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.
Spending more years on earth and in an IIT, I have developed an interest now in Roboitics and Algorthmic Algebraic Geometry as well.
You can find more details about the Research group and its members at our Group Page (AG Group Members)
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 NCMW – Derived categories and semi-orthogonal decompositions, Chennai Mathematical Institute, 17 Jun 2024 to 29 Jun 2024.
- Invited Speaker at 38th Annual Conference of Ramanujan Mathematical Society, IIT Guwahati, 22nd – 24th December, 2023.
- Invited Speaker at INDIAN WOMEN AND MATHEMATICS (IWM): Annual Conference, IISER Bhopal, July 13-15, 2023
- 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.