You are cordially invited to the seminars organized by the Department of Mathematics.
Speaker: Ratko Darda (Sabancı University)
“Manin’s conjecture beyond varieties”
Abstract: A central question in number theory asks how the solutions to polynomial equations are distributed among the rational numbers. The answer turns out to depend strongly on the geometry of the corresponding variety – the space defined by those equations.
When rational solutions are plentiful, their behavior is predicted by Manin’s conjecture, a deep insight from the 1990s that connects arithmetic counts with geometric invariants. This conjecture has guided much of modern research in Diophantine geometry.
Our recent work places Manin’s conjecture in a new setting—that of stacks, geometric objects that generalize varieties by capturing symmetries and moduli phenomena. This broader perspective not only extends the conjecture but also sheds light on arithmetic phenomena such as the occurrence of Galois extensions, a topic that, at first glance, seems unrelated to counting solutions of polynomial equations.
Date: November 17, Monday
Time: 11:00 (Turkey)
Place: Zoom
To request the event link, please send a message to turker.ozsari@bilkent.edu.tr