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DTSTART;TZID=America/New_York:20220203T090000
DTEND;TZID=America/New_York:20220203T100000
DTSTAMP:20260729T165047
CREATED:20240304T105610Z
LAST-MODIFIED:20240304T105610Z
UID:10002902-1643878800-1643882400@cmsa.fas.harvard.edu
SUMMARY:The Amplituhedron BCFW Triangulation
DESCRIPTION:Abstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells\, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.
URL:https://cmsa.fas.harvard.edu/event/2-3-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-2.3.2022.png
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DTSTART;TZID=America/New_York:20220208T090000
DTEND;TZID=America/New_York:20220208T100000
DTSTAMP:20260729T165047
CREATED:20240213T104820Z
LAST-MODIFIED:20240304T105941Z
UID:10002457-1644310800-1644314400@cmsa.fas.harvard.edu
SUMMARY:Invariant theory for maximum likelihood estimation
DESCRIPTION:Abstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola\, Kathlén Kohn\, and Philipp Reichenbach.
URL:https://cmsa.fas.harvard.edu/event/2-8-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-2.8.2022-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220215T090000
DTEND;TZID=America/New_York:20220215T100000
DTSTAMP:20260729T165047
CREATED:20240213T104814Z
LAST-MODIFIED:20240304T100739Z
UID:10002456-1644915600-1644919200@cmsa.fas.harvard.edu
SUMMARY:Equiangular lines and regular graphs
DESCRIPTION:Abstract: In 1973\, Lemmens and Seidel asked to determine N_alpha(r)\, the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently\, this problem has been almost completely settled when r is exponentially large relative to 1/alpha\, with the approach both relying on Ramsey’s theorem\, as well as being limited by it. In this talk\, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation\, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular\, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5). \nOur projection method generalizes to complex equiangular lines in C^r\, which may be of independent interest in quantum theory. Applying this method also allows us to obtain\nthe first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha)\, an extension of the Alon-Boppana theorem to dense regular graphs\, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r\, an improvement to Welch’s bound in coding theory.
URL:https://cmsa.fas.harvard.edu/event/2-15-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
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