# Mathematical Sciences Research Institute

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# Seminar

DAG Seminar: Spaces of Algebraic Cobordism and Derived Algebraic Geometry February 15, 2019 (01:30 PM PST - 02:30 PM PST)
Parent Program: Derived Algebraic Geometry MSRI: Simons Auditorium
Speaker(s) Elden Elmanto (Harvard University)
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In previous joint work with Hoyois, Khan, Sosnilo and Yakerson we obtained (up to group completion) a geometric description of the $0$-th space of the motivic sphere spectrum in terms of a certain torsor over an open subscheme of the Hilbert scheme of points in infinite dimensional affine space. The base scheme is smooth and turns out to describe the $0$-th space of Voevodsky's algebraic cobordism spectrum. The problem of describing the $n$-th space is currently in progress and the description involves the moduli of derived schemes of virtual dimension $-n$.

In this talk, I will discuss these results and some of its corollaries, especially those concerning generation results on Chow groups of smooth complex varieties. A gentle introduction to motivic homotopy theory and previous work will be included.

All this is joint with Hoyois, Khan, Sosnilo and Yakerson.

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