# Trimester Seminar

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

Organizers: Søren Galatius, Haynes Miller, Stefan Schwede, Peter Teichner

## Tuesday, May 12

14:00 - 16:00 Gong Show (Part 1)

17:00 - 18:00 Gong Show (Part 2)

Abstract: Young participants of the trimester program give a short presentation of their research topics. List of talks

## Tuesday, May 19

15:00 - 16:00 John Greenlees: Algebraic models of rational equivariant cohomology theories

17:00 - 18:00 Mike Hill: Equivariant Dyer-Lashof algebras

## Tuesday, June 2

17:00 - 18:00 Michael Weiss: Pontryagin classes and manifold calculus

## Tuesday, June 9

17:00 - 18:00 Dmitry Pavlov: Concordance theory for homotopy sheaves

## Thursday, June 11

14:00 - 15:00 Dustin Clausen: Variants of Thomason's Theorem

## Tuesday, June 23

15:00 - 16:00 David Gepner: Equivariant forms of elliptic cohomology

## Tuesday, July 7

15:00 - 16:00 Lennart Meier: Tmf_{0}(3) and Tmf_{1}(3)

## Tuesday, July 14

15:30 - 16:30 Chris Schommer-Pries: Extended 3-dimensional topological field theories

This talk takes place in the MPIM lecture hall (Vivatsgasse 7).

## Tuesday, July 21

15:00 - 16:00 Julia Bergner: Complete Segal objects and (∞,n)-categories

Abstract: In joint work with Rezk, we give a chain of Quillen equivalences of model categories between Θ_{n}-spaces and categories enriched in Θ_{n-1}-spaces. One of the intermediate models is given by complete Segal objects in Θ_{n-1}-spaces, and its properties are surprisingly subtle. We'll look at these objects, their model structure, and the comparisons to both Θ_{n}-spaces and Segal category objects in Θ_{n-1}-spaces.

## Tuesday, July 28

16:30 - 17:30 Andrew Blumberg: Categories of operadic modules over equivariant commutative rings

## Thursday, July 30

11:00 - 11:00 Constantin Teleman: Equivariant elliptic cohomology at the Tate curve and twisted K-theory

## Tuesday, August 4

15:00 - 16:00 Tibor Macko: The total surgery obstruction

## Tuesday, August 11

15:00 - 16:00 Mahmoud Zeinalian: Poisson geometry and Fricke-Klein coordinates on the moduli of local systems

Abstract: Length of the hyperbolic geodesic in a given free homotopy class of closed curves defines a function on the Teichmüller space. Poisson bracket of two such functions is intimately related to the hyperbolic geometry of the surface in several ways, for example through Wolpert’s cosine formula. This line of thinking has been extended to the study of the moduli of local systems in increasing levels of generality. I will describe some of these generalizations and make connections to string topology.

I will then describe some relations between the Chas-Sullivan (2-d)-shifted graded Lie algebra structure of the equivariant homology of the loop space and the (2-d)-shifted symplectic structure on the moduli of infinity local systems of perfect complexes on a d-dimensional closed and oriented manifold.

## Thursday, August 13

16:30 - 17:30 Gijs Heuts: Goodwillie approximations to higher categories

Abstract: Goodwillie calculus involves the approximation of functors between higher categories by so-called polynomial functors. We show how to a associate to a higher category a Goodwillie tower, consisting of categories which are polynomial in an appropriate sense. These approximations enjoy universal properties with respect to polynomial functors. Furthermore, such Goodwillie towers of higher categories may be classified in terms of the derivatives of the identity functor. This classification can be used to study various localizations of unstable homotopy theory, e.g. rational homotopy theory, but also "periodic" localizations.