Sebastian Thyssen

I'm a postdoctoral fellow in mathematics at the Ruhr University Bochum (RUB), Germany. Before that I did my PhD with Gerd Laures also here in Bochum. I'm very broadly interested in algebraic topology and algebraic geometry.

I have been a fellow of the GRK 1150 "Homotopy and Cohomology" for most of my PhD time. I also had the pleasure to spend most of the year 2013 at the Massachusetts Institute of Technology (MIT) in Camebridge, U.S. I was able to enjoy the fabulous collaboration between Harvard and MIT, attend seminars at both institutions, was invited to the 2013 Talbot Workshop on Chromatic Homotopy Theory in South Lake Tahoe, CA, and gave several talks myself all over the U.S.

Area of research

I work in the interplay of algebraic topology and arithmetic algebraic geometry. I'm particularly interested in the theory of topological automorphic forms (TAF), which is a (p-complete) generalization of the theory of topological modular forms (TMF) in the sense of considering derived moduli stacks of certain highly structured abelian schemes of arbitrary dimension n. My work involves a new approach to expansions of automorphic forms and topological realizations of such. I also think about genera associated to TAF theories, possible orientations for TAF-spectra and most important about how to produce examples of TAF theories with associated (chromatic) height at least 3.

I very much like working in this area as it combines many different flavors of mathematics...arithmetic algebraic geometry, algebraic topology, number theory and complex geometry. Though I can't claim to be an expert in all (not even in one) of these subjects I continue learning more about each of them and how they interact.

If you're interested in similar things, want to discuss them or have related ideas, feel free to send me an email.

News

My new article is on the arXiv. Check it out. In the article Hanno von Bodecker and I construct an explicit example of a TAF theory. We do this for the odd unimodular hermitian lattice of signature (1,1) over the Gaussian integers.

Writing

Here you can find my newest article that is joint work with Hanno von Bodecker. In it we construct a TAF type theory of height two for the odd unimodular hermitian lattice over then Gaussian integers. Moreover we construct the associated BP-genus with values in the ring of automorphic forms.

Soon you will also find a preprint my newest project which is also joint with Hanno. We consider the unimodular hermitian lattices of signature (1,1) and (2,1) over the Eisenstein integers and construct the corresponding TAF theories of heights two and three. This will be the first ever geometric cohomology theory of height three and we are pretty excited about it. Other buzz words describing our project are: curves of genus two and three, Jacobians, ball quotients, period maps, theta functions.

You can also find a report on the project which emerged out of my thesis. Note that the project is still ongoing as the results are not yet the results expected. In particular, the use of divided power structures limits applications massively. Comments, suggestions or ideas of how to overcome these difficulties are more than welcome.

Preprints

TAF via curves. (available soon.)
On p-local topological automorphic forms for U(1,1; Z[i])
Towards an expansion principle for topological automorphic forms. (Ongoing project.)

Expository and Notes

A note on genera, this is an expository note on genera, which is still work in progress.
MIT E-theory Conjectures Seminar notes, together with Mark Behrens, Drew Heard, Mike Hopkins, Geoffroy Horel, Tyler Lawson, Jacob Lurie, Eric Peterson, Tomer Schlank, Nat Stapleton. Transcript of contributed talks to the 2013 spring seminar, August 14th, 2013. These notes were written primarily by Eric Peterson
A short note on Hopf algebroids: Ext and primitives in (tensor powers of) the augmentation ideal.

Speaking

Talks

Here is a rather incomplete list of the talks I have given over the last few years.

University of Copenhagen, "Towards a construction of genera for (p-local topological) automorphic forms, March 2016
University of Barcelona, "An expansion principle for topological automorphic forms", November 2015
RUB, "Expansion principles for topological automorphic forms I + II", November 2014
University of Wuppertal, "On a Taylor type expansion for (topological) automorphic forms", November 2014
University of Regensburg, "On a Taylor type expansion for (topological) automorphic forms", June 2014
RUB, "Introduction to stacks" April 2014
Massachusetts Institute of Technology, "Higher q-expansions and TAF-character maps" , May 2013
University of California Stanford, "Higher q-expansions and TAF-character maps" , May 2013
University of California Berkeley "Higher q-expansions and TAF-character maps" , May 2013
Talbot Workshop on Chromatic Homotopy Theory, "Topological Modular Forms" , April 2013
RUB, "Construction of TMF" , February 2013
RUB, "A sheaf of cohomology theories" , January 2013
RUB, "Sheaves and Stacks" , January 2013

Courses

My position is funded through the DFG SSP 1786 "Homotopy Theory and Algebraic Geometry", so I have no teaching obligations right now. There were also no such obligations while I was funded by the GRK 1150 "Homotopy and Cohomology". Here you can find some courses I managed to give exercise classes in between.

Analysis I, Fall 2014.
Number theory, Spring 2014.
Mathematics for engineers I, Fall 2010.

I further served in preliminary courses in mathematics

Vorkurs für Mathematiker, Fall 2012.
Vorkurs für Mathematiker, Fall 2008.

Miscellaneous

I have organized the 24th NRW Topology Meeting together with Björn Schuster. It took place November 13-14, 2015 at the Ruhr University Bochum. You can find more details under 24th NRW Topology Meeting

Contact

Sebastian Thyssen
Office: NA 1/68, Department of Mathematics, Ruhr University Bochum, 44801 Bochum
Phone: +49 (0) 234 32 23212
Email: firstname period lastname (at) rub.de