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Applied Math Talk: Nonlocal Helmholz-Hodge decompositions for nonlocal operators given by Prof. Petronela Radu (University of Nebraska – Lincoln)

Zoom

Nonlocal theories have emerged with powerful models and methods to analyze and predict complex phenomena. Different versions of nonlocal operators have been proposed, each with its advantages and challenges. In this talk I will give an introduction to main ideas in the nonlocality framework and present two sets of results for Helmholtz-Hodge type decompositions.

Prof. Jemma Lorenat

Zoom

Title: A competent translation/a pitiful bungle: The Foundations of Geometry Abstract: David Hilbert’s Grundlagen der Geometrie is a rare example of a historical mathematics text that is still profitably read today and continues to inspire research in mathematics, computer science, and philosophy. The effort of publishing an English translation of Hilbert in 1902 involved a […]

Applied Math Talk: Multiwavelet discontinuous Galerkin methods and automated parameters for troubled cell indication given by Professor Jennifer Ryan (Colorado School of Mines)

This talk focuses on using a multiwavelet representation of the discontinuous Galerkin (DG) approximation for trouble cell indication. The multiwavelet representation is related to the jumps in the (derivatives of) the DG approximation. We then compare this indicator with other, more established indicators as well as machine learning approaches and demonstrate that it is possible […]

Prof. Satyan Devadoss

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Title: Unsolved Mathematics at Burning Man Abstract: Rising 12 feet tall with an 18-foot wingspan, a 2-ton unfolding dodecahedron comes to life at Burning Man, the world’s most influential large-scale sculpture showcase. The artwork is illuminated by 16,000 LEDs, requiring 6500 build-hours and $50,000 in donated funds, with an interior large enough to hold 15 […]

Applied Math Talk: Bounded-confidence models for opinion dynamics on online social networks given by Professor Heather Zinn Brooks (HMC)

Online social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online, the content that spreads on online social networks can have important consequences on public opinion, policy, and voting. To better understand the online content spread, mathematical modeling of opinion dynamics is becoming […]

Prof. Grigoriy Blekherman

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 […]

Moody Lecture: Prof. Nadia Abuelezam

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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 […]

Prof. Stephan Ramon Garcia

Zoom

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 […]

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

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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 […]

Prof. Sarah Marzen

Zoom

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 […]

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

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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 […]