Seminari del Dipartimento



The conjectures of Lang and Vojta

Ariyan Javanpeykar 

17-02-2022 - 10:00
Largo San Leonardo Murialdo, 1


 Why do some polynomial equations have only finitely many solutions in the integers? Lang-Vojta's conjecture provides a conjectural answer and relates this number-theoretic question to complex geometry. Indeed, conjecturally, a variety has only finitely many rational points if and only if it is hyperbolic. I will start out this talk explaining the Lang-Vojta conjectures, and will then present new results on dynamical systems of hyperbolic varieties, rational points on ramified covers of abelian varieties, the fundamental group of a variety covered by many pointed curves, and rigidity results for families of canonically polarised varieties. These results are mathematically independent, but all guided by the conjectures of Lang-Vojta.

Il seminario sarà presentato in presenza nell'aula M2. Tutti gli afferenti all'università Roma Tre potranno accedere previa esibizione del greenpass. Gli esterni che fossero interessati a partecipare possono contattare gli organizzatori all'email

Il seminario sarà anche seguibile via Teams seguendo il seguente Link:
org: Turchet Amos

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