Upcoming Seminars

Title: How much can one learn a PDE from its solution?
Seminar: Analysis and Differential Geometry
Speaker: Yimin Zhong of Auburn University
Contact: Yiran Wang, yiran.wang@emory.edu
Date: 2022-12-01 at 4:00PM
Venue: PAIS 230
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Abstract:
In this work we study a few basic questions for PDE learning from observed solution data. Using various types of PDEs, we show 1) how the approximate dimension (richness) of the data space spanned by all snapshots along a solution trajectory depends on the differential operator and initial data, and 2) identifiability of a differential operator from solution data on local patches. Then we propose a consistent and sparse local regression method (CaSLR) for general PDE identification. Our method is data driven and requires minimal amount of local measurements in space and time from a single solution trajectory by enforcing global consistency and sparsity.
Title: Complex Dynamics of Rational Maps
Seminar: Analysis and Differential Geometry
Speaker: Ylli Andoni of Emory University
Contact: Shanshuang Yang, syang05@emory.edu
Date: 2022-12-06 at 4:00PM
Venue: MSC W301
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Abstract:
We will look at the iteration of rational functions of one complex variable and study the behaviour of points in the complex sphere under such iterations. Such iterations split the plane into two sets, that of well-behaved and that of ill-behaved points known as the Fatou set and the Julia set respectively. The notion of equicontinuity will be used to formally define these two sets and we will relate this to normality as well. Properties of the Fatou and Julia sets will be looked at and topological consequences will be established as well.