Welcome to the webpage of Tanya Kaushal Srivastava. I am an Algebraic Geometer.
Current Position:
Assistant Professor
Indian Institute of Technology Gandhinagar
Palaj, Gandhinagar – 382355, Gujarat,India.
Email: ks(dot)tanya(at)iitgn(dot)ac(dot)in
Official Webpage: https://iitgn.ac.in/faculty/maths/fac-tanya
Till August 2021, I was an Infosys Posdoctoral fellow at Chennai Mathematical Institute. From November 2018 to 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
If you click on course name it should redirect you to the course webpage, some courses have resources. I plan to keep them updated.
Semester II 2023-24
- MA628: Algebra II: Galois Theory and Modules
Semester I 2023-24
- MA632: Applied Statistics
- MA691-IV: Special Topics-Elliptic Curves and Surfaces.
Semester II 2022-23
- MA 202: Statistics & Probability to would be (could be or maybe) engineers at IIT GN
- MA636: Riemannian Geometry. This is for math enthusiasts. Not much prerequisite is asked for. The details will be regularly updated here.
Semester I 2022-23
- MA510: Topology
Semester II 2021-22
- MA 202: Statistics, Probability and Numerical methods for Engineers at IIT GN.
- From September 2021-December 2021, I taught a course on Algebraic Curves and Riemann Surfaces at Chennai Mathematical Institute, details are here.
Long before that when Covid just began…
Publications
- Counting Twisted Derived Equivalent Tame Ordinary K3 surfaces, joint with Sofia Tirabassi, Mathematics Research Letters, Accepted since Dec 2022. (ArXiv Link)
- Pathologies of Hilbert scheme of points on supersingular Enriques surface in characteristic 2 (Arxiv Link) , Bulletin des Sciences Mathematiques, 2021. (https://doi.org/10.1016/j.bulsci.2021.102957)
- 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 .
Preprints
-
An example for Kuznetsov-Shinder conjecture, ArXiv Link: https://arxiv.org/abs/2401.00648
We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.
Under Preparation
- 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.
Invited Talks
- Invited Speaker at R
- Invited Speaker at
- Invited speaker at Derived Categories, Arithmetic, and Reconstruction in Algebraic Geometry, Banff, Canada, 3-8th July 2022.
- Indian Institute of Science Education and Research (IISER), Mohali, Alumni Research Seminar, 14th January 2022.
- Tata Institute of Fundamental Research (TIFR), Bombay, Algebraic Geometry Guest Research Seminar, 5th March 2021.
- Tata Institute of Fundamental Research (TIFR), Bombay, Graduate student Guest Research Seminar, 2th March 2021.
- Chennai Mathematical Institute, Chennai, Research Seminar talk, 25th Feb 2021.
- 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
Current Seminar Series:
- Currently, I am organizing GANIT: Geometry, Algebra, Numbers & Integers, Topology Seminar at IITGN. It is conducted in Hybrid mode. In case you would like to give a talk please just write me an email. And if you would like to recieve regular updates, please register here: https://forms.gle/reeFJ5tfsHtDrkpKA.
Other Seminars (Happening or Happened!)
- Upcoming Seminar: Mirror Symmetry: Constructions available in positive characteristics, Chennai Mathematical Institute/IIT GN.
- Learning Seminar: Sheaves on Topology, IITGN, Semester II, 2021-22.
- Working Seminar on Derived Algebraic Geometry, IST Austria, 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
- Learning Seminar: Perverse Sheaves, Sheffield, UK, Summer 2021.
- 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
- Multiple Talks at Learning seminar on Perverse sheaves, Sheffield, UK, Summer 2021.
- 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 in Seminar on “Derived categories and variation of GIT quotients”, Freie Universit\”at Berlin, Winter 2017-18.
- 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 in Seminar on “Rationality of varieties and decomposition of the diagonal”, Humboldt Universitat, Winter 2016-17.
- 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 crystal 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.