Andreas Krug

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Andreas Krug

FB 12 / Mathematik und Informatik
Philipps-Universität Marburg
Hans-Meerwein-Str. 6/ Campus Lahnberge
35032 Marburg
Germany

Phone	0049-6421-28-26557
Email	andkrug ( add @outlook.de)
Room	06D04

Since October 2015, I am working as an assistant of Sönke Rollenske at the University of Marburg.
Before, I was a visiting fellow at the University of Warwick. There, I was founded by the DFG (German Research Foundation) and my host was Miles Reid.
Prior to that, I was a postdoc in Bonn in the group of Daniel Huybrechts and a PhD student of Marc Nieper-Wißkirchen at the University of Augsburg.

Research interests

Derived categories of coherent sheaves
Hilbert schemes of points on surfaces
Calabi-Yau varieties

Publications

Logarithmic Higgs Bundles on punctual Hilbert schemes.
With Indranil Biswas. Preprint arXiv:1903.01641, 17 pages.
Stability of Tautological Bundles on Symmetric Products of Curves.
Preprint arXiv:1809.06450, 11 pages.
Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points.
Preprint arXiv:1808.05931, 17 pages.
Universal functors on symmetric quotient stacks of Abelian varieties.
With Ciaran Meachan. Preprint arXiv:1710.08618, 34 pages.
Formality of P-objects.
With Andreas Hochenegger. Compos. Math. 155 (2019), no. 5, 973–994.
Derived categories of resolutions of cyclic quotient singularities.
With David Ploog and Pawel Sosna. Q. J. Math. 69 (2018), no. 2, 509–548.
Remarks on the derived McKay correspondence for Hilbert schemes of points and tautological bundles.
Math. Ann. 371 (2018), no. 1–2, 461–486.
Varieties with P-units.
Trans. Amer. Math. Soc. 370 (2018), no. 11, 7959–7983.
Symmetric quotient stacks and Heisenberg actions.
Math. Z. 288 (2018), no. 1–2, 11–22.
Equivalences of equivariant derived categories.
With Pawel Sosna. J. Lond. Math. Soc. (2) (2015), no. 1, 19–40.
P-functor versions of the Nakajima operators.
Preprint arXiv:1405.1006, 41 pages. To appear in Alg. Geom.
On the derived category of the Hilbert scheme of points on an Enriques surface.
With Pawel Sosna. Selecta Math. (N.S.) 21 (2015), no. 4, 1339–1360.
Spherical functors on the Kummer surface.
With Ciaran Meachan. Nagoya Math. J. 219 (2015), 1–8.
On derived autoequivalences of Hilbert schemes and generalised Kummer varieties.
Int. Math. Res. Not. 20 (2015), 10680-10701.
Tensor products of tautological bundles under the Bridgeland-King-Reid-Haiman equivalence.
Geom. Dedicata 172 (2014), 245-291.
Extension groups of tautological sheaves on Hilbert schemes.
J. Algebraic Geom. 23 (2014), no.3, 571-598.

Here is an electronic copy of my Habilitation thesis. The body of the thesis consists of nine of the above research papers. However, there is a long introduction (25 pages) which might be of some interest. It gives a summary of the papers of mine and makes an attempt to give an overview of related work of other authors on derived categories.

Here is a lecture script (in German language) for the Linear Algebra course for students of Computer Science and Physics which I gave in Marburg in the Winter term 2018/19.

Talks

Videos of a mini course (three lectures) on derived categories and the McKay correspondence
that I gave at the Winter School on Algebraic Surfaces at KIAS (Seoul) in January 2016.
(The above link directs to the KIAS Media Archive. There, the videos can be found in the category 'Center & Programs' not 'Mathematics'.)

Beamer slides of a short talk on Hilbert schemes, symmetric quotient stacks, and categorical Heisenberg actions
that I gave at the Workshop on Lie Theory in Rauischholzhausen in March 2016.

Beamer slides of my Habilitation talk (in German language) on the Weil Conjectures that I gave at the University of Marburg in November 2017.

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