• Date:  2024-03-20 (Wed) 
• Place:  129-406  (SNU)
• Speaker:  Matt Larson (Stanford University)   

• Pretalk (15:45 ~ 16:45)

Title: Topology of singularities of complex hypersurfaces
Abstract: The Milnor fibration is a powerful tool to study the topology of a singularity of a complex hypersurface. It can be used to compute the cohomology of a deleted neighborhood of the singularity, which is used to analyze some exotic spheres. I will describe the fundamental theorems governing the topology of hypersurface singularities and how the Milnor fibration can be used to compute topological invariants of them.

• Research talk (17:00 ~ 18:00)

Title: The monodromy conjecture for simplicial nondegenerate singularities
Abstract: Let f be a polynomial with integer coefficients. The monodromy conjecture predicts a relationship between the Igusa zeta function of the hypersurface V(f), which governs the number of solutions to f = 0 (mod p^n) for a prime p, and the eigenvalues of the monodromy action on the cohomology of the Milnor fiber, which is a topological invariant of the complex hypersurface. When f is nondegenerate with respect to its Newton polyhedron, which is true for "generic" polynomials, there are combinatorial formulas for both the Igusa zeta function and the eigenvalue of monodromy. I will describe recent results (joint with S. Payne and A. Stapledon) which prove a version of the monodromy conjecture for nondegenerate polynomials which have a simplicial Newton polyhedron.