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DTSTART;TZID=America/Los_Angeles:20230417T161500
DTEND;TZID=America/Los_Angeles:20230417T171500
DTSTAMP:20260505T204010
CREATED:20221207T193543Z
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SUMMARY:Applied Math Seminar: Emily de Jong (Caltech)
DESCRIPTION:Title: Modeling size distributions and collisions in cloud microphysics \nAbstract:\nFeedbacks between a warming atmosphere\, emission of aerosols\, and clouds and precipitation are one of the most difficult aspects for climate models to accurately capture. While these models operate at resolutions of tens or hundreds of kilometers\, many of the physics that determine how and where clouds form or precipitate function at the micron droplet scale. This separation of scales means that most of these “microphysics” must be modeled with only a few approximate quantities and physical equations. These simplifications lead to large uncertainties about the future climate\, such as the sensitivity of global warming to human-emitted aerosols.   \nThis talk presents two promising techniques for mathematically representing droplet size distributions and the microphysics that govern how droplets within the distribution evolve. The first method attempts to span a gap in complexity between a simple method of moments and expensive “bin” or spectral representations by collocating smooth basis functions over the droplet size domain. With intelligently selected basis functions\, this approach can represent the process of cloud droplets coalescing to form rain with bin-like accuracy\, but with a degree of complexity that is attainable for global simulations. Next\, we present a high-complexity high-fidelity Lagrangian approach known as the superdroplet method. This approach shows promise as a research tool to verify and train future microphysics models\, but it is currently incomplete in its purview of droplet physics. We describe a probabilistic approach to representing collisional breakup\, an often-overlooked process that can impact precipitation rates\, cloud lifetime\, and aerosol processing.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-emily-de-jong-caltech/
LOCATION:Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu
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DTSTART;TZID=America/Los_Angeles:20230418T121500
DTEND;TZID=America/Los_Angeles:20230418T131000
DTSTAMP:20260505T204010
CREATED:20230211T054504Z
LAST-MODIFIED:20230411T184945Z
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SUMMARY:Systems of homogeneous polynomials over finite fields with maximum number of common zeros (Sudhir Ghorpade\, IIT Bombay)
DESCRIPTION:It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It is meaningful to ask similar questions for systems of several polynomials in several variables of a fixed degree\, provided the base field F is finite. These questions become particularly interesting and challenging when one restricts to polynomials that are homogeneous\, and considers zeros (other than the origin) that are non-proportional to each other. More precisely\, we consider the following question: \nGiven a system of a fixed number of linearly independent homogeneous polynomial equations of a fixed degree with coefficients in a fixed finite field F\, what is the maximum number of common zeros they can have in the corresponding protective space over F?The case of a single homogeneous polynomial (or in geometric terms\, a projective hypersurface) corresponds to a classical inequality proved by Serre in 1989. For the general case\, an elaborate conjecture was made by Tsfasman and Boguslavsky\, which was open for almost two decades. Recently significant progress in this direction has been made\, and it is shown that while the Tsfasman-Boguslavsky Conjecture is true in certain cases\, it can be false in general. Some new conjectures have also been proposed. We will give a motivated outline of these developments. If there is time and interest\, connections to coding theory or to the problem of counting points of sections of Veronese varieties by linear subvarieties of a fixed dimension will also be outlined. \nThis talk is mainly based on joint works with Mrinmoy Datta and with Peter Beelen and Mrinmoy Datta.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sudhir-ghorpade-iit-bombay/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20230419T161500
DTEND;TZID=America/Los_Angeles:20230419T173000
DTSTAMP:20260505T204010
CREATED:20230122T184542Z
LAST-MODIFIED:20230414T152218Z
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SUMMARY:A Brief History of Calculating Machines (Prof. Yousef Daneshbod\, University of La Verne)
DESCRIPTION:Title: A Brief History of Calculating Machines \nSpeaker: Yousef Daneshbod\, Department of Mathematics\, University of La Verne \nAbstract: Calculating machines are digital or analog devices designed to perform mathematical calculations. These machines have a long history\, with the earliest known examples dating back to ancient times\, when people used sticks and stones for counting. However\, the first mechanical calculators were invented in early modern period thanks to the theoretical development of mathematics and the growing need for more sophisticated computations. Today\, calculating machines are all around us; changing the way we live our lives. In this talk\, I will explain the evolution of early calculating machines and the key people involved with its development. \n\n\n\n\n\nDr. Yousef Daneshbod\, Associate Professor of Mathematics has been teaching at the University of La Verne since 2007. Prior to joining La Verne\, he was a Lecturer in Mathematics at Calpoly Pomona and an Adjunct Professor at Citrus College. Dr. Daneshbod received his B.S. and M.S both in mechanical engineering from Shiraz University in Iran. In the year 2001 he abandoned his studies for a PhD in mechanical engineering just one year before completion and along with his wife immigrated to the U.S. His love for mathematics motivated him to pursue a PhD degree in applied mathematics from the Claremont Graduate University\, eventually graduating in the summer of 2006. Dr. Daneshbod believes that the combination of clear classroom notes along with symbolic computer software can serve as an excellent pedagogical tool for making mathematics much more fun and intuitive for the students. His primary fields of interest include mathematical modeling in microfluidics\, theoretical and computational mechanics and wave propagation in anisotropic media. He is also interested in mathematics education in a liberal arts setting where he tries to inspire his students by exposing them to historical sketches of famous scientists and mathematicians.
URL:https://colleges.claremont.edu/ccms/event/prof-yousef-daneshbod/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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