Mahesh Kakde | |
|---|---|
| Born | 1983 (age 40–41) |
| Occupation | Algebraic number theorist |
| Employer | Indian Institute of Science |
| Known for | Partial 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
- ^ a b "Mahesh Kakde". Mathematics Genealogy Project. Retrieved 19 December 2022.
- ^ a b c d Kakde, Mahesh (2021). "Curruculum vitae" (PDF). Retrieved 3 December 2022.
- ^ 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.
- ^ 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.
- ^ Dasgupta, Samit; Kakde, Mahesh (4 September 2022). "On the Brumer-Stark Conjecture". arXiv: 2010.00657 [ math.NT].
- ^ Dasgupta, Samit; Kakde, Mahesh; Silliman, Jesse; Wang, Jiuya (26 October 2023). "The Brumer–Stark Conjecture over Z". arXiv: 2310.16399 [ math.NT].
- ^ Dasgupta, Samit; Kakde, Mahesh (3 March 2021). "Brumer-Stark Units and Hilbert's 12th Problem". arXiv: 2103.02516 [ math.NT].
- ^ Houston-Edwards, Kelsey (25 May 2021). "Mathematicians Find Long-Sought Building Blocks for Special Polynomials". Quanta Magazine.
-
^ 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.
- ^ "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.
- ^ "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.
- ^ "Dr Mahesh Kakde | India Science, Technology & Innovation - ISTI Portal". www.indiascienceandtechnology.gov.in. Retrieved 10 December 2022.
- ^ "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.
- ^ "Indian Institute of Science". Retrieved 3 December 2022.
- ^ "Duke Mathematicians Present at 2022 International Congress of Mathematicians". Department of Mathematics. Retrieved 3 December 2022.
- ^ a b "Infosys Prize - Laureates 2022 - Mahesh Kakde". www.infosysprize.org. Retrieved 3 December 2022.
External links
Mahesh Kakde | |
|---|---|
| Born | 1983 (age 40–41) |
| Occupation | Algebraic number theorist |
| Employer | Indian Institute of Science |
| Known for | Partial 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
- ^ a b "Mahesh Kakde". Mathematics Genealogy Project. Retrieved 19 December 2022.
- ^ a b c d Kakde, Mahesh (2021). "Curruculum vitae" (PDF). Retrieved 3 December 2022.
- ^ 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.
- ^ 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.
- ^ Dasgupta, Samit; Kakde, Mahesh (4 September 2022). "On the Brumer-Stark Conjecture". arXiv: 2010.00657 [ math.NT].
- ^ Dasgupta, Samit; Kakde, Mahesh; Silliman, Jesse; Wang, Jiuya (26 October 2023). "The Brumer–Stark Conjecture over Z". arXiv: 2310.16399 [ math.NT].
- ^ Dasgupta, Samit; Kakde, Mahesh (3 March 2021). "Brumer-Stark Units and Hilbert's 12th Problem". arXiv: 2103.02516 [ math.NT].
- ^ Houston-Edwards, Kelsey (25 May 2021). "Mathematicians Find Long-Sought Building Blocks for Special Polynomials". Quanta Magazine.
-
^ 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.
- ^ "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.
- ^ "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.
- ^ "Dr Mahesh Kakde | India Science, Technology & Innovation - ISTI Portal". www.indiascienceandtechnology.gov.in. Retrieved 10 December 2022.
- ^ "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.
- ^ "Indian Institute of Science". Retrieved 3 December 2022.
- ^ "Duke Mathematicians Present at 2022 International Congress of Mathematicians". Department of Mathematics. Retrieved 3 December 2022.
- ^ a b "Infosys Prize - Laureates 2022 - Mahesh Kakde". www.infosysprize.org. Retrieved 3 December 2022.