule

8 October 15:00-16:00 TALK 1
16:00-16:30 Coffee break
16:30-17:30 TALK 2
9 October 10:00-11:00 TALK 3
11:00-11:30 Coffee break
11:30-12:30 TALK 4
Lunch
14:30-15:30 TALK 5
11:00-11:30 Coffee break
16:00-17:00 TALK 6
10 October 10:00 - 11:00 TALK 7
11:00 - 11:30 Coffee break
11:30 - 12:30 TALK 8

The location of the talks will be made precise soon.
Titles and abstracts: TBA.

Abstracts

  • Connor Malin: A simple construction of the self duality of E_n
    The interaction of the little disks operad E_n and Koszul duality has been, and continues to be, studied throughout the past 30 years. In particular, what is the relation between $E_n$ and its Koszul dual? We survey the history of this problem, and then describe our recent construction of an explicit, simple, and geometrically defined map which witness the equivalence of the $E_n$ operad and its Koszul dual, in the category of spectra.
  • Samuel Muñoz: On the homotopy type of spaces of long knots
    For given p less than d, the space of "long knots" is the embedding space rel boundary of the p-disc into the d-disc. By work of Boavida de Brito—Weiss et al., when d-p is at least 3, its homotopy type is closely related to that of the space of operad maps from E_p to E_d, where E_n denotes the little n-discs operad. In this talk, I will explain a computation of this homotopy type away from the prime 2 and in the so-called "concordance embedding stable range" which, by developments of Goodwillie—Krannich—Kupers, is at least 2d-p-5. The description features objects internal to surgery theory as well as relative algebraic K-theory/topological cyclic homology, appearing as part of an analogue for embeddings of a theorem of Weiss—Williams. I will also explain how this computation recovers rationally the 0- and 1-loop order parts of the hairy graph complex of Fresse—Turchin—Willwacher.
  • Adela Zhang: Operations on mod p TAQ cohomology and spectral partition Lie algebras.
    The bar spectral sequence for algebras over a spectral operad relates Koszul duality phenomena in several contexts. We apply this spectral sequence to the Koszul dual pair given by the (non-unital) E_∞ operad and the spectral Lie operad. When the input are trivial E_∞-HF_p algebras, we obtain the structure of operations on mod p TAQ cohomology and the homotopy groups of spectral partition Lie algebras, building on the work of Brantner–Mathew. In the colimit, the unary operations are Koszul dual to the Dyer–Lashof algebra in the sense of Priddy. There is also a shifted restricted Lie structure that can be detected by the homotopy fixed points spectral sequence, reflecting the Koszul duality between the commutative operad and the shifted Lie operad over F_p