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Mahesh Kakde

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Mathematician

Mahesh Kakde
Born1983 (age 40–41)
Akola, India
OccupationAlgebraic number theorist
EmployerIndian Institute of Science
Known forPartial results for the Brumer-Stark conjecture and Hilbert's 12th problem

Mahesh Ramesh Kakde (born 1983) is a mathematician working in algebraic number theory.

Biography

Mahesh Kakde was born on 1983 in Akola, India. He obtained a Bachelor of Mathematics degree at the Indian Statistical Institute in Bangalore in 2004, and a Certificate of Advanced Study in Mathematics at the University of Cambridge in 2005. He completed his PhD under the supervision of John Coates at the University of Cambridge in 2008. He subsequently worked at Princeton University, University College London, and King's College London, before becoming a professor at the Indian Institute of Science in 2019.

Research

Kakde proved the main conjecture of Iwasawa theory in the totally real μ = 0 case. Together with Samit Dasgupta and Kevin Ventullo, he proved the Gross–Stark conjecture. In a joint project with Samit Dasgupta, they proved the Brumer–Stark conjecture away from 2 in 2020, and later over Z {\displaystyle \mathbb {Z} } in 2023. Generalising these methods, they also gave a solution to Hilbert's 12th problem for totally real fields. Their methods were subsequently used by Johnston and Nickel to prove the equivariant Iwasawa main conjecture for abelian extensions without the μ = 0 hypothesis.

Awards

In 2019, Kakde was awarded a Swarnajayanti Fellowship.

Together with Samit Dasgupta, Kakde was one of the invited speakers at the International Congress of Mathematicians 2022, where they gave a joint talk on their work on the Brumer–Stark conjecture.

In 2022, Kakde received the Infosys Prize for his contributions to algebraic number theory. In his congratulatory message, Jury Chair Chandrashekhar Khare noted that " work on the main conjecture of non-commutative Iwasawa theory, on the Gross-Stark conjecture and on the Brumer-Stark conjecture has had a big impact on the field of algebraic number theory. His work makes important progress towards a p-adic analytic analog of Hilbert’s 12th problem on construction of abelian extensions of number fields."

References

  1. ^ "Mahesh Kakde". Mathematics Genealogy Project. Retrieved 19 December 2022.
  2. ^ Kakde, Mahesh (2021). "Curruculum vitae" (PDF). Retrieved 3 December 2022.
  3. Kakde, Mahesh (2013). "The main conjecture of Iwasawa theory for totally real fields". Inventiones Mathematicae. 193 (3): 539–626. arXiv:1008.0142. Bibcode:2013InMat.193..539K. doi:10.1007/s00222-012-0436-x. S2CID 253745808.
  4. Dasgupta, Samit; Kakde, Mahesh; Ventullo, Kevin (2018). "On the Gross–Stark Conjecture". Annals of Mathematics. 188 (3): 833–870. doi:10.4007/annals.2018.188.3.3. S2CID 53554124.
  5. Dasgupta, Samit; Kakde, Mahesh (4 September 2022). "On the Brumer-Stark Conjecture". arXiv:2010.00657 .
  6. Dasgupta, Samit; Kakde, Mahesh; Silliman, Jesse; Wang, Jiuya (26 October 2023). "The Brumer–Stark Conjecture over Z". arXiv:2310.16399 .
  7. Dasgupta, Samit; Kakde, Mahesh (3 March 2021). "Brumer-Stark Units and Hilbert's 12th Problem". arXiv:2103.02516 .
  8. Houston-Edwards, Kelsey (25 May 2021). "Mathematicians Find Long-Sought Building Blocks for Special Polynomials". Quanta Magazine.
  9. Johnston, Henri; Nickel, Andreas (30 November 2021). "An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications". arXiv:2010.03186 . In the present article, we prove the EIMC (with uniqueness) in important cases without assuming any μ = 0 {\displaystyle \mu =0} hypothesis. The proof relies on the classical (non-equivariant) Iwasawa main conjecture proven by Wiles and the recent groundbreaking work of Dasgupta and Kakde on the strong Brumer–Stark conjecture.
  10. "List of Awardees - SwarnaJayanti Fellowships Scheme - 2018-19" (PDF). Government of India, Department of Science and Technology. Archived (PDF) from the original on 14 May 2021. Retrieved 19 December 2022.
  11. "List of Awardees – SwarnaJayanti Fellowships Scheme – 2019-20" (PDF). Government of India, Department of Science and Technology. Archived (PDF) from the original on 9 November 2020. Retrieved 10 December 2022.
  12. "Dr Mahesh Kakde | India Science, Technology & Innovation - ISTI Portal". www.indiascienceandtechnology.gov.in. Retrieved 10 December 2022.
  13. "This IISc professor uses a novel method to prove deep relationships between different Stark elements". Edex Live. 20 January 2021. Archived from the original on 22 January 2021. Retrieved 19 December 2022.
  14. "Indian Institute of Science". Retrieved 3 December 2022.
  15. "Duke Mathematicians Present at 2022 International Congress of Mathematicians". Department of Mathematics. 14 July 2022. Retrieved 3 December 2022.
  16. ^ "Infosys Prize - Laureates 2022 - Mahesh Kakde". www.infosysprize.org. Retrieved 3 December 2022.

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