# Mid-Atlantic Topology Seminar 2019

#### Event date: Saturday, October 26, 2019

There will be a one day Mid-Atlantic Topology Seminar at University of Virginia on Saturday, October 26. Speakers will be:

• Maria Basterra (University of New Hampshire)
• Mona Merling (University of Pennsylvania)
• Dylan Wilson (University of Chicago)
• W. Stephen Wilson (Johns Hopkins University)

This seminar is a regional conference with a goal of bringing together the mid-Atlantic algebraic topology community. It will also serve as one of the inaugural activities for the NSF RTG grant that the Topology and Geometry group at UVA recently received.

All talks will be held in Clark Hall 107. Free parking is available in the C1 parking lot behind Clark Hall, next to Kerchof Hall.

##### Schedule

(coffee and pastries: 9-9:30)

9:30 – 10:30 W. Stephen Wilson (Johns Hopkins University)

Title: $v_n$ torsion free H-spaces

Abstract: For some years there have been $(k-1)$-connected irreducible H-spaces, $Y_k$, with no p-torsion in homology or homotopy. All p-torsion free H-spacesa are products of these spaces and they show up regularly in the literature. Boardman and I have generalized theses spaces and theorems using $(k-1)$ connected H-spaces, $Y_k$, that have no $v_n$ torsion in homology or homotopy (to be defined). These spaces seem ripe for exploitation in the environment of chromatic homotopy theory.

(break: 10:30-11)

11:00–12:00 Mona Merling (University of Pennsylvania)

Title: Spectral Mackey functors as multifunctors

Abstract: I will discuss a new perspective on spectral Mackey functors as multifunctors. The main application I will talk about is the construction of a map from the suspension G-spectrum of a smooth G-manifold M to the equivariant A-theory of M, whose fiber, on fixed points, exhibits a “tom Dieck style” splitting into stable h-cobordism spaces.
This is joint work with Cary Malkiewich.

(lunch: 12-2)

2:00-3:00 Dylan Wilson (Harvard)

Title: Real Hochschild homology and the norm of $F_2$.

Abstract: We study a spectral sequence computing the homotopy fixed points of the $C_2$ action on the smash square of $HF_2$. As an application, we give another proof of the $C_2$-Segal conjecture as well as a stronger, ‘quantitative’ variant. This is joint work with Jeremy Hahn.

(break: 3-3:30)

3:30—4:30 Maria Basterra (University of New Hampshire)

Title : Inverting operations in operads

Abstract : We describe a variant of the Dwyer-Kan hammock localization that allows us to construct a localization for operads with respect to submonoids of one-ary operations. The construction is functorial. It associates to an operad O and a submonoid of one-ary operations W, an operad LO and a canonical map O to LO which takes elements in W to homotopy invertible operations. Furthermore, we give a functor from the category of O-algebras to the category of LO-algebras satisfying an appropriate universal property. This is joint work with Irina Bobkova, Kate Ponto, Ulrike Tillmann and Sarah Yeakel.

Last updated: Sunday, September 29, 2019