Non-Commutative Geometry Seminar @ Keller 404
Apr 14 @ 3:00 pm – 4:00 pm

See organizers Rufus, Alan or Robin for details.

Special Mini-Course: Elodie Pozzi @ Keller 401
Apr 14 @ 3:30 pm – 4:30 pm

Speaker: Elodie Pozzi (U. de Bordeaux)

Title: Hardy spaces of generalized analytic functions in the unit disc

Colloquium: Brett Wick (Washington U.)
Apr 15 @ 3:30 pm – 4:30 pm

Speaker: Brett D. Wick (Washington U.)

Title: Commutators and BMO

Abstract: In this talk we will discuss the connection between functions with bounded mean oscillation (BMO) and commutators of Calderon-Zygmund operators. In particular, we will discuss how to characterize certain BMO spaces related to second order differential operators in terms of Riesz transforms adapted to the operator and how to characterize commutators when acting on weighted Lebesgue spaces.

Analysis Seminar – Brett D. Wick @ Keller 301
Apr 20 @ 2:30 pm – 3:30 pm

Speaker: Brett D. Wick, Washington University

Title: Two Weight Estimates for Commutators

Abstract: In this talk we discuss a modern proof of a result by Bloom
which characterizes when the commutator of a function and the Hilbert
transform is bounded on weighted L^p spaces. Our method of proof
extends Bloom’s result to all dimensions and Calderon-Zygmund
operators. This talk is based on joint work with Irina Holmes and
Michael Lacey.

PhD Defense – Eric Reckwerdt @ Keller 402
Apr 20 @ 3:30 pm – 4:30 pm


Dissertation Draft

Abstract: Weak amenability of discrete groups was introduced by Haagerup and co-authors in the 1980’s. It is an approximation property known to be stable under direct products and free products. In this thesis we show that graph products of weakly amenable discrete groups are weakly amenable (with Cowling-Haagerup constant 1). Along the way we construct a wall space associated to the word length structure of a graph product and also give a method for extending completely bounded functions on discrete groups to a completely bounded function on their graph product.
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Analysis Seminar – Ji Li @ Keller 401
Apr 21 @ 3:30 pm – 4:30 pm

Speaker: Ji Li, Macquarie University

Title: Weak factorization of Hardy spaces and characterization of BMO spaces in the Bessel setting

Abstract: It is well-known that the classical Hardy space $H^p$, $0 “A function $f$ is in $H^1( \mathbb{D})$ if and only if there exist $g,h \in H^2(\mathbb{D})$ with $f= g\cdot h$ and $\|f\|_{H^1(\mathbb{D})}=\|g\|_{H^2(\mathbb{D})}\|h\|_{H^2(\mathbb{D})}$.”

This factorization plays an important role in studying function theory and operator theory connected to the spaces $H^1(\mathbb{D})$, $H^2(\mathbb{D})$ and the space $BMOA(\mathbb{D})$ (analytic BMO). The analogue of the Riesz factorization theorem, sometimes referred to as strong factorization, is not true for real-variable Hardy space $H^1(\mathbb{R}^n)$. Nevertheless, Coifman, Rochberg and Weiss provided a suitable replacement that works in studying function theory and operator theory of $H^1(\mathbb{R}^n)$, the weak factorization via a bilinear form related to the Riesz transform (Hilbert transform in dimension 1).

We study the analogue of the result of Coifman, Rochberg and Weiss for the Hardy spaces associated with differential operators $L$ developed in recently ten years. Then we further provide a characterization of BMO spaces associated with $L$ in terms of the commutators related to the Riesz transform $\nabla L^{-1/2}$. Examples of such operators $L$ include the Neumann Laplacian and the Bessel operators.

This is joint work with Xuan Duong, Brett D. Wick and Dongyong Yang.

Colloquium: Romain Tessera
Apr 26 @ 3:30 pm – 4:30 pm

Speaker: Romain Tessera (Université Paris-Sud)

Title: Local-to-Global rigidity of affine buildings

Abstract: It is well-known that every simply connected homogeneous Riemannian manifold M is “characterized up to isometry” by its ball of radius 1. Precisely: if N is another (not necessarily homogeneous) simply connected Riemannian manifold whose balls of radius 1 are all isometric to a ball of radius 1 in M, then M and N must be isometric.
In this talk, we investigate an analogous property for singular metric spaces, such as Cayley graphs of finitely generated groups, affine buildings…
This is joint work with Mikael de la Salle.

Undergraduate Colloquium – Nodari Sitchinava (ICS, UH Mānoa) @ Bilger 335
Apr 28 @ 3:00 pm – 3:50 pm