This special topic school is on problems of "point counting" in number theory, with connections to analytic number theory, algebraic number theory, algebraic geometry, harmonic analysis, and logic. Recent work has resolved nearly all cases of a long-standing 1980's conjecture of Serre on counting rational points in projective thin sets, and lecture series will describe two approaches to these problems. First: determinant methods, which originated in work of Bombieri and Pila in the 1990's, and have been successfully developed in a wide variety of settings. Second: the polynomial sieve method, which was developed recently by Bonolis, Pierce and Woo, and has connections to character sums, L-functions, and the Generalized Riemann Hypothesis. Problems of counting points are also inherently connected to studying heights. Lecture series will describe ongoing work in the theory of heights of algebraic numbers, with connections to Diophantine analysis, the geometry of numbers, and the structure of number fields.
The deadline for the application for participation is January 4, 2027.
Our Global Mobility Fellowships provide participation opportunities for selected researchers and PhD students from countries of the Global South in the Special Topic Schools of the Hausdorff School for Mathematics. For more information, please visit our website.
Lecture series by:
- Shabnam Akhtari (Penn State University)
- Raf Cluckers (CNRS, University of Lille/KU Leuven)
- Jonathan Pila (University of Oxford)
- Martin Widmer (Graz)
- Katharine Woo (ETH)
Scientific Organizers:
- Shabnam Akhtari (Penn State University)
- Raf Cluckers (CNRS, University of Lille/KU Leuven)
- Lillian Pierce (Duke University)