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2017 André Aisenstadt Recipient

CRM > Prizes > André Aisenstadt Prize > Recipient > Jacob Tsimerman (University of Toronto)

2017 André Aisenstadt Prize in Mathematics Recipient
Jacob Tsimerman (University of Toronto)

[ français ]

Jacob Tsimerman (University of Toronto) will give a lecture on November 10, 2017.

Vendredi 10 novembre 2017 / Friday, November 10, 2017

Centre de recherches mathématiques
Pavillon André-Aisenstadt
Université de Montréal
Salle 6254 16:00 - 17:00

Jacob Tsimerman (University of Toronto)


[ Slideshow ]

Transcendence theorems and Hodge Theory

The Ax-Schanuel theorem is a powerful result in functional transcendence which describes ‘all the algebraic interactions’ of the exponential function, and has proven to be a powerful tool in various number theoretic and algebraic settings. We shall describe a vast generalization of this result to the shimura and hodge-theoretic settings, and how one can use model theoretic tools such as o-minimality to attack such transcendental questions. We shall then give applications of these results to arithmetic questions.

These are joint works with B. Bakker, and with N. Mok and J. Pila.

Le café sera servi à 15h30 et une réception suivra la conférence au Salon Maurice-L’Abbé (salle 6245). / Coffee will be served before the conference and a reception will follow at Salon Maurice-L’Abbé (Room 6245).

BIOGRAPHY

The International Scientific Advisory Committee of the Centre de recherches mathématiques (CRM) is pleased to announce that Jacob Tsimerman, of the University of Toronto, is the 2017 André Aisenstadt Prize recipient.

Just six years beyond his PhD, Jacob Tsimerman is an extraordinary mathematician whose work at the interface of transcendence theory, analytic number theory and arithmetic geometry is remarkable for its creativity and insight.

Jacob proved the existence of Abelian varieties defined over number fields that are not isogenous to the Jacobian of a curve. This had been conjectured by Katz and Oort and follows from the André-Oort conjecture. In joint work with several collaborators, Jacob established non-trivial bounds for the 2-torsion in the class groups of number fields. For quadratic fields, this can be done by genus theory but the general case was a complete mystery. With Bakker, Jacob has established geometric analogues of the Frey-Mazur uniform boundedness results for elliptic curves over function fields. Their approach has yielded powerful results with methods amenable to far more general applications.

Among Jacob's most notable accomplishments are his recent breakthroughs on the André-Oort conjecture. This conjecture about Shimura varieties, at the intersection of diophantine geometry and the arithmetic of automorphic forms, has been a central theme in Arithmetic Geometry for many years. Jacob already made important progress on it in his thesis, but in the last few years, working together with Pila, he created many of the technical tools for proving the case of the Siegel modular variety. There was still one piece that had to be completed on the size of Galois orbits. Jacob settled this final component in a brilliant short paper which showed that it follows from an average form of the Colmez conjecture. The latter has been proved by Andreatta, Goren, Howard and Madapusi-Perla, and independently by Yuan and Zhang, thus giving a complete unconditional proof of the André-Oort conjecture for this Shimura variety.

Besides being a brilliant and innovative researcher, Jacob is also an excellent expositor and teacher. Moreover, he has been active in Math Outreach through his work helping to train the Canadian team for the International Math Olympiad. He is currently the Chair of the Canadian IMO Committee.