### About me

I am a graduate student in Mathematics at Northwestern University, supervised by Paul Goerss.

### Research interests

I am interested in homotopy theory understood in the broad sense. Most recently I was thinking about the relation between spectra and comodules.

### Preprints

Synthetic spectra and the cellular motivic category (arXiv:1803.01804) - To any Adams-type homology theory one can associate a notion of a synthetic spectrum, this is a spherical sheaf on the site of finite E-projective spectra. I show that ∞-category of synthetic spectra based on E is in a precise sense a deformation of Hovey's stable homotopy theory of comodules whose generic fibre is given by the ∞-category of spectra. In the case of MU, I show that the even variant of this construction coincides with the cellular motivic category after p-completion.

Moduli of Π-algebras (arXiv:1705.05761) - I describe a homotopy-theoretic approach to the moduli of Π-algebras of Blanc-Dwyer-Goerss using the ∞-category of product-preserving presheaves on finite wedges of positive-dimensional spheres, reproving their results in this setting.

On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis (arXiv:1411.6691) - I prove coherence theorems related to dualizability in symmetric monoidal bicategories, classify two-dimensional framed topological field theories and give a new proof of the Cobordism Hypothesis in dimension two. This paper was written as my Master's thesis at Bonn University and was supervised by Christopher Schommer-Pries.

### Non-mathematical interests

I love spending time with my dogs, though unfortunately, they live in Poland. Here's a picture of one of them, Ida.

日本語を勉強して、少し話せる。

© 2017 Piotr Pstrągowski