# Seminars in geometry/topology

The Topology Seminar Spring 2020 will be on Mondays 13:15 - 14:15 (or 14:00 - 15:00) in room 734, Sentralbygg 2.

## January 23, 10:15 - 11:15, room 734, Sentralbygg 2

Kathryn Hess (EPFL): Equivariant flavors of (topological) Hochschild homology

Abstract: Relative topological Hochschild homology of $C_n$-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this talk I will present tools for computing relative THH and explain how to apply them to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum. I will describe in particular an equivariant version of the Bökstedt spectral sequence, the formulation of which requires further development of the Hochschild of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson. (Joint work with Katharine Adamyk, Teena Gerhardt, Inbar Klang, and Hana Kong.)

## January 23, 14:15 - 15:15, room 734, Sentralbygg 2

Jose Perea (Michigan State University): Topological dimensionality reduction

Abstract: When dealing with complex high-dimensional data sets, several machine learning tasks rely on having appropriate low-dimensional representations. These reductions are often phrased in terms of preserving statistical or metric information and may fail to recover important topological features. We will describe in this talk several schemes to take advantage of the underlying topology of a data set, in order to produce informative low-dimensional coordinates.

## February 10, 13:15 - 14:15, room 734, Sentralbygg 2

Joachim Kock (Universitat Autònoma de Barcelona):

Abstract: