Welcome to the webpage of **Tanya Kaushal Srivastava. **I am an Algebraic Geometer.

Current Position:

Insfosys Postdoctoral FellowChennai Mathematical Institute,

H1, SIPCOT IT Park, Siruseri

Kelambakkam 603103

India

Email:tanyak(at)cmi(dot)ac(dot)in

Till October 2020, I was a postdoc in Hausel group at IST Austria. Before that I was a PhD student of Prof. Dr. Hélène Esnault at Freie Universität Berlin. And even before that I was a BS-MS student at IISER Mohali, India.

##### Reserach Interests

The question that I am really curious about:

*Which geometrical properties of an algebraic variety can be determined by its derived category of coherent sheaves?*

Attempts to answer this question has related a lot of fields of mathematics ranging from differential geometry, algebraic geometry, representation theory to number theory and even to physics, notably string theory.

##### Teaching

## Publications

- Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences. Revised pdf ,
*Archiv der Mathematik*, DOI: 10.1007/s00013-020-01564-y, 1-13, 2021. **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 .

## Accepted for Publication

**Pathologies of Hilbert scheme of points on supersingular Enriques surface in characteristic 2**(Arxiv Link) ,, 2021.**accepted Bulletin des Sciences Mathematiques**

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 G\”ottsche-Soergel does not hold over characteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties in positive characteristic than as given by Beauville-Bogolomov decomposition theorem over $\mathbb{C}$. 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.

## Under Preparation

joint with Katrina Honigs.**Fully Faithfulness Criterion for Functors of (Twisted) Derived Categories,**

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.

## Invited Talks

- Fourth Meeting for Young Women in Mathematics, University of Freiburg, May 1-3, 2019.
- University of Hannover at Guest Research Seminar in the group of Prof. Dr. Matthias Schuett, 13 December 2018.
- University of Bergen at Guest Research Seminar in the group of Prof. Dr. Sofia Tirabassi, 30 May 2016, Norway.

## Seminars Organized

- Working Seminar on Derived Algebraic Geometry, Summer 2019. (Organizer with Quoc Ho)
- Formal Goemetry and Deformation Theory, FU Berlin, Winter 2017/18, (Organizer with Pedro A. Castillejo ).
- p-adic Hodge Theory, FU Berlin, Summer 2017, (Organizer with Marcin Lara).
- Crystalline Cohomology, FU Berlin, winter 2016/17, (Organizer with Efstathia Katsigianni).

## Past Seminars

- Algebraic Geometry-Number theory Seminar, IST Austria, Fall 2018- Summer 2020.
- Abhyankar’s Conjecture, Freie Universität Berlin, Summer 2018.
- p-adic Simpson correspondence , FU Berlin, Winter 2017/18.
- Langlands correspondence for function fields, FU Berlin, Summer 2017.
- Berkovich spaces, singularity theory and birational geometry, FU Berlin, Winter 2016/17.
- 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.

## Talks at seminars

- Talk on
**Varieties with trivial canonical bundle**, IST Austria, August 2020. - Talk on
**Lie algebra attached to smooth projective variety and hyperkahlers**, IST Austria, March 2020. - Talks on
**Virtual fundamental classes and dg scheme**in Seminar on “Derived Algebraic Geometry”, IST Austria, Summer 2019. - Mini Lecture series on
**Derived categories of Ordinary K3 surfaces**in Working Seminar, IST Austria, Spring 2019. - Talk on
**Formal Patching**in Seminar on “Abhyankar’s Conjecture”, Freie Universitat Berlin, Summer 2018. - Talk on
**Semistable Higgs Bundles**in Seminar on “$p$-adic Simpson correspondence”, Freie Universit\”at Berlin, Winter 2017-18. - Talk on
**Introduction to Deformation theory**in Seminar on “Formal Geometry and Deformation Theory”, Freie Universit\”at Berlin, Winter 2017-18. - Talk on
**Locally Noetherian Formal Schemes**in Seminar on “Formal Geometry and Deformation Theory”, Freie Universit\”at Berlin, Winter 2017-18. - Talk on
**The Comparison Theorem**in Seminar on “Formal Geometry and Deformation Theory”, Freie Universitat Berlin, Winter 2017-18. - Talk on
**Derived categories and semi-orthogonal decompositions** - Talk on
**Crystalline Cohomology and crystalline sheaves**in Seminar on “$p$-adic Hodge Theory”, Freie Universitat Berlin, Summer 2017. - Talk on
**Almost Mathematics and Purity Theorem**in Seminar on “$p$-adic Hodge Theory”, Freie Universitat Berlin, Summer 2017. - Talk on
**Shtukas for GL2, II**in Seminar on “Langlands correspondence for function fields”, Freie Universitat Berlin, Summer 2017. - Talk on
**Koll\’ar’s paper on Nonrational hypersurfaces** - Talk on
**$p$-adic integration and the Igusa zeta function**in Seminar on “Berkovich spaces, birational geometry and motivic zeta functions”, Freie Universitat Berlin, Winter 2016-17. - Talk on
**Comparison Isomorphisms and $p$-adic Hodge theory**in Seminar on “Crystalline cohomology”, Freie Universitat Berlin, Winter 2016-17. - Talk on
**Properties of crystalline Cohomology**in Seminar on “Crystalline Cohomology”, Freie Universitat Berlin, Winter 2016-17. - Talk on
**Introduction to Crystalline Cohomology**in Seminar on“Crystalline cohomology”, Freie Universitat Berlin, Winter 2016-17. - Talk on
**D-modules of K3 surfaces and Unirational varieties**in Seminar on “D-modules”, Freie Universitat Berlin, Summer 2016 - Talk on
**Skeleta of curves**in Seminar on “Berkovich Spaces”, Humboldt Universit\”at Berlin, Summer 2016 - Talk on
**Model Categories**in Seminar on “Motivic Galois groups and periods”, Freie Universitat Berlin, Summer 2016 **Mini lecture series on Introduction to Derived Categories**, Freie Universitat Berlin, Winter 2015-16.- Talk on
**Supersingular K3 crysta**l in Seminar on “Supersingular K3 surfaces are Unirational”, Freie Universitat Berlin, Winter 2015-16. - Talk on
**Functoriality, Affine stratification and Chow ring of Projective varieties**in Seminar on “Intersection Theory”, Freie Universitat Berlin, Winter 2015-16.

## Past Conferences and Summer/Winter Schools (Participation/Talks)

- Wild Ramification and Irregular Singularities, Warsaw, Poland, September 23-27, 2019.
- Periods and Motives, HU Berlin, Germany, 8-12 July, 2019.
- Derived algebraic geometry and its applications, MSRI Berkley, USA, March 25-29, 2019.
- 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.

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