Unless specified, all seminars are Wednesday 4-5pm via Zoom. For Zoom information please send email to hfli@math.buffalo.edu

September 29

Abstract

October 20

called fiberwise amenability. Another one is called almost elementariness, which is a new finite-dimensional approximation property. I will explain

how these notions relate to almost finiteness defined by Matui and refined by Kerr and show our almost elementariness implying tracial Z-stability

of reduced groupoid C*-algebras. As an application. This implies that Matui's almost finiteness in the groupoid setting also implies Z-stability when

the groupoid is minimal 2nd countable and topological amenable. This was open in general before. I will also present more applications if time

permits. This is based on joint work with Jianchao Wu.

November 3

Weighted sstimates for the Bergman and Szego projections on strongly pseudoconvex domains

the mapping properties of these operators on L^p and other function spaces have been extensively studied. In this talk, we discuss some recent

results for these operators on strongly pseudoconvex domains with near minimal boundary smoothness. In particular, weighted L^p estimates are

obtained, where the weight belongs to a suitable generalization of the Bekolle-Bonami or Muckenhoupt class. For these domains with less

boundary regularity, we use an operator-theoretic technique that goes back to Kerzman and Stein. We also obtain weighted estimates for the

endpoint p=1, including weighted weak-type (1,1) estimates. Here we use a modified version of singular-integral theory and a generalization of the

Riesz-Kolmogorov characterization of precompact subsets of Lebesgue spaces. This talk is based on joint work with Brett Wick and Cody Stockdale.

November 10

Non-orientable link cobordisms and torsion order in Floer homologies

oriented knot cobordism using a version of knot Floer homology. In this talk I will be discussing some similar inequalities for non-orientable knot

cobordisms using the torsion orders of unoriented versions of knot Floer homology and instanton Floer homology. This is a joint work with Marco

Marengon.

November 17

Construction of a C*-algebraic quantum groupoid from purely algebraic data

spaces are needed, which can be daunting. Things can become simpler if there exists a certain projection, E, which can be considered as Delta(1). At

the purely algebraic level, there exists a natural notion called Weak Multiplier Hopf algebras, which include as special cases Hopf algebras, Multiplier

Hopf algebras, and Weak Hopf algebras. In this talk, we will start from only a purely algebraic data of a WMHA, assuming the existence of a left-invariant functional, and aim to construct a

C*-algebraic object, which should be a C*-algebraic quantum groupoid. The construction data will be all purely algebraic, and we will use tools from

the (vN and C*-) weight theory.

December 1

Chain groups and center reconstruction for locally compact groups

chain group of that category: the universal group by which the category in question can be graded.

Trying to extend this to locally compact groups raises a number of interesting questions I will mention, along with extensions of Muger's theorem to

various classes of groups (e.g. discrete groups with infinite conjugacy classes, semisimple connected Lie groups, and others).

December 8

Shifted sums of Hecke eigenvalue squares

open, but Matomaki, Radziwill and Tao showed that the asymptotic formulas hold for almost all shifts. In this talk, we will talk about an analogue of

the additive divisor problem for Hecke eigenvalue squares.

Past Analysis Seminar