Introduction:
We plan to organize a seminar on homogeneous dynamics and L-functions, mainly studying the following two works of Khayutin:
K21: Equidistribution on Kuga–Sato varieties of torsion points on CM elliptic curves
K19: Joint equidistribution of CM points
In terms of the learning order, we intend to read K21 first, using it as a relatively accessible example to become familiar with Khayutin's methods, and then move on to K19. Our initial goal is to understand how, by means of measure rigidity and the relative trace formula, the equidistribution problem for torus orbits can be reduced to subconvexity estimates for L-functions or sieve methods, and then to learn methods for handling these analytic number theory problems.
The seminar is planned to start on September 23, and will meet once every two weeks on Wednesdays at 10 a.m. in Morningside 610.
If you have any questions, please feel free to contact us (mcmoffice@math.ac.cn).
Organizers:
Ruida Di
Time & Venue:
Each Wednesdays, once every two weeks, MCM610
Upcoming talks:
Date: October 14, 2026
Time: 10:00-11:30
Place: MCM 610
Speaker: Mengyang Wang (AMSS)
Title: Geometric Expansion of Relative Trace Formula
Abstract: In this talk, we will use the geometric expansion of the relative trace formula to reduce the problem of calculating the measure of Bowen balls to the computation of relative orbital integrals. Using an invariant map, we will then reformulate these orbital integrals as an ideal-counting problem, which in turn leads to a modified Hecke \(L\)-function. Finally, we will explain how a subconvex bound for this modified Hecke \(L\)-function yields the desired estimate. The proof of the subconvex bound will be deferred to the next talk.
Date: September 23, 2026
Time: 10:00-12:00
Place: MCM 610
Speaker: Mengyang Wang (AMSS)
Title: Equidistribution on Kuga-Sato variety, Measure Rigidity of Torus Orbits and Relative Trace Formula.
Abstract: This talk introduces Khayutin's approach to the equidistribution of genus orbits of special points on Kuga–Sato varieties. We will explain how the problem is reformulated in terms of adelic torus orbits and how measure rigidity restricts the possible limiting measures. We will then discuss how the geometric expansion of a relative trace formula converts cross-correlation bounds into arithmetic counting problems, and outline their connection to subconvexity estimates for Hecke L-functions.
