My general research is in algebraic topology. I am particulary interested in stable homotopy theory, in which I study spectra with additional structures. Homotopy theorists have generalized the notion of rings with multiplication that are associative and/or commutative up to higher homotopies. These objects are called E_1 or E_∞ ring spectra. There is a natural dual notion of coalgebras, which are spectra or modules X, in which, instead of an associative unital multiplication X ⊗ X → X, we require a co-unital comultiplication X → X ⊗ X, which is coassociative up to higher homotopies. These are called E_1-coalgebras. If we require cocommutativity to be up to higher homotopies, we call them E_∞-coalgebras. There is also a notion of comodules over a coalgebra, dual to modules over an algebra. In my research, I use both model categories and quasicategories (i.e. ∞-categories) to describe the homotopy theory of coalgebras and comodules.
My Research
Publications & Preprints
7
Spanier-Whitehead duality for topological coHochschild homology, with Haldun Özgür Bayındır, (submitted).
6
5
4
Rigidification of Connective Comodules, (submitted).
3
Highly Structured Coalgebras and Comodules, PhD thesis (May 2020).
2
Koszul Duality in Higher Topoi, with Jonathan Beardsley, (submitted).
1
Coalgebras in symmetric monoidal categories of spectra, with Brooke Shipley, Homology, Homotopy and Applications 21 (2019), no.1, 1-18.
4
MIT
Cofiber Sequences of Thom Spectra over B(ℤ/2)^n, Master thesis advised by Haynes Miller (Fall 2014).
Previous Projects
EPFL
Group Cohomology, EPFL Master project supervised by Jacques Thévenaz (Spring 2014).
An Introduction to Stable Homotopy Theory, EPFL Master project supervised by Kathryn Hess (Fall 2013).
The Serre Spectral Sequence (using Dress' construction), EPFL Bachelor project supervised by Kathryn Hess (Spring 2013).
Fiber Bundles in Homotopy Theory (in French), EPFL Bachelor project supervised by Kathryn Hess (Fall 2012).