Algebra and Number Theory Seminar
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Posted February 6, 2020

Last modified February 27, 2020

John Doyle, Louisiana Tech University

Dynamical modular curves and uniform boundedness of preperiodic points

In the mid-1990's, Merel proved the strong uniform boundedness conjecture for torsion points on elliptic curves over number fields. Around the same time, work of Nguyen-Saito and Abramovich established the function field analogue by showing that the gonalities of the modular curves X_1(n) tend to infinity. By studying the geometry of dynamical modular curves, one can prove uniform boundedness for preperiodic points for certain interesting families of polynomial maps over function fields. I will discuss this result as well as a consequence for the dynamical uniform boundedness conjecture over number fields, originally posed by Morton and Silverman. This is joint work with Bjorn Poonen.

Computational Mathematics Seminar

Posted February 15, 2020

3:30 pm - 4:30 pm Digital Media Center 1034
Li Wang, University of Texas at Arlington

Probabilistic Semi-supervised Learning via Sparse Graph Structure Learning

Abstract: We present a probabilistic semi-supervised learning (SSL) framework based on sparse graph structure learning. Different from existing SSL methods with either a predefined weighted graph heuristically constructed from the input data or a learned graph based on the locally linear embedding assumption, the proposed SSL model is capable of learning a sparse weighted graph from the unlabeled high-dimensional data and a small amount of labeled data, as well as dealing with the noise of the input data. Our representation of the weighted graph is indirectly derived from a unified model of density estimation and pairwise distance preservation in terms of various distance measurements, where latent embeddings are assumed to be random variables following an unknown density function to be learned and pairwise distances are then calculated as the expectations over the density for the model robustness to the data noise. Moreover, the labeled data based on the same distance representations is leveraged to guide the estimated density for better class separation and sparse graph structure learning. A simple inference approach for the embeddings of unlabeled data based on point estimation and kernel representation is presented. Extensive experiments on various data sets show the promising results in the setting of SSL compared with many existing methods, and significant improvements on small amounts of labeled data. div

Geometry and Topology Seminar
Seminar website

Posted January 30, 2020

3:30 pm - 4:30 pm Lockett 233
Eva Elduque, University of Michigan

TBA

Harmonic Analysis Seminar
Abstract and additional information

Posted February 7, 2020

Last modified February 16, 2020

Gestur Olafsson, Mathematics Department, LSU

Toeplitz operators and representation theory II

We will discuss the basic ideas how representation theory can be used in the Theory of Toeplitz operators. We start with a general set up of a group acting on a complex manifold with a quasi-invariant measure such that there are non-trivial holomorphic L^2-functions and discuss how that leads to Toeplitz operators. We then introduce several examples. We then connect this to representation theory and explain how representation theory can be used to obtain commutative C^*-algebras of Toeplitz operators. Finally we describe how those ideas can be used to determine the spectrum of the so obtained C^*-algebra by constructing an isomorphism into a L^2-space which is easier to understand. The talks should be accessible to graduate students. We will at least use two seminar talks for the material.

Most of this material is a joint work with M. Dawson and R. Quiroga.

Colloquium
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Posted February 9, 2020

3:30 pm - 4:20 pm Lockett 232
Thang Le, Georgia Tech

TBD

Applied Analysis Seminar
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Posted December 2, 2019

3:30 pm Lockett 233
Rudi Weikard, University of Alabama at Birmingham

Title pending

Geometry and Topology Seminar
Seminar website

Posted November 11, 2019

3:30 pm - 4:30 pm Lockett 233
Zhenkun Li, MIT

TBA

Geometry and Topology Seminar
Seminar website

Posted February 7, 2020

3:30 pm - 4:30 pm Lockett 233
Mitul Islam, University of Michigan

TBA

Colloquium
Questions or comments?

Posted January 29, 2020

3:30 pm - 4:20 pm Lockett 232
Phillip Isett, UT Austin

TBD

Algebra and Number Theory Seminar
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Posted January 14, 2020

Spring Break

Algebra and Number Theory Seminar
Questions or comments?

Posted January 14, 2020

3:10 pm - 4:00 pm 232 Lockett
Walter Bridges, Louisiana State University

TBA

Geometry and Topology Seminar
Seminar website

Posted January 21, 2020

3:30 pm - 4:30 pm Lockett 233
Kyle Hayden, Columbia University

TBA

Algebra and Number Theory Seminar
Questions or comments?

Posted January 14, 2020

3:10 pm - 4:00 pm 232 Lockett
Shashika Mestrige, Louisiana State University

TBA

Undergraduate Student Colloquium

Posted February 14, 2020

Steve Butler, Iowa State University

Undergraduate Student Colloquium Talk

Harmonic Analysis Seminar
Abstract and additional information

Posted February 7, 2020

Last modified February 16, 2020

Raul Quiroga, Centro de Investigacion en Matematicas (cimat)

To be Announced

Posted February 14, 2020

Steve Butler, Iowa State University

Graduate Student Colloquium

Algebra and Number Theory Seminar
Questions or comments?

Posted January 14, 2020

Last modified January 15, 2020

Alyson Deines, Center for Communications Research La Jolla (CCR-L)

TBA

Colloquium
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Posted January 15, 2020

3:30 pm - 4:20 pm Lockett 232
Lenhard Ng, Duke University

TBD

Undergraduate Student Colloquium

Posted January 13, 2020

Last modified February 8, 2020

Shelly Harvey, Rice University

Undergraduate Talk

Posted January 13, 2020

Last modified February 8, 2020

Shelly Harvey, Rice University

Graduate talk