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UID:f07458e391f1047195351efd1c168623
CATEGORIES:Applied and Computational Math Seminar
CREATED:20240129T155815
SUMMARY:Understanding Multivariate Gaussian Models via Toric Geometry
LOCATION:Hill 705
DESCRIPTION:<p><span style="color: #212529; font-family: 'Open Sans', sans-serif; font-
 size: 16px; font-style: normal; font-weight: 400; letter-spacing: normal; o
 rphans: 2; text-align: start; text-indent: 0px; text-transform: none; widow
 s: 2; word-spacing: 0px; white-space: normal; background-color: #ffffff; fl
 oat: none;">Lately, algebraic geometry has been offering a novel approach t
 o advancing problems on multivariate Gaussian models. This is done by ident
 ifying Gaussian distributions with symmetric matrices and analyzing the set
  of polynomials that vanish on these matrices, referred to as ideals. The t
 alk will focus on Brownian motion tree (BMT) models – Gaussian models in ph
 ylogenetics. These models have a hidden toric geometry, which we use to adv
 ance questions on their maximum likelihood estimate. Lastly, motivated by t
 he need to classify toric statistical models, we introduce the symmetry Lie
  group of an ideal and an associated algorithm as a means to detect non-tor
 ic structures in a general setting. No prior knowledge on toric ideals or B
 MT models&nbsp;is assumed.</span></p>
CONTACT:Aida Maraj (Harvard University)
DTSTAMP:20260907T105033
DTSTART;TZID=America/New_York:20240207T110000
DTEND;TZID=America/New_York:20240207T120000
SEQUENCE:0
TRANSP:OPAQUE
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