Upcoming Talks

The seminar will meet online at 16:30 EDT on Monday.

In accordance with MIT guidelines, the seminar will be meeting on Zoom until further notice. Click here to join the seminar on Zoom. If you do not have Zoom installed, you will be prompted to install it. The Zoom meeting room number is 132-540-375.

http://math.mit.edu/topology/topology_seminar.ics

• Oct 052020

Jonathan Campbell (Center for Communications Research La Jolla)

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Homotopy Theory and Hilbert's Third Problem

In this talk I'll explain how one might attack Hilbert's Generalized Third Problem via homotopy theory, and describe recent progress in this direction. Two n-dimensional polytopes, $P$, $Q$ are said to be scissors congruent if one can cut $P$ along a finite number of hyperplanes, and re-assemble the pieces into $Q$. The scissors congruence problem, aka Hilbert's Generalized Third Problem, asks: when can we do this? What obstructs this? In two dimensions, two polygons are scissors congruent if and only if they have the same area. In three dimensions, there is volume and another invariant, the Dehn Invariant. In higher dimensions, very little is known — but the problem is known to have deep connections to motives, values of zeta functions, the weight filtration in algebraic K-theory, and regulator maps. I'll give a leisurely introduction to this very classical problem, and explain some new results obtained via homotopy theoretic techniques. This is all joint with Inna Zakharevich.

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• Oct 192020

Ben Knudsen (Northeastern University)

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Smooth structures and embedding calculus

We ask when embedding calculus can distinguish pairs of smooth manifolds that are homeomorphic but not diffeomorphic. We prove that, in dimension 4, the answer is "almost never". In contrast, we exhibit an infinite list of high-dimensional exotic spheres detected by embedding calculus. The former result implies that the algebraic topology of knot spaces is insensitive to smooth structure in dimension 4, answering a question of Viro. The latter result gives a partial answer to a question of Francis and hints at the possibility of a new classification of exotic spheres in terms of a stratified obstruction theory applied to compactified configuration spaces. This talk represents joint work with Alexander Kupers.

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• Oct 262020

• Nov 022020

• Nov 092020

• Nov 162020

• Nov 302020

• Dec 072020

Jeremy Hahn (MIT)

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In response to the accessibility ruling, we have implemented Kerberos authentication for the recordings of past talks.