Time：14:00-15:00, Friday, July 11 2025
Venue：E4-233
Host: Xing Gu, ITS
Speaker：Marc Levine, University Duisburg-Essen
Biography: Prof. Levine graduated from the Massachusetts Institute of Technology (bachelor's degree in 1974) and earned his doctorate in 1979 from Brandeis University under Teruhisa Matsusaka. He was an assistant professor at the University of Pennsylvania from 1979 and at Northeastern University from 1984, where he has been an associate professor since 1986 and a professor since 1988. Since 2009, he has been an Alexander von Humboldt Professor at the University Duisburg-Essen. In 2001 he received the Wolfgang Paul Award of the Alexander von Humboldt Foundation, and in 2006 received the Humboldt Research Award. In 2013 he was elected to the Leopoldina. In 2018 he was awarded the Senior Berwick Prize of the London Mathematical Society.
Prof. Levine works in algebraic geometry, in particular in the development of analogues of concepts from algebraic topology in algebraic geometry and the theory of motives (motivic cohomology, motivic homotopy, algebraic K-theory). He developed, together with Fabien Morel, the theory of algebraic cobordism, an algebraic geometry analog of the theory of cobordism in algebraic topology. In 2002, he was an invited speaker at the ICM in Beijing.
Title：Enumerative geometry-classical, quadratic and real
Abstract: Enumerative geometry is a branch of algebraic geometry with a rich history. The goal is to count solutions to geometric problems: how many intersection points do two plane curves have, how many lines in 3-space intersect four general lines, how many cubic plane curves passing through 8 general points are rational, how many rational cubic space curves lie on a general quintic hypersuface in four space … Over the complex numbers, these questions can be approached through intersection theory, the calculus of counting intersections of subvarieties of a given variety. Over other fields, such as the reals, the rationals, or finite fields, these essentially geometric methods do not suffice. Here we discuss a recent approach to these more subtle aspects of enumerative geometry that involves another classical theory: the theory of quadratic forms.
