|A: Arithmetic and Groups|
A1: Arithmetic, geometry and representations
|scherotz at uni-muenster dot de|
|Telefon||+49 251 83-33722|
Frau Gabi Dierkes
Telefon +49 251 83-33730
Fax +49 251 83-32720
|Adresse||Prof. Dr. Sarah Scherotzke |
Fachbereich Mathematik und Informatik der Universität Münster
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Recently, I started to work in the field of derived algebraic geometry and will take part in the MSRI program in derived algebraic geometry.
I worked on the geometry of quiver varieties and their use in categorifying representations of quantum groups and cluster algebras.
I am also interested in triangulated categories, their t-structures and stability conditions.
My thesis was on Auslander-Reiten theory for algebras and derived categories, on support varieties for small quantum groups and classifications of Hopf algebras.
Publications and preprints
- The categorified Grothendieck-Riemann-Roch theorem This is joint with Marc Hoyois, Pavel Safronov and Nicolo Sibilla.
- Additive invariants of logarithmic schemes This is joint with Nicolo Sibilla and Mattia Talpo.
- On a logarithmic version of the derived McKay correspondence Compositio. This is joint with Nicolo Sibilla and Mattia Talpo.
- Higher traces, noncommutative motives, and the categorified Chern character Advances in Mathematics. This is joint with Marc Hoyois and Nicolo Sibilla.
- Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes Geometry and Topology. This is joint with David Carchedi, Nicolo Sibilla and Mattia Talpo.
- Quiver varieties and Hall algebras London Math. Soc. (2016) 112 (6), 1002-1018. This is joint with Nicolo Sibilla.
- Derived loop stacks and categorification of orbifold products To appear in Journal of non-commutative Geometry. This is joint with Nicolo Sibilla.
- Desingularisation of quiver Grassmannians via Nakajima categories Algebras and Representation theory.
- Generalized quiver varieties and triangulated categories to appear in Mathematische Zeitschriften.
- Component Cluster for acyclic quiver Colloquium Mathematicum 144 (2016), 245-264.
- The nonequivariant coherent-constructible correspondence and tilting Selecta Mathematica (NS) (2016), Vol.22, Issue 1,38--416. This is joint with Nicolo Sibilla.
- Desingularizations of quiver Grassmannians via graded quiver varieties Advances in Mathematics 256 (2014) 318-347. This is joint with Bernhard Keller.
- Graded quiver varieties and derived categories J. reine angew. Math.(Crelles Journal) 2016 (713). This is joint with Bernhard Keller.
- Linear recurrence relations for cluster variables of affine quivers Advances in Mathematics 228 (2011) 1842-1862. This is joint with Bernhard Keller.
- The integral Cluster Category Int Math Res Notices Vol. 2012, No.12, 2867-2887. This is joint with Bernhard Keller.
- Rank Varieties for Hopf Algebras Journal of Pure Applied Algebra 215 (2011), no.5, 829 to 838. This is joint with Matthew Towers .
- Finite and bounded Auslander-Reiten Components in the Derived Category Journal of Pure Applied Algebra 215 (2011), no.3, 232-241.
- Euclidean components for a class of self-injective algebras Colloquium Mathematicum 115 (2009), no. 2, 219 to 245.
- Classification of pointed rank one Hopf algebras Journal of Algebra 319 (2008) 2889 to 2912.
- Formulas for primitive Idempotents in Frobenius Algebras and an Application to Decomposition maps Representation Theory 12 (2008), 170 to 185. This is joint with Max Neunhöffer.
- Euclidean Auslander-Reiten components in the bounded derived Category