Mahesh Kakde

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[1] (born 1983) is a mathematician working in algebraic number theory.

Biography

Mahesh Kakde was born on 1983 in Akola, India.[2] 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.[2] He completed his PhD under the supervision of John Coates at the University of Cambridge in 2008.[1][2] 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.[2]

Research

Kakde proved the main conjecture of Iwasawa theory in the totally real μ = 0 case.[3] Together with Samit Dasgupta and Kevin Ventullo, he proved the Gross–Stark conjecture.[4] In a joint project with Samit Dasgupta, they proved the Brumer–Stark conjecture away from 2 in 2020,[5] and later over in 2023.[6] Generalising these methods, they also gave a solution to Hilbert's 12th problem for totally real fields.[7][8] Their methods were subsequently used by Johnston and Nickel to prove the equivariant Iwasawa main conjecture for abelian extensions without the μ = 0 hypothesis.[9]

Awards

In 2019, Kakde was awarded a Swarnajayanti Fellowship.[10][11][12][13]

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.[14][15]

In 2022, Kakde received the Infosys Prize for his contributions to algebraic number theory.[16] In his congratulatory message, Jury Chair Chandrashekhar Khare noted that "[Kakde’s] 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."[16]

References

  1. ^ a b "Mahesh Kakde". Mathematics Genealogy Project. Retrieved 19 December 2022.
  2. ^ a b c d 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 [math.NT].
  6. ^ Dasgupta, Samit; Kakde, Mahesh; Silliman, Jesse; Wang, Jiuya (26 October 2023). "The Brumer–Stark Conjecture over Z". arXiv:2310.16399 [math.NT].
  7. ^ Dasgupta, Samit; Kakde, Mahesh (3 March 2021). "Brumer-Stark Units and Hilbert's 12th Problem". arXiv:2103.02516 [math.NT].
  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 [math.NT]. In the present article, we prove the EIMC (with uniqueness) in important cases without assuming any hypothesis. The proof relies on the classical (non-equivariant) Iwasawa main conjecture proven by Wiles [Wil90] and the recent groundbreaking work of Dasgupta and Kakde [DK20] 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. Retrieved 3 December 2022.
  16. ^ a b "Infosys Prize - Laureates 2022 - Mahesh Kakde". www.infosysprize.org. Retrieved 3 December 2022.