About me
I am a second year PhD student in algebraic topology at The Copenhagen Centre for Geometry and Topology with advisors Robert Burklund and Jesper Grodal. My main interests are in stable homotopy theory and higher algebra.
Preprints
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On the deformation theory of $\mathbb{E}_\infty$-coalgebras (submitted) arxiv link
We introduce a notion of formally étale coalgebras and show that they admit unique, functorial lifts along square zero extensions of $\mathbb{E}_{\infty}$-rings. Using this, we show that Weil-restriction of coalgebras defines a coalgebra version of the spherical Witt-vector construction. -
The algebraic K-theory of algebraic tori (joint with Bai, Carmeli and Juran; in preparation)
We construct a $KGL$-based Fourier transform for étale sheaves of connective spectra and use it to compute the algebraic $K$-theory spectrum of an algebraic torus $T$ as the $KGL$-group ring of the delooping of the character lattice $\Lambda^\ast(T)$.
Stuff I am thinking about
A non-exhaustive, infrequently updated list of things that are on my mind.
Power operations on arithmetic cohomology theories - Many invariants arising in algebraic geometry can be though of as taking values in a derived category with some additional bells and whistles. However, they also usuall have the structure of commutative algebras in those categories, what can we learn about a scheme from the $\mathbb{E}_{\infty}$-ring structure on its cohomology?
Higher chromatic prismatic cohomology - One can define a version of prismatic cohomology replacing $\delta$-rings with power operations over higher height Morava $E$-theory. The redshift philosphy suggests that this should not actually contain new information, but does it?
Has thou considered the coalgebra?
Other writing
Expository material and notes.
The rationalization of the $K(n)$-local sphere pdf
Notes for a talk I gave in the Topics in Topology seminar at KU.
Galois categories and the etale fundamental group pdf
My bachelor thesis, with some minor edits.
Topological Cyclic Homology pdf
Lecture notes on $THH$, $TC$ and friends for the popular TV-series.
CV and contact
My CV as of 12.06.24: Curriculum Vitae
Feel free to reach out to me under my email: florian.riedel@pm.me
My office is at:
Department of Mathematical Sciences
Universitetsparken 5,
2100 Copenhagen