Informal Geometry and Topology Seminar
Questions or comments?

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233
Abel Lopez, Louisiana State University

TBD

Colloquium
Questions or comments?

Posted September 24, 2019

Last modified November 2, 2019

John Voight, Dartmouth College

Heuristics for units in number rings

Units in number rings are gems of arithmetic, the most famous being the golden ratio and the integer solutions x,y to Pell's equation x^2 - D*y^2 = +/-1 for D > 0. Like gems, they are embedded deeply within. Refined questions about the structure of units remain difficult to answer, for example: how often does it happen that Pell's equation has a solution to the -1 equation? More generally, how often in a number ring is it that all totally positive units are squares? Absent theorems, we may still try to predict the answer to these questions. In this talk, we present heuristics (and some theorems!) for signatures of unit groups inspired by the Cohen-Lenstra heuristics for class groups, but involving an lustrous structure of number rings we call the 2-Selmer signature map. This is joint work with David S. Dummit and Richard Foote and with Ben Breen, Noam Elkies, and Ila Varma.

Undergraduate Student Colloquium

Posted October 15, 2019

Last modified October 16, 2019

Steven Leth, University of Northern Colorado

TBA

Applied Analysis Seminar
Questions or comments?

Posted November 8, 2019

Last modified November 9, 2019

F. Alberto Gr¨unbaum, University of California, Berkeley

Quantum walks: a nice playground for old and new mathematics.

I will give an ab-initio talk trying to show how some time honored pieces of analysis can be used to answer questions about recurrence of quantum walks. I will start with a quick review of classical random walks and then show how Schur functions (the same I. Schur of many other deep topics) are useful in the quantum case. Recently these Schur functions have been seen to be useful in getting a topological classification of quantum walks that respect certain symmetries but go beyond the translation invariant case. I will not assume any previous knowledge about quantum walks. This is joint work with Jean Bourgain, Luis Velazquez, Reinhard Werner, Albert Werner and Jon Wilkening.

Posted October 15, 2019

Last modified October 16, 2019

Steven Leth, University of Northern Colorado

TBA

Algebra and Number Theory Seminar
Questions or comments?

Posted October 11, 2019

3:10 pm - 4:00 pm 285 Lockett
Ignacio Nahuel Zurrian, Universidad Nacional de Cordoba (National University of Cordoba)

TBA

Computational Mathematics Seminar

Posted September 9, 2019

Last modified October 13, 2019

Yakui Huang, Hebei University of Technology

On the Asymptotic Convergence and Acceleration of Gradient Methods

Abstract: We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two dimensional strictly convex quadratic function. It is shown that, for the general quadratic function, the proposed stepsize asymptotically converges to the reciprocal of the largest eigenvalue of the Hessian. Furthermore, based on this spectral property, we propose a periodic gradient method by incorporating the Barzilai-Borwein method. Numerical comparisons with some recent successful gradient methods show that our new method is very promising.

Informal Geometry and Topology Seminar
Questions or comments?

Posted September 11, 2019

1:30 pm - 3:00 pm Lockett 233
John Lien, Louisiana State University

TBD

Harmonic Analysis Seminar
Abstract and additional information

Posted August 16, 2019

3:30 pm - 4:20 pm
Tao Mei, Balyor University

TBA

Colloquium
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Posted September 10, 2019

3:30 pm - 4:20 pm TBD
Leonid Berlyand, Department of Mathematics, Penn State University

TBD

Applied Analysis Seminar
Questions or comments?

Posted September 6, 2019

3:30 pm - 4:30 pm Lockett 233
Isaac Michael, Louisiana State University

TBA

Algebra and Number Theory Seminar
Questions or comments?

Posted October 11, 2019

3:10 pm - 4:00 pm 285 Lockett
Kent Vashaw, Louisiana State University

TBA

Colloquium
Questions or comments?

Posted September 13, 2019

3:30 pm - 4:20 pm TBD
Eric Rowell, Texas A&M

TBD

Geometry and Topology Seminar
Seminar website

Posted November 11, 2019

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

TBA