Wed, Nov 19

Analysis Seminar
Alexandru Chirvasitu (UB)
Spectrum incompressibility and continuous commutativity preservers
4:00PM, Mathematics Building, 110 Mary Talbert Way, University at Buffalo, NY 14260, USA

The Kaplansky-Aupetit question of whether Jordan epimorphisms between unital semisimple Banach algebras can be characterized as linear spectrum-shrinking surjections has spawned a vast literature on adjacent problems having to do with characterizing associative/Jordan morphisms as maps preserving various properties orinvariants. The talk's central result is to the effect that continuous, commutativity-preserving, spectrum-shrinking maps from \(X\) to the \(n\times n\)matrices are either conjugations or transpose conjugations whenever \(n\ge 3\)and \(X\) is any one of: the general linear, special linear or unitary \(n\timesn\) group, the set of semisimple matrices in either of the first two, or the set of \(n\times n\) normal matrices. Such maps in particular automatically preserve spectra, hence the title's ``incompressibility''. The proof leverages among other things the Fundamental Theorem of Projective Geometry, characterizing isomorphisms between lattices of subspaces as those induced by semi-linear isomorphisms.(joint with I. Gogi\'{c} and M. Toma\v{s}evi\'{c})

Mon, Dec 1

Algebra Seminar
Mahdi Asgari, Oklahoma State University and Cornell
Some dyadic Hecke algebras 
4:00PM, Mathematics Building, 110 Mary Talbert Way, University at Buffalo, NY 14260, USA

The Iwahori-Hecke algebras (in their variousincarnations) are ubiquitous in the representation theory of both finite groupsof Lie type, thanks to the works of Lusztig and others, and \(p\)-adic groups,following work of Howe-Moy and Bushnell-Kutzko among many others. In this talkI will focus on these objects in the often overlooked case of \(p=2\) and reporton current joint work with Dan Barbasch. I hope to also explain our motivationfor this study, which stems from studying certain interesting representationsof non-linear cover groups.

Mon, Dec 8

Algebra Seminar
Mihai Fulger, University of Connecticut
Infinitesimal successive minima and convex geometry 
4:00PM, 250 Mathematics Building

We introduce infinitesimal successive minima of a line bundle at a point. We define them in terms of base loci and show that they are also the lengths of the largest simplex contained in the generic infinitesimal Newton-Okounkov body (iNObody) of the line bundle at the point.  We characterize when the generic iNObody is simplicial. When the point is sufficiently general, we prove that the body is Borel-shaped, a property inspired by generic initial ideals. In particular, it satisfies simplicial lower bounds and polytopal upper bounds determined by its widths, which are again the infinitesimal successive minima. This is joint work with Victor Lozovanu

Fri, Feb 13

Applied Math Seminar
Di Qi (Purdue University)
4:00PM

Fri, Apr 10

Applied Math Seminar
Yulong Lu (U Minnesota)
4:00PM