[Liste-CICMA] Michael Lipnowski, University of Toronto, December 16 at 16hrs.
martinez at crm.umontreal.ca
Tue Dec 13 15:07:09 EST 2016
Michael Lipnowski University of Toronto
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Burnside Hall Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Topological Explosion and Supercancellation in Arithmetic Statistics
Abstract: The fundamental question (*) How many solutions does a system of polynomial equations have modulo a fixed prime number p? drives the burgeoning field of arithmetic statistics.
Understanding the statistical behavior of the number of solutions within families of algebraic varieties of increasing complexity is subtle due to "topological explosion". We will describe several interesting families exhibiting topological explosion and the "supercancellation" necessary for proving that the statistics of (*) are captured by reasonable heuristic models.
We will also discuss joint work with Jacob Tsimerman on the failure of supercancellation for abelian varieties of large dimension over finite fields. This failure results in some statistically counterintuitive behavior. For example, most principally polarized abelian varieties of large dimension over a fixed finite field are essentially powers of elliptic curves and do not obey Cohen-Lenstra heuristics.
Responsable des laboratoires
Centre de recherches mathématiques
Université de Montréal
Case postale 6128, Succursale centre-ville
tel: (514) 343-7574
(514) 398-3826 (mercredis)
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