Frank Calegari
Frank Calegari | |
|---|---|
 Calegari at Oberwolfach in 2011 | |
| Born | 15 December 1975 |
| Citizenship | Australia United States |
| Alma mater | University of California, Berkeley |
| Relatives | Danny Calegari (brother) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Chicago Institute for Advanced Study |
| Thesis | Ramification and Semistable Abelian Varieties (2002) |
| Doctoral advisor | Ken Ribet |
Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program.
Early life and education
[edit]Frank Calegari was born on December 15, 1975.[1] He has both Australian and American citizenship.[1]
He won a bronze medal and a silver medal at the International Mathematical Olympiad while representing Australia in 1992 and 1993 respectively.[2] Calegari received his PhD in mathematics from the University of California, Berkeley in 2002 under the supervision of Ken Ribet.[3]
Career
[edit]Calegari was a Benjamin Peirce Assistant Professor at Harvard University from 2002 to 2006.[1] He then moved to Northwestern University, where he was an assistant professor from 2006 to 2009, an associate professor from 2009 to 2012, and a professor from 2012 to 2015.[1] He has been a professor of mathematics at the University of Chicago since 2015.[1][4]
Calegari was a von Neumann Fellow of mathematics at the Institute for Advanced Study from 2010 to 2011.[5]
Calegari was an editor at Mathematische Zeitschrift from 2013 to 2021.[1] He has been an editor of Algebra & Number Theory and an associate editor of the Annals of Mathematics since 2019.[1][6][7]
Research
[edit]Calegari works in algebraic number theory, including Langlands reciprocity and torsion classes in the cohomology of arithmetic groups.[4]
In collaboration with Vesselin Dimitrov and Yunqing Tang, Calegari proved[8] the unbounded denominators conjecture of A.O.L. Atkin and Swinnerton-Dyer[9]: if a modular form f(τ) is not modular for some congruence subgroup of the modular group, then the Fourier coefficients of f(τ) have unbounded denominators. It has been known for decades[10] that if f(τ) is modular for some congruence subgroup, then its coefficients have bounded denominators.
Also in collaboration with Dimitrov and Tang, he proved the linear independence of and [11]
Awards
[edit]Calegari held a 5-year American Institute of Mathematics Fellowship from 2002 to 2006 and a Sloan Research Fellowship from 2009 to 2012.[1][12] He was inducted as a Fellow of the American Mathematical Society in 2013.[1]
Selected publications
[edit]- Calegari, Frank (2011). "Even Galois representations and the Fontaine–Mazur conjecture". Inventiones Mathematicae. 185 (1): 1–16. arXiv:0907.3427. Bibcode:2011InMat.185....1C. doi:10.1007/s00222-010-0297-0. ISSN 0020-9910. S2CID 8937648.
- Calegari, Frank; Emerton, Matthew (2005). "On the ramification of Hecke algebras at Eisenstein primes". Inventiones Mathematicae. 160 (1): 97–144. arXiv:math/0311368. Bibcode:2005InMat.160...97C. doi:10.1007/s00222-004-0406-z. ISSN 0020-9910. S2CID 14827842.
- Calegari, Frank; Emerton, Matthew (2009). "Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms". Annals of Mathematics. Second Series. 170 (3): 1437–1446. arXiv:0704.0662. doi:10.4007/annals.2009.170.1437. ISSN 0003-486X.
- Calegari, Frank; Geraghty, David (2018). "Modularity lifting beyond the Taylor–Wiles method". Inventiones Mathematicae. 211 (1): 297–433. arXiv:1207.4224. Bibcode:2018InMat.211..297C. doi:10.1007/s00222-017-0749-x. ISSN 0020-9910. S2CID 16364057.
- Calegari, Frank; Geraghty, David (2020). "Minimal modularity lifting for nonregular symplectic representations". Duke Mathematical Journal. 169 (5): 801–896. arXiv:1907.08691. doi:10.1215/00127094-2019-0044. ISSN 0012-7094. S2CID 85504517.
Personal life
[edit]Mathematician Danny Calegari is Frank Calegari's brother.[13]
References
[edit]- ^ a b c d e f g h i "Frank Calegari (WebCV)" (PDF). Frank Calegari. Retrieved 2 September 2024.
- ^ "Frank Calegari". International Mathematical Olympiad. Retrieved 6 March 2020.
- ^ Frank Calegari at the Mathematics Genealogy Project
- ^ a b "Frank Calegari". University of Chicago. Retrieved 6 March 2020.
- ^ "Francesco Damien Calegari". Institute for Advanced Study. 9 December 2019. Retrieved 6 March 2020.
- ^ "Mathematische Zeitschrift | Editors". Springer Science+Business Media. Retrieved 6 March 2020.
- ^ "Editorial Board". Annals of Mathematics. Retrieved 6 March 2020.
- ^ Calegari, Frank; Dimitrov, Vesselin; Tang, Yunqing (2021), The Unbounded Denominators Conjecture, p. 1-62, doi:10.48550/ARXIV.2109.09040, retrieved 9 January 2025
- ^ Atkin, A. O. L.; Swinnerton-Dyer, H. P. F. (1971), "Modular forms on noncongruence subgroups", Combinatorics (Univ. California, 1968): Proceedings of Symposia in Pure Mathematics, vol. XIX, American Mathematical Society, pp. 1–26
- ^ Shimura, Gorō (1971). Introduction to the Arithmetic Theory of Automorphic Functions. Princeton, N.J: Princeton University Press. ISBN 978-0-691-08092-5.
- ^ Calegari, Frank; Dimitrov, Vesselin; Tang, Yunqing (2024), The linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$, doi:10.48550/ARXIV.2408.15403, retrieved 9 January 2025
- ^ "Frank Calegari". Frank Calegari. Retrieved 6 March 2020.
- ^ "Family, Collaborators, Students". Retrieved 6 March 2020.
External links
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