IST Postdoctoral Fellow
Hausel’s group
IST Austria.
I am soon moving to CMI, India and this webpage has been moved to www.mathface.com
Teaching
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.
Current Seminars
 WienBudapest AG, recurring.
 Algebraic GeometryNumber Theory Seminar @ IST Austria, recurring.
Publications and Notes
 On Derived Equivalences of K3 Surfaces in Positive Characteristic, Documenta Matematica, 24, 11351177, 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
 Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences (under minor revision for Archiv der Mathematik) (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.
In preparation

Pathologies of Hilbert scheme of points on supersingular Enriques surface in characteristic 2 (Email for draft)
I show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, $Hilb^n(X)$, for $n \geq 2$ are simply connected, symplectic varieties but are not irreducible symplectic as Hodge number $h^{2,0} > 1$, even though a supersingular Enriques surface is an irreducible symplectic variety. These are new classes of varieties which appear only in characteristic 2 and show that the hodge number formula for GottscheSoergel does not hold over characteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor CalabiYau, thereby showing that there are strictly more classes of simply connected varieties in positive characteristic than as given by BeauvilleBogolomov decomposition theorem over $\C$. Moreover, they give examples of varieties in each dimension 2n that admit liftings to characteristic zero to varieties which do not have trivial canonical bundle.
 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 FourierMukai 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 FourierMukai partner of an ordinary K3 surface.
Notes/Slides
 Slides on Talk at IST Austria (19 June 2020) on Varieties with trivial canonical bundle in positive characteristic: pdf
This talk gives examples of Varieties with trivial canonical bundle in positive characteristic, which are irreducible symplectic varieties but don’t lift to Irreducible symplectic varieties (or Hyperkahlers) in char 0. Talk was given in the spirit of the remark that we don’t have a good definition of irreducible symplectic Varieties in positive characteristic.
Past seminars:

 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 ).
 padic Simpson correspondence , FU Berlin, Winter 2017/18.
 padic 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.
 DModules, 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 46, 2018.
 Géométrie Algébrique en Liberté (GAEL), Strasbourg University, Strasbourg, 1822 June 2018.
 A Tale of Algebra and Geometry, Pisa, Italy, June 47, 2018.
 Crystals and Geometry in characteristic p, Munich, Germany, 46 April, 2018.
 Enumerative Invariants from Differential Graded Lie Algebras and Categories, Montegufoni, Italy, March 25 – 31, 2018.
 Algebraic Geometry with fancy coefficients, Caen, France, 1317 November, 2017.
 Current Trends in Algebraic and Arithmetic Geometry, Texel, The Netherlands, 27 August1 September, 2017
 Stacks Project Workshop, University of Michigan, Ann Arbor, USA, 31 July4 August, 2017.
 Higgs Bundles, K3 Surfaces and Moduli, Humboldt Universität zu Berlin, 10 – 12 July 2017.
 Integral padic Hodge Theory, Universität Bielefeld, 1012 April 2017.
 padic Analytic Geometry and Differential Equations, CIRM Luminy, 27 – 31 March 2017.
 Higher Dimensional Algebraic Geometry and Characteristic p, CIRM Luminy, 1216 September 2016.
 IRTG Student Conference, Leiden, September 3,2016.
 Current Trends in Algebraic and Arithmetic Geometry, Vlieland, August 29September 2, 2016.
 Motives and Complex Multiplication, Ascona, 1519 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 A¹Homotopy Invariance in Algebraic Geometry and Homotopy Theory , Zinnowitz/Usedom, Germany, April 38, 2016
 Hausdorff School: Derived Categories: Dimensions, Stability Conditions, and Enhancements, MPI Bonn, 29 March – 2 April 2016
 HCM Workshop: Recent developments in integral padic cohomology theories , Bonn, Germany ,February 28March 3 2016.
 BMS Student Conference, Berlin, February 17–19, 2016.
 Recent Advances in Algebraic and Arithmetic Geometry, Siena, August 24–28, 2015.