I am teaching a course on Moduli Space of Curves in Spring 2020 and you will find the details here.
I took a (virtual) Quiz as a final exam for the course, you can find the details and quiz slides here.
Publications and Notes
- On Derived Equivalences of K3 Surfaces in Positive Characteristic, Documenta Matematica, 24, 1135-1177, 2019.
- PhD Thesis: On Derived Equivalences of K3 Surfaces in Positive Characteristic , Supervisor: Prof. Dr. Hélène Esnault, 2018.
- The First digit 1, Resonance, 2013 .
- Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences (Preprint pdf)
I show that for Abelian Varieties, every automorphism lifts as a morphism if and only if it lifts as a derived autoequivalence to a characteristic zero lift. But even for the case of elliptic curves, there are more ways to lift an automorphism as an autoequivalence than just as a morphism, although in this case the autoequivalence we get are just twist of the lift of automorphism with the lift of the structure sheaf of the graph of the automorphism.
- Fully Faithfulness Criterion for Functors of (Twisted) Derived Categories, joint with Katrina Honigs
We give another proof for the Caldararu’s criterion of checking when a twisted Fourier-Mukai functor gives an equivalence and we are working on extending a modified version of this criterion to positive characteristic and even more generally to the setting of smooth proper Deligne Mumford stacks in positive characteristic, the coarse moduli space of such stacks can have at worst quotient singularities, which being in positive characteristic need not be even Cohen Macaulay, unlike in the case of characteristic zero.
- Counting Twisted Derived Equivalent Ordinary K3 Surfaces, joint with Sofia Tirabassi and Piotr Achinger.
We show that every Brauer class over an ordinary K3 surface has a preferred lift to the canonical lift of the underlying K3 surface and then we are working on a theory of moduli space of twisted K3 surfaces in characteristic p to be able to count the number of twisted derived Fourier-Mukai partner of an ordinary K3 surface.
- Working Seminar on Derived Algebraic Geometry, Summer 2019.
- Abhyankar’s Conjecture, Freie Universität Berlin, Summer 2018.
- Formal Goemetry and Deformation Theory, FU Berlin, Winter 2017/18, (Organizer with Pedro A. Castillejo ).
- p-adic Simpson correspondence , FU Berlin, Winter 2017/18.
- p-adic Hodge Theory, FU Berlin, Summer 2017, (Organizer with Marcin Lara).
- Langlands correspondence for function fields, FU Berlin, Summer 2017.
- Berkovich spaces, singularity theory and birational geometry, FU Berlin, Winter 2016/17.
- Crystalline Cohomology, FU Berlin, winter 2016/17,(Organizer with Efstathia Katsigianni ).
- IRTG doctoral seminar, Rationality of varieties and decomposition of the diagonal, Winter 2016/17.
- Motivic Galois Groups and Periods, FU Berlin, Summer 2016.
- D-Modules, FU Berlin, Summer 2016.
- Berkovich Spaces, HU Berlin, Summer 2016.
- Supersingular K3 Surfaces, FU Berlin, Winter 2015.
- Intersection Theory, FU Berlin, Winter 2015.
- Literature seminar, HU Berlin, Winter 2015.
Past Conferences and Summer/Winter Schools (Participation/Talks)
- The Arithmetic of Derived Categories, Trento, Italy, July 4-6, 2018.
- Géométrie Algébrique en Liberté (GAEL), Strasbourg University, Strasbourg, 18-22 June 2018.
- A Tale of Algebra and Geometry, Pisa, Italy, June 4-7, 2018.
- Crystals and Geometry in characteristic p, Munich, Germany, 4-6 April, 2018.
- Enumerative Invariants from Differential Graded Lie Algebras and Categories, Montegufoni, Italy, March 25 – 31, 2018.
- Algebraic Geometry with fancy coefficients, Caen, France, 13-17 November, 2017.
- Current Trends in Algebraic and Arithmetic Geometry, Texel, The Netherlands, 27 August-1 September, 2017
- Stacks Project Workshop, University of Michigan, Ann Arbor, USA, 31 July-4 August, 2017.
- Higgs Bundles, K3 Surfaces and Moduli, Humboldt Universität zu Berlin, 10 – 12 July 2017.
- Integral p-adic Hodge Theory, Universität Bielefeld, 10-12 April 2017.
- p-adic Analytic Geometry and Differential Equations, CIRM Luminy, 27 – 31 March 2017.
- Higher Dimensional Algebraic Geometry and Characteristic p, CIRM Luminy, 12-16 September 2016.
- IRTG Student Conference, Leiden, September 3,2016.
- Current Trends in Algebraic and Arithmetic Geometry, Vlieland, August 29-September 2, 2016.
- Motives and Complex Multiplication, Ascona, 15-19 August 2016.
- Shimura Varieties, Leiden, June 20–22, 2016.
- Arakelov Theory and Automorphic Forms, Berlin, June 6–9, 2016.
- Day of Algebraic and Arithmetic Geometry, Berlin, May 20, 2016.
- Motivic Homotopy Theory, Berlin, March 7, 2016.
- Workshop: Generalizations of A¹-Homotopy Invariance in Algebraic Geometry and Homotopy Theory , Zinnowitz/Usedom, Germany, April 3-8, 2016
- Hausdorff School: Derived Categories: Dimensions, Stability Conditions, and Enhancements, MPI Bonn, 29 March – 2 April 2016
- HCM Workshop: Recent developments in integral p-adic cohomology theories , Bonn, Germany ,February 28-March 3 2016.
- BMS Student Conference, Berlin, February 17–19, 2016.
- Recent Advances in Algebraic and Arithmetic Geometry, Siena, August 24–28, 2015.