Moritz Groth


About me

I am a former Ph.D. student of Stefan Schwede and now a postdoc of Ieke Moerdijk in Nijmegen (Netherlands). The new webpage is here.

My interests include abstract homotopy theory and stable homotopy theory. In particular, I am interested in the theory of and the relation between different models from higher category theory as there are -among others- Model Categories, Infinity Categories, and Derivators.

Preprints

A short course on infinity-categories (July 2010)

These notes are meant to give a concise introduction to the theory of infinity categories (aka. quasicategories) as developed in particular by Jacob Lurie and Andre Joyal. Some central ideas one finds in Lurie's Higher Topos Theory and Derived Algebraic Geometry I-III are covered.

Derivators, pointed derivators, and stable derivators (February 2012)

In this preprint, we develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the functors belonging to the stable derivator can be turned into exact functors with respect to these triangulated structures. Along the way, we give a simplification of the axioms of a pointed derivator and a reformulation of the base change axiom in terms of Grothendieck (op)fibration. Furthermore, we have a new proof that a combinatorial model category has an underlying derivator.

Monoidal and enriched derivators (July 2011)

In this preprint, we develop the theory of monoidal derivators and the related notions of derivators being tensored, cotensored, or enriched over a monoidal derivator. The passage from model categories to derivators respects these notions and hence gives rise to natural examples. We also introduce the notion of the center of additive derivators which allows for a convenient formalization of linear structures on additive derivators and graded variants thereof in the stable situation. As an illustration, we discuss some derivators related to chain complexes and symmetric spectra.

Talks

January 2012, UQAM, Montreal, Canada:
Two talks on Derivators, pointed derivators, and stable derivators

October-December 2011, Radboud University, Nijmegen, Netherlands:
Six talks on Derivators, pointed derivators, and stable derivators

November 2011, Universität Bielefeld, Deutschland:
Talk on Derivators, pointed derivators, and stable derivators

August 2011, Universität Hamburg, Deutschland, Conference on Structured Ring Spectra:
10-minutes bell-show talk on Derivators, pointed derivators, and stable derivators and Monoidal and enriched derivators, the slides are here

July 2011, Universität Osnabrück, Deutschland:
Three talks on A short course on infinity-categories

June 2011, Universität Regensburg, Deutschland:
Four 2-hour talks on A short course on infinity-categories

September 2010, Harvard University, Massachusetts:
Two talks on Derivators, pointed derivators, and stable derivators

September 2010, University of Notre Dame, Indiana:
Four talks on A short course on infinity-categories

January 2010, University of Warsaw, Poland:
Three talks on A short course on infinity-categories

Teaching

WS2010/11 Seminar on model categories (joint with Prof. Dr. Schwede)
SS2010 Seminar on p-adic analysis (joint with Dr. Welter)

Contact

Mathematisches Institut
Rheinische Friedrich-Wilhelms-Universität Bonn
Endenicher Allee 60
D-53115 Bonn
Germany

Office: Room 4.017
Phone: +49-228-73-3310
Email: mgroth at math.uni-bonn.de