[Colloquium] Colloquium: Combinatorics, Hodge Theory, and Beyond (Karim Adiprasito)

[Mat Wimberly]

Hi all,

The Department of Mathematics will be hosting a Colloquium today at 3:00pm
by Karim Adiprasito of Hebrew University and University of Copenhagen. The
zoom link can be found below.

*Abstract:*

I will survey applications of Hodge Theory to combinatorics, and, quite
surprisingly, how Hodge-Riemann relations and Lefschetz type theorems can
be proven using combinatorial methods, in settings that are beyond
classical projective algebraic geometry.

I then go one step further, and discuss how many triangles a PL embedded
simplicial complex in R^4 can have (the answer, generalizing a result of
Euler and Descartes, is at most 4 times the number of edges). I discuss how
to reduce this problem to a Lefschetz property beyond projective structure,
and indicate the proof of the Lefschetz property in this case, replacing
positivity with anisotropy of subspaces in the Hodge-Riemann pairing.
If time permits, I will then discuss relations to the Singer conjecture for
aspherical manifolds.
*Zoom Link:*
Topic: Karim Adiprasito: Combinatorics, Hodge Theory, and Beyond
Time: Sep 30, 2020 03:00 PM Central Time (US and Canada)

Join Zoom Meeting
https://uchicago.zoom.us/j/97140278548?pwd=ZVhaQy81UlZrQ3M0SEZnNENLVlRhZz09

Password: 509471

Thanks,
Mat

-- 
*Mat Wimberly | Project Assistant III*
*matwimberly at math.uchicago.edu <matwimberly at math.uchicago.edu>*
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