Welcome

I am Lukas, a mathematician, but also a travel and sports enthusiast, and a nature-lover.  In one sentence, I like to explore the world in as many facets as possible.

I am an algebraic geometer. In particular, I am interested in the geometry and topology of varieties with klt singularities. I also like to think about algebraic group actions and invariant theory.

I do lots of different sports, such as downhill mountainbiking, ski touring, mountain running, snowkiting, kitesurfing, spearfishing, apnoe diving. Previously, I also played waterpolo.

During my travels, I explored a few quite extraordinary places, such as the mountains and seas of Papua New Guinea, the far east of Turkey, Albania, remote Greek islands, and parts of the Ho Chi Minh trail.

If you want to find out more, just check out the rest of my page!

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Math
 

I am a Walter-Benjamin fellow in the Algebraic Geometry group of Stefan Kebekus  at the University of Freiburg and principal investigator in my research project 'Fundamental and Divisor Class Group: Finiteness and Interplay' funded by the DFG (German research foundation).

Before that, I was a postdoc in the Arithmetic Geometry group of Annette Huber-Klawitter also at the University of Freiburg.

Even before that, I obtained my PhD in Nov. 2019 with summa cum laude from the University of Tübingen. My advisor was Jürgen Hausen.

I am interested in varieties with klt singularities, in particular their geometry and topology. My main tools are Cox rings, group actions, and orbifolds. I aim to generalize existing notions and fields of application of Cox rings and investigate their interplay with fundamental groups.

You can find my CV here.

 


Upcoming
 

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August 22-26, 2022, I will be at the Simons conference Stability and Moduli at Stony Brook and give a talk.


Research
 


Preprints
 

12.

11.

Iteration of Cox rings of klt singularities

Joint with Joaquin Moraga, arXiv:2103.13524, submitted.


publications
 

10.

The Jordan property for local fundamental groups

Joint with Stefano Filipazzi, Joaquin Moraga, and Roberto Svaldi, Geometry and Topology 26 (2022), no. 1, 283-319.

9.

Gorensteinness and iteration of Cox rings for Fano type varieties

Mathematische Zeitschrift 301 (2022), 1047–1061.

8.

The local fundamental group of a Kawamata log terminal singularity is finite

Inventiones Mathematicae 226 (2021), no. 3, 845-896.

5.

Canonical threefold singularities with a torus action of complexity one and k-empty polytopes

Joint with D. Hättig, Rocky Mountain J. of Mathematics 50 (2020), no. 3, 881-939.

4.

Hilbert series of the Grassmannian and k-Narayana numbers

Communications in Mathematics 27 (2019), no. 1, 27-41.

3.

Covariants of SL4(C) and incidence geometry of P3(C)

Journal of Physics: Conference Series 1194, 012015 (2019).

Log terminal singularities, platonic tuples and iteration of Cox rings

Joint with Ivan Arzhantsev, Jürgen Hausen, and Milena Wrobel, European Journal of Mathematics 4 (2018), no.1, 242-312.


Other Writings
 

1.

Finiteness and klt singularities

Oberwolfach Report 24/2020, Komplexe Analysis - Algebraicity and Transcendence (2020), 18-23.


TRavel
 

 


Mountain
 

In the mountains, I do sports such as downhill mountainbiking, trail/mountain running, road cycling and hiking - in summer. In winter, I like to go ski mountaineering and snowkiting. 

I also enjoy searching for mushrooms, which happens mostly in the mountains!