Want to suggest a speaker? Send an email to Mahya Ghandehari or Constanze Liaw.
Seminars will be held on Tuesdays from 1:30 pm-2:30 pm in Ewing 336.
Information about the Courtyard Newark - University of Delaware Hotel
|Dr. Apoorva Khare, Indian Institute of Science ||Dr. Apoorva Khare, Indian Institute of Science ||PRN238||Title: Polymath 14: Groups with norms
Abstract: Consider the following three properties of a general group G:
(1) Algebra: G is abelian and torsion-free.
(2) Analysis: G is a metric space that admits a "norm", namely, a translation-invariant metric d(.,.) satisfying: d(1,g^n) = |n| d(1,g) for all g in G and integers n.
(3) Geometry: G admits a length function with "saturated" subadditivity for equal arguments: l(g^2) = 2 l(g) for all g in G.
While these properties may a priori seem different, in fact they turn out to be equivalent. The nontrivial implication amounts to saying that there does not exist a non-abelian group with a "norm".
We will discuss motivations from analysis, probability, and geometry; then the proof of the above equivalences; and finally, the logistics of how the problem was solved, via a PolyMath project that began on a blogpost of Terence Tao.
(Joint - as D.H.J. PolyMath - with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao.)||1/29/2020 7:30:00 PM||1/29/2020 8:30:00 PM||False|
|Dominique Guillot, University of Delaware||Dominique Guillot, University of Delaware||EWG 336||Title:TBA
Abstract: TBA ||2/25/2020 6:30:00 PM||2/25/2020 7:30:00 PM||False|
|Dr. Yemen Choi, Lancaster University||Dr. Yemen Choi, Lancaster University||EWG 336||Title:TBA<br></br>
Abstract:||3/3/2020 6:30:00 PM||3/3/2020 7:30:00 PM||False|
|Dr. Josh Isralowitz, SUNY at Albany||Dr. Josh Isralowitz, SUNY at Albany||EWG 336||Title:TBA<br></br>
Abstract:||3/17/2020 5:30:00 PM||3/17/2020 6:30:00 PM||False|
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