Join two Applied Math/Math alumni do discuss their AI/ML work at American Express. We give an overview of Amex as a company, discuss some of our projects, and provide information on where to find current openings. We’ll also have time to answer questions on life in industry or other topics of interest.

Place:   Math, 402 and
Zoom: https://arizona.zoom.us/j/83541348598 
Password:  BB2022

In this talk, we will discuss the decay results on a 2D magnetohydrodynamic (MHD) system with only vertical dissipation or horizontal dissipation. For vertical dissipation, we show that the H^2-norm of any perturbation near a background magnetic field actually decays algebraically in time. Mathematically this result along with its proof offers a new and effective approach to the large-time behavior on partially dissipated systems. For horizontal dissipation, we show the stability result on the perturbations near a background magnetic field. In addition, the solution converges to its horizontal average asymptotically.

https://arizona.zoom.us/j/82763762677

Anderson acceleration (AA) is a popular extrapolation technique used to accelerate the convergence of fixed-point iterations. It requires the storage of a (usually) small number of solution and update vectors, and the solution of an optimization problem that is generally posed as least-squares and solved efficiently by a thin QR decomposition. First developed in 1965 in the context of integral equations, this method has recently been increasing in popularity as a Jacobian-free approach to converging to discrete nonlinear PDE solutions, not to mention applications in optimization and machine learning. The convergence behavior of AA is still not fully understood, and its dependence on the selection of parameters including the algorithmic depth remains an active field of research. In this talk we will discuss understanding and improving the behavior of the algorithm using standard tools and techniques from numerical linear algebra.  We will also numerically demonstrate how the filtering and dynamic depth selection procedures developed concurrently with recent theory can be used to control the condition number of the least-squares problem and improve both the efficiency and robustness of accelerated solves.

Place: Math, 402 and
Zoom   https://arizona.zoom.us/j/83758253931
Password:  applied

Metamaterials are artificial materials with properties that go well beyond what offered by nature, providing unprecedented opportunities to tailor and enhance the control of waves. In this talk, I discuss our recent activity in electromagnetics and nano-optics, showing how suitably tailored meta-atoms and their arrangements open exciting venues for enhanced wave-matter interactions. I will discuss unusual scattering, absorption and waveguiding responses, from cloaking and scattering suppression, to nonreciprocity and topological phenomena, enhanced nonlinear effects at subwavelength scales, and bound states in the continuum. Physical insights into the underlying phenomena and new devices based on these concepts will be presented.

Bio:  Andrea Alù is a Distinguished Professor at the City University of New York (CUNY), the Founding Director of the Photonics Initiative at the CUNY Advanced Science Research Center, and the Einstein Professor of Physics at the CUNY Graduate Center. He received his Laurea (2001) and PhD (2007) from the University of Roma Tre, Italy, and, after a postdoc at the University of Pennsylvania, he joined the faculty of the University of Texas at Austin in 2009, where he was the Temple Foundation Endowed Professor until Jan. 2018. Dr. Alù is a Fellow of NAI, AAAS, IEEE, MRS, OSA, SPIE and APS. He has received several scientific awards, including a Vannevar Bush Faculty Fellowship, the 2021 Blavatnik National Award for Physical Sciences and Engineering, the 2020 IEEE Kiyo Tomiyasu Award, the 2016 ICO Prize in Optics, the 2015 NSF Alan T. Waterman award, the 2013 OSA Adolph Lomb Medal, and the 2011 URSI Issac Koga Gold Medal.

Structured Latent Attribute Models (SLAMs) are popular statistical tools for developing diagnostic-based assessments in education, psychology, and other social and behavioral sciences. SLAMs can be viewed as a family of restricted discrete latent variable models, which assume that multiple discrete latent attributes explain the dependence of observed variables in a highly structured fashion. Though widely used, such structured latent class models often suffer from nonidentifiability due to the models' discrete nature and complex restricted structure. The first part of this talk introduces our recent identifiability results on SLAMs by considering both strict and partial identifiability of the model parameters. The developed identifiability conditions only depend on the design matrix and are easily checkable, which provides useful practical guidelines for designing statistically valid diagnostic tests. The second part of the talk further discusses likelihood-based approaches to estimate the latent structures and the model parameters.

Many arithmetically interesting operators act on spaces of modular forms. One of the these operators is the Atkin-Lehner involution, which splits a space of modular forms into a direct sum of a plus-eigenspace and a minus-eigenspace. I will first say a bit about the classical split in the dimensions between these two eigenspaces, and then refine this story to account for congruences between modular forms. This is an application of a new technique for counting mod-p modular forms recursively in the weight by establishing deep congruences between traces of certain Hecke operators. Joint with Samuele Anni and Alexandru Ghitza.

Modular forms are holomorphic functions with a wealth of symmetries.  Even though these functions are borne out of complex analysis, their Fourier coefficients contain a wealth of arithmetic information.  Even bounding the sizes of these coefficients involve very deep mathematics -- the best bounds follow from Deligne's proof of the Weil conjectures, for which he was awarded the Fields medal.

In this talk, rather than looking at complex absolute values, we will instead focus on the p-adic size of p-th Fourier coefficient for a prime number p.  We will state a conjecture (the ghost conjecture) which gives an exact description of these sizes for all modular forms.  This funnily named conjecture converts difficult automorphic questions into more accessible combinatorial ones.  We will discuss the state of this conjecture and its applications to several open questions on slopes of modular forms.

For details, see  https://science.arizona.edu/academics/graduation-convocation

https://arizona.zoom.us/j/81887284125

The Mathematics Educator Appreciation Day Conference (MEAD) is Arizona's largest mathematics education event!

MEAD 2023 is FREE for ALL Arizona teachers and administrators! 

Join us for a day of professional learning and community building, featuring a keynote address from Peg Smith, recipient of NCTM's Lifetime Achievement Award!  Peg will speak to how the 5 Practices are a Tool for Supporting Equitable Mathematics Classrooms.