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October 2020

Prof. Grigoriy Blekherman

October 14, 2020 @ 4:15 pm - 5:30 pm

Title: Nonnegative Polynomials and Sums of Squares Abstract: Is x4-2x3+7x2-2x+1 nonnegative for any value of x? One way of showing that this holds is by writing x4-2x3+7x2-2x+1=1/2(x2-3x+1)2+1/2(x2+x+1)2. Studying the relationship between non-negativity and sums of squares has a distinguished history in mathematics starting with work of David Hilbert and Hilbert's 17th problem. I will discuss the history and some modern applications of sums of squares in optimization and combinatorics. Prof. Blekherman is on the Mathematics faculty at Georgia Tech; he…

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Moody Lecture: Prof. Nadia Abuelezam

October 21, 2020 @ 4:15 pm - 5:30 pm

Title: Injustice, Inequity, and Inequality: Lessons at the Intersection of Mathematics, Epidemiology, and Racism Registration information for this talk at: https://www.hmc.edu/mathematics/moody-lecture-series/ Abstract:The COVID-19 pandemic has exposed existing health inequities for communities of color in the United States. Racism is a known structural cause of these health inequities. Counterfactuals are essential to our understanding of causal relationships in epidemiology, but how do you formulate a counterfactual for racism? This talk will explore the basis for counterfactual thinking in epidemiology and the…

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Applied Math Talk: Thin liquid film resulting from a distributed source on a vertical wall given by Yadong Ruan (CGU)

October 26, 2020 @ 3:00 pm - 4:00 pm

In this talk, we will talk about the thin film model derived for liquid film resulting from a distributed source on a vertical wall and some distinct properties about the model. We will discuss the different behavior and properties of the model with and without considering surface tension. When the surface tension is neglected, a critical source strength is found below which the film flows entirely upward due to the airflow, and above which some of the flow is carried…

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Prof. Stephan Ramon Garcia

October 28, 2020 @ 4:15 pm - 5:30 pm

Title: Combinatorics and the Kitchen Sink Abstract: Numerical semigroups are simple combinatorial objects that lead to deep and subtle questions. We answer in one fell swoop virtually all asymptotic questions about factorization lengths in numerical semigroups. Surprisingly, this uses tools from complex, harmonic, and functional analysis, probability theory, algebraic combinatorics, and computer-aided design! Our results yield uncannily accurate predictions that agree with numerical computations, along with some totally unexpected byproducts. This work was partially supported by NSF Grant DMS-1800123. Joint…

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November 2020

Applied Math Seminar: Numerical approximation of statistical solutions of hyperbolic systems of conservation laws given by Professor Franziska Weber (Carnegie Mellon University)

November 2, 2020 @ 3:00 pm - 4:00 pm

Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions for multi-dimensional hyperbolic systems of conservation laws. We present a numerical algorithm to approximate statistical solutions of conservation laws and show that under the assumption of 'weak statistical scaling', which is inspired by Kolmogorov's 1941 turbulence theory, the approximations converge in an appropriate topology to statistical solutions. We will show numerical experiments which indicate that the assumption might…

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Prof. Sarah Marzen

November 4, 2020 @ 4:15 pm - 5:30 pm

Title: Training dynamical systems to predict their input Abstract: Evolved systems seem to predict their environment. Even bacteria can implicitly predict future concentrations of scarce sugar or antibiotics, and emerging evidence suggests that even our retinae are able to predict what we see. How? We explore some basic design principles for what causes a system to predict its input, finishing with a call to arms for mathematicians to develop a better framework for understanding input-dependent dynamical systems or recurrent networks.…

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Applied Math Seminar: Multiscale analysis and high-order schemes for nonlinear multilevel Maxwell-Bloch equations given by Prof. Qing Xia (Rensselaer Polytechnic Institute)

November 9, 2020 @ 3:00 pm - 4:00 pm

In this talk, we will present a recent study of the Maxwell-Bloch equations that model the nonlinear interactions of light and matter, where the light is modeled classically by the Maxwell's equations with dispersions and the medium is modeled quantum-mechanically by the multilevel rate equations. We will show the connection between rate equations and the density matrix, where the former formulation is widely used in the engineering community and the latter in the Physics literature. A multiscale analysis of the…

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Prof. Eva Kanso

November 11, 2020 @ 4:15 pm - 5:15 pm

Title: Sea star locomotion Abstract: The oral surface of sea stars (starfish) is lined with arrays of tube feet that enable them to achieve highly controlled locomotion on various terrains and to even gallop and bounce. The activity of the tube feet is orchestrated by a nerve net that is distributed throughout the body; there is no central brain. How such a decentralized nervous system produces a coordinated locomotion is yet to be understood. To examine the sensorimotor control underlying…

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Prof. Gregory DeAngelo

November 18, 2020 @ 4:15 pm - 5:30 pm

Title: The Effect of Criminal Justice Decisions on Community Safety Abstract: During this talk we will, time permitting, examine several law enforcement actor's impact on community safety, including law enforcement, prosecutors and judges. To start, we examine the impact of law enforcement race and gender on use of force. We first show that conditioning on arrests has the potential to greatly impact the results obtained. Instead, we make use of an instrumental variable approach to examine the as-if random assignment…

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Social hour

November 23, 2020 @ 3:00 pm - 4:00 pm

Join us for a social hour with applied mathematicians at Claremont Colleges and University of Utah.

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