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Pawel Sosna
Fachbereich Mathematik
Bereich AD
Bundesstraße 55
20146 Hamburg
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Raum 1511
Tel.: +49 40 42838-9353
Fax: +49 40 42838-5190
E-Mail:
pawel.sosna (at) math.uni-hamburg.de
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About me
I am a postdoc in the Research Training Group 1670 "Mathematics inspired by String Theory and Quantum Field Theory" of the German Research Foundation (DFG). My research interests are algebraic geometry and homological algebra. In particular, I think about derived categories of coherent sheaves on surfaces, stability conditions on triangulated categories, differential graded categories and autoequivalences of Calabi-Yau and hyperkähler manifolds.
Articles and preprints
- (with D. Ploog) On autoequivalences of some Calabi-Yau and hyperkähler varieties [arXiv:1212.4604].
- (with C. Böhning and H.-C. Graf v. Bothmer) On the Jordan-Hölder property for geometric derived categories [arXiv:1211.1229].
- (with C. Böhning, H.-C. Graf v. Bothmer and L. Katzarkov) Determinantal Barlow surfaces and phantom categories [arXiv:1210.0343].
- (with C. Böhning and H.-C. Graf v. Bothmer) On the derived category of the classical Godeaux surface [arXiv:1206.1830].
- Scalar extensions of triangulated categories, to appear in Appl. Categ. Structures [SpringerLink].
- Linearisations of triangulated categories with respect to finite group actions, Math. Res. Lett. 19 (2012), no. 5, 1007-1020 [InternationalPress].
- Fourier-Mukai partners of canonical covers of bielliptic and Enriques surfaces [arXiv:1101.1044], to appear in Rend. Semin. Mat. Univ. Padova.
- Stability conditions under change of base field, Math. Nachr. 285 (2012), no. 2-3, 364-376 [WileyOnlineLibrary].
- Derived equivalent conjugate K3 surfaces, Bull. Lond. Math. Soc. 42 (2010), no. 6, 1065-1072 [pdf], the slightly longer arxiv-version is here: [arXiv:0905.4333].
Other Publications
- Derived categories and scalar extensions, Bonner Mathematische Schriften 400 (my PhD thesis at the University of Bonn, 2010) [pdf].
- Tensor triangulated categories in algebraic geometry, diploma thesis, FU Berlin, 2007 [pdf]. Beware of typos.
Teaching
I am teaching a course on "Some topics in the representation theory of finite-dimensional algebras" this semester. Roughly speaking, the topic of the course are path algebras of quivers. These appear in subjects other than representation theory, for instance, in algebraic geometry (e.g. ''non-commutative resolutions of singularities'') or in physics (e.g. ''quiver quantum mechanics''). The goal is to give a gentle introduction to some basic concepts and to prove Gabriel's theorem which classifies the representation finite hereditary finite-dimensional algebras. Here are the lecture notes describing what was done so far: [pdf]. Comments are welcome at all times.
In the summer semester 2012 I taught a course on triangulated categories. Here are the lecture notes: [pdf]. Comments are welcome at all times.
Organisation
I am co-organising the "Moduli spaces in algebraic geometry and physics" summer school which will be held in Hamburg, August 12-16, 2013.
The North German Algebraic Geometry Seminar is a joint seminar of the Algebraic Geometry groups in Bremen, FU Berlin, HU Berlin, Hamburg, Hannover, Göttingen, Groningen and Oldenburg. I co-organised its last Hamburg meeting which took place May 03-04, 2012. The homepage of the meeting is here.
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