| Friday 17 May 2024 | |
| Events for day: Monday 06 May 2024 |
| 14:30 - 16:00 Lecture Controlling Growth Rate of Rational Points by Systole School MATHEMATICS Let $X$ be a complex ball quotient by a nonuniform neat lattice in $PU(n,1)$. Using hyperbolic geometry, we establish a uniform lower bound on the volume of subvarieties of $X$ in terms of the systole, a geometric quantity that measures the shortest closed geodesic in $X$. We combine this result with the strategy of Bombieri-Pila to show that if the toroidal compactification of $X$ is defined over a number field $K,$ then, under a mild assumption on $X,$ the systole of $X$ controls the growth rate of $K$-rational points on $X$. Online via zoom: Meeting ID: 908 611 6889 Passcode: 362880 Venue: Niavaran, ... |