Tata Institute of Fundamental Research

Homi Bhabha Road, Colaba

Mumbai 400005

India

Office: A334

Email: cravi[at] math[dot] tifr[dot] res[dot] in

I am a tenure-track Reader at the School of Mathematics in Tata Institute of Fundamental Research, Mumbai.

Broadly, my area of research interest is algebraic geometry. I am particularly interested in algebraic K-theory, algebraic cycles and motives in the context of algebraic stacks and equivariant algebraic geometry. I am currently working on problems related to cohomology of algebraic stacks.

May 2024–Present | Reader (tenure-track), Tata Institute of Fundamental Research, Mumbai, India |

Dec 2022–May 2024 | Assistant Professor, Indian Statistical Institute, Bangalore, India |

Jan 2022–Dec 2022 | Postdoctoral Researcher, Max Planck Institute for Mathematics, Bonn, Germany, Mentor: Prof. Dr. Peter Scholze |

Sep 2018–Dec 2021 | Postdoctoral Researcher, SFB Higher invariants, University of Regensburg, Germany, Research group: Prof. Dr. Ulrich Bunke |

Sep 2016–Aug 2018 | Postdoctoral Researcher, University of Oslo, Norway RCN Frontier Research Group Project Motivic Hopf equations, Principal Investigator: Prof. Paul Arne Østvær |

Jul 2016–Aug 2016 | Visiting fellow, Tata Institute of Fundamental Research, Mumbai, India |

Jul 2011–Jul 2016 | Ph.D. in Mathematics, Tata Institute of Fundamental Research, Mumbai, India, Advisor: Prof. Amalendu Krishna |

Jul 2009–May 2011 | Master of Mathematics, Indian Statistical Institute, Bangalore, India |

Jul 2006–Jul 2009 | B.Sc. in Mathematics, Sri Venkateswara College, University of Delhi, New Delhi, India |

- Sem II, 2023-24: Reading Seminar: Intersection Homology
- Sem II, 2023-24: B16: Topology (BMAT2)
- Sem I, 2023: E23: Algebraic Topology (BMAT3)
- Sem II, 2022-23: Reading Seminar: O-minimality and Hodge theory
- Sem II, 2022-23: Topology II (Ph.D. course)

*Cohomological and categorical concentration, with A. A. Khan (Preprint, 30 pages, 2023) [arXiv]**Equivariant generalized cohomology via stacks, with A. A. Khan (Preprint, 37 pages, 2022, last updated 01.2024) [arXiv]**Localization theorems for algebraic stacks, with D. Aranha, A. A. Khan, A. Latyntsev, H. Park (Preprint, 78 pages, 2022) [arXiv]**Generalized cohomology theories for algebraic stacks, with A. A. Khan (Preprint, 94 pages, 2021) [arXiv]**Categorical Milnor squares and K-theory of algebraic stacks, with T. Bachmann, A. A. Khan, V. Sosnilo (Selecta Mathematica, 28 (2022), no. 5, paper no. 85) [arXiv]**Virtual equivariant Grothendieck-Riemann-Roch formula, with B. Sreedhar (Documenta Mathematica, 26, (2021), 2061-2094) [arXiv]**Rigidity in equivariant algebraic K-theory, with N. Naumann (Annals of K-theory, 5, no. 1, (2020), 141–158) [arXiv]**Rigidity for equivariant psuedo pretheories, with J. Heller and P. A. Østvær (Journal of Algebra, 516, (2018), 373-395) [arXiv]**A Grothendieck-Lefschetz theorem for equivariant Picard groups (Journal of Pure and Applied Algebra, 222, no. 10, (2018), 3248-3254) [arXiv]**Algebraic K-theory of quotient stacks, with A. Krishna (Annals of K-Theory, 3, no. 2, (2018), 207-233) [arXiv]**Equivariant vector bundles, their derived category and K-theory on affine schemes, with A. Krishna (Annals of K-Theory, 2, no. 2, (2017), 235-275) [arXiv]*