Jacob Tsimerman

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Jacob Tsimerman (born April 26, 1988 in Kazan ) is a Canadian mathematician who specializes in number theory and algebraic geometry .

Tsimerman moved to Israel with his family in 1990 and to Canada in 1996. In 2003 and 2004 he won gold medals at the International Mathematical Olympiad (for Canada), of which 2004 with a perfect result. He studied from 2004 at the University of Toronto with a bachelor's degree in 2006 and received his doctorate from Princeton University with Peter Sarnak in 2011 . As a post-doctoral student , he was a Junior Fellow at Harvard University . He has been an Assistant Professor at the University of Toronto since 2014 .

Tsimerman made significant advances in the André-Oort conjecture (named after Yves André and Frans Oort ) about sub -varieties of Shimura varieties , according to which the Zariski degree of special points of a Shimura variety is a union of Shimura varieties. It was proven by Emmanuel Ullmo , Andrei Yafaev and Bruno Klingler in 2006 , assuming the generalized Riemann presumption (English acronym : GRH) , but was otherwise largely open. In his dissertation, Tsimerman made progress in the André-Oort conjecture, in which he proved lower bounds for the Galois orbits of special points up to dimension 6, while Ullmo and Yafaev could only prove such bounds up to dimension three. Another important result of his dissertation was the proof that there are Abelian varieties over that are not Jacobi varieties of stable algebraic curves . With this, he answered a question from Nicholas Katz and Frans Oort: Ching-Chi Lai and Frans Oort had previously proven this, assuming the André Oort conjecture.

He made further progress with Jonathan Pila , including the proof of the André-Oort conjecture for certain modular spaces of Abelian surfaces and the proof of the Ax-Lindemann theorem for the modular spaces of principally polarized Abelian varieties, which is one of the strategies for proving André's conjecture -Oort is. Finally, Tsimerman succeeded in proving the conjecture for principle-polarized Abelian varieties in any dimension (without the requirement of the GRH), which had been long sought. To do this, he proved a lower bound for the Galois orbit of specific points in more than six dimensions using a recently proven version of a conjecture by Pierre Colmez (1993).

In 2015 he received the SASTRA Ramanujan Prize , in 2017 the André Aisenstadt Prize and in 2019 the Coxeter James Prize . In 2014 he became a Sloan Fellow. In 2018 he was invited speaker at the ICM in Rio (Functional Transcendence and arithmetic applications).

Fonts

  • Towards an unconditional proof of the Andre-Oort conjecture and surrounding problems , 2011. (Dissertation)
  • The André-Oort conjecture for . Annals of Mathematics, Volume 187, 2018, pp. 379-390, Preprint 2015. Arxiv
  • Brewer's seal for arithmetic tori and lower bounds for Galois orbits of special points. In: Journal of the American Mathematical Society. Volume 25, 2012, pp. 1091-1117. Arxiv
  • The existence of an abelian variety over isogeneous to no Jacobean. In: Annals of Mathematics. Volume 176, 2012, pp. 637-650. Arxiv
  • with Jonathan Pila: Ax-Lindemann for . In: Annals of Mathematics. Volume 179, 2014, pp. 659-681. Arxiv
  • with Manjul Bhargava , Arul Shankar: On the Davenport-Heilbronn theorems and second order terms. In: Inventiones Mathematicae. Volume 193, 2013, pp. 439-499. Arxiv
  • with Jonathan Pila: André-Oort conjecture for the moduli space of abelian surfaces. In: Composition Mathematica. Volume 149, 2013, pp. 204-216. Arxiv
  • with Benjamin Bakker: p-torsion monodromy representations of elliptic curves over geometric function fields , Annals of Mathematics, Volume 184, 2016, pp. 709–744
  • with Jonathan Pila, Ngaiming Mok: Ax-Schanuel for Shimura Varieties , Annals of Mathematics, Volume 189, 2019, pp. 945–978, Arxiv
  • with Benjamin Bakker: The Ax-Schanuel Conjecture for Variations of Hodge Structures , Inventiones Mathematicae, Volume 217, 2019, pp. 77–94, Arxiv

Web links

Individual evidence

  1. ↑ Jacob Tsimerman in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ F. Andreatta, E.-Z. Goren, B. Howard, K. Madapusi-Pera: Faltings heights of abelian varieties with complex multiplication. Preprint 2015
personal data
SURNAME Tsimerman, Jacob
BRIEF DESCRIPTION Canadian mathematician
DATE OF BIRTH April 26, 1988
PLACE OF BIRTH Kazan