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 .
Preprints ( In preparation)
- Autoequivalences of Abelian Varieties over C from Automorphisms over p.
I show that for the case of elliptic curves, even though the genus is not zero, still every automorphism lifts as a morphism if and only if it lifts as a derived autoequivalence to a characteristic zero lift, which is not the case for higher dimensional Abelian varieties, where there will exist non-liftable automorphisms that lift as a derived autoequivalence. 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 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. I am investigating the case of higher dimensional
Abelian varieties now with non-liftable automorphism, to understand what derived equivalences they induce.
- 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.