Speaker: Dinxin Zhang (Yau Mathematical Sciences Center, Tsinghua University)
Time: 10:00-11:00, Oct 10, 2024
Room: C1124, the Material and Science Research Building (section C)
Suppose V is a subspace of C^n, cut out by polynomial equations of degree ≤ d. Let B(V) be the sum of the compactly supported Betti numbers of V. In the 90s, Katz demonstrated that B(V) does not exceed Cd^(n+1) for some constant C depending only on n. Previously, Milnor and Thom had provided a less accurate upper bound of Cd^(2n). In this talk, I will explain how to deduce a sharper upper bound, B(V) ≤ Cd^n, using the characteristic p method. Time permitting, I will also discuss the relation of this bound with the Hodge theory of polynomial maps. This is a joint work with Daqing Wan.
