Time: 13:00
Speaker: James Richardson (Western)
Title: "Presentable infinity categories"
Room: MC 107

Abstract: I will introduce presentable quasicategories and discuss some of their properties. I will then discuss their relationship with combinatorial model categories.

Time: 15:30
Speaker: Pinaki Mondal (School of Mathematics, Physics and Technology at The College of the Bahamas)
Title: "Milnor number, intersection multiplicity and number of zeroes of systems of polynomials"
Room: MC 107

Abstract: We talk about two of the original problems that shaped the theory of Newton polyhedra: the problem of computing the Milnor number of the singularity at the origin of a generic polynomial, and computing the number of zeroes of generic polynomials. The former was addressed by Kushnirenko, who gave a beautiful formula in terms of Newton diagrams in a special case.Bernstein (following work of Kushnirenko) solved completely the latter problem for the case of (C^*)^n. In the case of C^n the problem was partially solved following the work of Khovanskii, Huber-Sturmfels, and many others. We give complete solution to both these problems. A common theme in our solution to both problems is the computation of intersection multiplicity at the origin of the hypersurfaces determined by n generic polynomials.