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"An Introduction to A1-Enumerative Geometry"

Geometry-Topology Seminar

Thursday, October 15, 2020 - 4:30pm

Thomas Brazelton

UPenn

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/91890239234 This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

 Abstract: We will discuss an exciting new direction in enumerative geometry, called A1-enumerative geometry or enriched enumerative geometry. This growing body of work incorporates methods from motivic homotopy theory in order to investigate enumerative problems over arbitrary fields, producing solutions valued in the Grothendieck—Witt ring, which can then be geometrically interpreted over your favorite field. We will discuss various recent results in the program of Kass and Wickelgren, and provide an introduction to the main tool of A1-enumerative geometry, which is a Brouwer degree for varieties as developed by Morel.