Biography:Mahesh Kakde
Mahesh Kakde | |
|---|---|
| Born | 1983 (age 40–41) Akola, India |
| 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 [math]\displaystyle{ \mathbb Z }[/math] 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
- ↑ 1.0 1.1 "Mahesh Kakde". https://www.mathgenealogy.org/id.php?id=132686.
- ↑ 2.0 2.1 2.2 2.3 Kakde, Mahesh (2021). "Curruculum vitae". http://math.iisc.ac.in/~maheshkakde/Kakde_CV_Nov2021.pdf.
- ↑ Kakde, Mahesh (2013). "The main conjecture of Iwasawa theory for totally real fields". Inventiones Mathematicae 193 (3): 539–626. doi:10.1007/s00222-012-0436-x. Bibcode: 2013InMat.193..539K. https://www.researchgate.net/publication/45932481.
- ↑ 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. https://annals.math.princeton.edu/2018/188-3/p03.
- ↑ Dasgupta, Samit; Kakde, Mahesh (2022-09-04). "On the Brumer-Stark Conjecture". arXiv:2010.00657 [math.NT].
- ↑ Dasgupta, Samit; Kakde, Mahesh; Silliman, Jesse; Wang, Jiuya (2023-10-26). "The Brumer–Stark Conjecture over Z". arXiv:2310.16399 [math.NT].
- ↑ Dasgupta, Samit; Kakde, Mahesh (2021-03-03). "Brumer-Stark Units and Hilbert's 12th Problem". arXiv:2103.02516 [math.NT].
- ↑ Houston-Edwards, Kelsey (2021-05-25). "Mathematicians Find Long-Sought Building Blocks for Special Polynomials". Quanta Magazine. https://www.quantamagazine.org/mathematicians-find-polynomial-building-blocks-hilbert-sought-20210525/.
- ↑ Johnston, Henri; Nickel, Andreas (2021-11-30). "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 [math]\displaystyle{ \mu = 0 }[/math] 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". Government of India, Department of Science and Technology. https://dst.gov.in/sites/default/files/list%20of%20SJF%20candidates%20for%20the%20year%202018-19.pdf.
- ↑ "List of Awardees – SwarnaJayanti Fellowships Scheme – 2019-20". Government of India, Department of Science and Technology. https://dst.gov.in/sites/default/files/LIST%20OF%20SwarnaJayanti%20Fellowship%20AWARDEES%20-%202019-20%20%281%29_0.pdf.
- ↑ "Dr Mahesh Kakde | India Science, Technology & Innovation - ISTI Portal". https://www.indiascienceandtechnology.gov.in/nationalfellows/dr-mahesh-kakde.
- ↑ "This IISc professor uses a novel method to prove deep relationships between different Stark elements" (in en). 2021-01-20. https://www.edexlive.com/news/2021/jan/20/this-iisc-professoruses-a-novel-method-to-prove-deep-relationships-between-different-stark-elements-17426.html.
- ↑ "Indian Institute of Science" (in en). https://iisc.ac.in/events/prof-mahesh-kakde-invited-to-speak-at-the-2022-international-congress-of-mathematicians-in-st-petersburg-russia/.
- ↑ "Duke Mathematicians Present at 2022 International Congress of Mathematicians" (in en). https://math.duke.edu/news/duke-mathematicians-present-2022-international-congress-mathematicians.
- ↑ 16.0 16.1 "Infosys Prize - Laureates 2022 - Mahesh Kakde" (in en). https://www.infosysprize.org/laureates/2022/mahesh-kakde.html.
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