University of Southern California; Member, School of Mathematics
September 9, 2020
This talk will form part of a series of three talks focusing on Broué’s Abelian Defect Group Conjecture, which concerns the modular representation theory of finite groups. We will pay particular attention here to the ‘geometric’ form of the conjecture which concerns finite reductive groups such as GLn(q) and SLn(q). Broué’s conjecture gives a strong structural reason for many numerical coincidences one sees amongst characters and is part of a general ‘local/global phenomena’ that is abundant in the theory.
Surveys of young stellar objects (YSOs) populating nearby molecular clouds are bringing us closer to an integrated picture of star and cluster formation, one that incorporates processes spanning many orders of magnitude in size, from accretion on stellar scales to the formation of clusters and associations on molecular cloud scales. Following a spectacular 15 years of infrared astronomy with Spitzer and Herschel, we now have a nearly compete census of the dusty YSOs (those with disks or infalling envelopes) in the clouds within 500 pc of the Sun.
In a joint work with Laurent Côté we show the following result. Any Lagrangian plane in the cotangent bundle of an open Riemann surface which coincides with a cotangent fibre outside of some compact subset, is compactly supported Hamiltonian isotopic to that fibre. This result implies Hamiltonian unlinkedness for Lagrangian links in the cotangent bundle of a (possibly closed Riemann surface whose components are Hamiltonian isotopic to fibres.