Time：15:00-16:00, Tuesday, October 13 2026
Venue：E14-215
Speaker：Ruiran Sun, Xiamen Univesity
Title：On the global rigidity of period maps for certain families of varieties
Abstract：Motivated by Farb's question on the global rigidity of period maps and the effective Geometric Shafarevich Conjecture, we introduce the notion of $h$-deformation rigidity: a holomorphic map is $h$-deformation rigid if it is the unique holomorphic map in its homotopy class. Using harmonic mapping theory, we develop a geometric criterion for this property and prove $h$-deformation rigidity for several natural period maps between moduli spaces or Shimura varieties. In particular, we study the global rigidity problem for the period map induced by Kummer construction, and obtain some explicit estimate on $\#\mathrm{Hol}_{\mathrm{nc}}(\mathcal A_2,\mathcal F_4)$ via $h$-deformation rigidity and lattice theory. This talk is based on joint work with Cong Ding and Fei Si.
