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Come listen to some of our members give talks on topics they are interested in or have worked on in the past! At this meeting, we will have Yash Agarwal giving a talk "Charting Hidden Dimensions", Levi Walker talking on "H_2 Optimal Model Reduction on GPUs", Aryan Palit talking on "Collaborative Filtering in Dating Apps", and Richard Morgan talking on "Uncovering non-linear gene interactions using Graph Embeddings". If you want to give a talk in the future, reach out to one of our officers! We plan on having another one of these meetings this semester.
The discoveries made by LIGO in gravitational wave astrophysics have been hailed as a triumph of experimental methods in physics – and they are. However, this paper will analyze the fact that – as the LIGO researchers know well – it would not have been possible to derive secure inferences from those experiments without significant formal advances (in numerical relativity, effective one-body systems and dynamics of two-body systems, linearization of the field equations, and the like). These advances, by researchers including Pretorius and Choquet-Brouhat, made it possible to move from the pioneering methods used to analyze the 1980s discoveries by Hulse and Taylor, to the even broader and more flexible LIGO framework. The paper will demonstrate that inferences about black holes and other binary systems in the LIGO project encode a complex set of choices involving higher-order formal relationships, which in turn reflect decisions about what is worth pursuing in experiment and theory-building. The answer to the question of whether LIGO is a triumph of experiment or theory is “Both – and neither: one truly novel feature of LIGO is the way they work with the relationship between theory, experiment, simulation, and testing”.
Mathematical models have long been useful tools for examining drivers of infectious disease emergence, spread, and control. In this talk, I will introduce population and infectious disease models and discuss my recent work in using models to study mosquito-borne diseases. Mosquito-borne diseases that have been historically endemic to areas with tropical climates have been spreading in temperate regions of the world with greater frequency in recent years. Numerous factors contribute to this spread, including urbanization; increases in global travel; and changes in temperature, precipitation, and humidity patterns leading to anomalies from historical averages. Mathematical, statistical, and computational modeling can help us understand how these different influences impact transmission and spread of pathogens, and models are useful for projecting how potential future changes in these factors could affect pathogen dynamics. Although models have been employed for years to study disease dynamics, diseases emerging in new regions present particular challenges. I will focus on here on recent modeling work for better understanding the emergence of dengue fever in Central Argentina. Dengue, caused by a virus transmitted by Aedes aegypti mosquitoes, first emerged in temperate Argentinian cities in 2009, and multiple outbreaks of increasing incidence have occurred since. With particular focus on the role of meteorological influences on dengue emergence, I present mathematical models designed to study seasonal Ae. aegypti and dengue dynamics in temperate Argentinian cities. I will show how different seasonal patterns influence the risk of outbreaks and how projected increases in average temperatures may influence future transmission risk. I will also discuss the implications of our work for dengue and mosquito mitigation strategies, and address some of the issues and areas for improvement in modeling emerging pathogens transmitted by mosquitoes.
Since the dawn of time, mathematicians have wondered about triangles. Only in the 19th and 20th centuries did they realize the set of all triangles itself forms a space! Master this space, and you understand triangles. We will explore a similar space of elliptic curves, a.k.a. parallelograms central in number theory. Time permitting, we will see other examples of moduli spaces and a first glimpse of the stack structure inherent to all these spaces.
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