** **In the graph chain complex work of Kontsevich, he computed the graphic orbifold Euler characteristic and showed it may be fascinatingly expressed through Bernoulli numbers. Inspired by this, Madeline Brandt, Juliette Bruce, and Daniel Corey in arXiv: 2301.10108 define a virtual Euler characteristic for any finite set of isomorphism classes of matroids of rank r, then prove this expression simplifies over the finite field F_2 (i.e. binary matroids). Additionally, they apply their methods to craft recursive formulas for subsets of the Grassmannian in the Grothendieck ring of varieties. In the talk, we briefly overview the combinatorial and algebro-geometric aspects of matroids and the Grassmannian before then delving into a discussion of their methods. We conclude the talk with various future directions one could take their work as well.

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# Combinatorial Algebraic Geometry: The Virtual Euler Characteristic for Binary Matroids

Andrew Tawfeek (University of Washington)

Friday, February 3, 2023 - 10:30am to 11:20am

Thomson Hall (THO) 325

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