Seminari del Dipartimento

 

Geometria

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 amos.turchet@uniroma3.it.

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

https://teams.microsoft.com/l/meetup-join/19%3a83395ad07b844acdafb3fff3e977ef5d%40thread.tacv2/1643808710522?context=%7b%22Tid%22%3a%22ffb4df68-f464-458c-a546-00fb3af66f6a%22%2c%22Oid%22%3a%22cade3502-1fa9-4fd8-a9e6-8a2cc994de29%22%7d
org: Turchet Amos

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