Frank Calegari

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 Frank Calegari was born on December 15, 1975. He has both Australian and American citizenship. Calegari received his PhD in mathematics from the University of California, Berkeley in 2002 under the supervision of Ken Ribet.

Career Calegari was a Benjamin Peirce Assistant Professor at Harvard University from 2002 to 2006.

Calegari was a von Neumann Fellow of mathematics at the Institute for Advanced Study from 2010 to 2011.

Calegari was an editor at Mathematische Zeitschrift from 2013 to 2021.

Research Calegari works in algebraic number theory, including Langlands reciprocity and torsion classes in the cohomology of arithmetic groups.

In collaboration with Vesselin Dimitrov and Yunqing Tang, Calegari proved the unbounded denominators conjecture of A.O.L. Atkin and Swinnerton-Dyer: if a modular form is not modular for some congruence subgroup of the modular group, then the Fourier coefficients of have unbounded denominators. It has been known for decades that if 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 . This work, along with their work on the Unbounded Denominators conjecture, adds context to the efforts made to understand Roger Apery's proof of the irrationality of .

Awards Calegari held a 5-year American Institute of Mathematics Fellowship from 2002 to 2006 and a Sloan Research Fellowship from 2009 to 2012. He was inducted as a Fellow of the American Mathematical Society in 2013, He was elected a Fellow of the Royal Society in 2026.

Calegari was a plenary speaker at the 2022 International Congress of Mathematicians, where he gave a lecture entitled "30 years of modularity since Fermat's Last Theorem."

Calegari was awarded the 2026 Cole Prize in Number Theory jointly with Vesselin Dimitrov and Yunqing Tang.

Selected publications

Personal life Mathematician Danny Calegari is Frank Calegari's brother.