Mathematics Department - Complex Analysis and Geometry Seminar - Spring 2017

Complex Analysis and Geometry Seminar - Spring 2017



Organizer(s)

Xiaojun Huang, Jian Song, Sagun Chanillo

Archive



Upcoming Talks


Friday, March 24th

Special Complex Analysis and Geometry Seminar

Yumeng Ou, MIT

"Sparse domination of singular integral operators"

Time: 10:30 AM
Location: Hill 705
Abstract: It is discovered recently by Lacey (and refined by Lerner) that Calder'on-Zygmund (CZ) operators, which are a priori non-local, can be dominated pointwisely by a class of local, positive, sparse averaging operators. This in particular implies sharp weighted norm inequalities for CZ operators. In a series of joint works with A. Culiuc and F. Di Plinio, we show that sparse domination can be obtained in contexts well beyond CZ theory, such as for rough homogeneous singular integrals, Bochner-Riesz multipliers, and even modulation invariant multilinear singular integrals including the bilinear Hilbert transforms. Many new sharp weighted estimates for these operators then follow immediately.





Past Talks


Friday, February 17th

Andrew Zimmer , University of Chicago

"Metric spaces of non-positive curvature and applications in several complex variables"

Time: 10:30 AM
Location: Hill 705
Abstract: In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps.

Some of what I will talk about is joint work with Gautam.


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