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Texas A&M University
Mathematics

Events for 10/06/2022 from all calendars

Working Seminar on Banach and Metric Spaces

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Time: 09:30AM - 11:00AM

Location: BLOC 302

Speaker: Ryan Malthaner, Texas A&M University

Title: On Lipschitz free spaces isometric to subspaces of L1-spaces (after Godard)


Number Theory Seminar

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Time: 2:30PM - 3:30PM

Location: BLOC 302

Speaker: Louis Gaudet, Rutgers University

Title: The least Euler prime via a sieve approach

Abstract: Euler primes are primes of the form $p = x^2+Dy^2$ with $D>0$. In analogy with Linnik’s theorem, we can ask if it is possible to show that $p(D)$, the least prime of this form, satisfies $p(D) \ll D^A$ for some constant $A>0$. Indeed Fogels showed this in 1962, but it wasn’t until 2016 that an explicit value for $A$ was determined by Thorner and Zaman, who showed one can take $A=694$. Their work follows the same outline as the traditional approach to proving Linnik’s theorem, relying on log-free zero-density estimates for Hecke L-functions and a quantitative Deuring-Heilbronn phenomenon. In an ongoing work (as part of my PhD thesis) we propose an alternative approach to the problem via sieve methods that avoids the use of the above technical results on zeros of the Hecke L-functions. We hope that such simplifications may result in a better value for the exponent $A$.


Colloquium

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Time: 4:00PM - 5:00PM

Location: Bloc 117

Speaker: Enrique Zuazua, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Description: Title: Dynamics, Control and Numerics

Abstract: Norbert Wiener defined “Cybernetics” as “the science of control and communication in the animal and the machine”, anticipating some of the goals and the future development of Artificial Intelligence.

The traditional Applied Mathematics program, combining modelling, analysis, numerical approximation, and scientific computing, when facing practical applications, must often be complemented by additional efforts to address control issues, to better understand how dynamics changes when varying free parameters. This frequently leads to new complex and fascinating analytical and computational challenges that require significant unexpected further developments.

We will lecture on some recent success stories that arise when facing, for instance, source identification problems, and the regulation of collective dynamics.

We shall also discuss the issue of the optimal placement of sensors and actuators, which plays a key role when designing efficient control mechanisms.

Control techniques also play an unexpected relevant role in other contexts such as the large time asymptotics for partially dissipative systems in fluid mechanics.

We will describe the links between these problems and their analytical and numerical treatment, as one further manifestation of the unity and interconnections of all mathematical disciplines.

We shall conclude pointing towards some perspective for future research.