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January 2021

CCMS Field Meeting

January 27 @ 4:15 pm - 5:15 pm

Hosted by David Bachman. This is a time for us to welcome each other back from break, share any news relevant to mathematics in Claremont, and break out into smaller discipline-specific groups to coordinate future course rotations.

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February 2021

Prof. Heather Zinn-Brooks

February 3 @ 4:15 pm - 5:30 pm

Title: Networks in social systems Abstract: The spread of memes and misinformation on social media, political redistricting, interactions in animal populations, and the dynamics of voters during elections are among the many things that people study in the field of complex systems. All of these phenomena involve the interactions of individual parts, which come together to produce rich, complex collective dynamics. Obtaining a better understanding of how these interacting parts–whether they are Twitter accounts, penguins, or voters–respond to each other…

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Prof. Henry Schellhorn

February 10 @ 4:15 pm - 5:15 pm

Title: No-arbitrage pricing in a market for position on a multilane freeway, with an application to lane changing Abstract: We introduce a trading mechanism allowing cars to change position in a multilane congested freeway by doing peer-to-peer transactions. For the car initiating the operation, or incoming car, the goal can be to increase speed, to have less speed variability, to join a platoon, or to join an exit lane that is slower but full. We focus in this paper on…

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Dr. Homan Igehy

February 17 @ 4:15 pm - 5:15 pm

Title: Quantitative Investment and Modern Portfolio Theory Abstract: Investment strategies come in many flavors. Quantitative strategies incorporate or fully direct investment based on mathematical models. One of the cornerstones of investment is portfolio management, and modern portfolio theory can serve as a basis for quantitative portfolio management. In this talk, we will discuss quantitative investing and how modern portfolio theory can be incorporated into it. We’ll take an intuitive approach toward understanding modern portfolio theory and discuss how it can…

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Prof. Lori Ziegelmeier

February 24 @ 4:15 pm - 5:30 pm

Title: Using Topology to Measure Shape in Data Abstract: Data of various kinds is being collected at an enormous rate, and in many different forms. Often, the data are equipped with a notion of distance that reflects similarity in some sense. Using this similarity measure, certain topological features--e.g. the number of connected components, loops, and trapped volumes--can be ascertained and can provide insight into the structure of these complex data sets. In this talk, I will introduce topology and a…

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March 2021

Ioana Dumitriu

March 3 @ 4:15 pm - 5:30 pm

Title: Spectral gap in random regular graphs and hypergraphs Abstract: Random graphs and hypergraphs have been used for decades to model large-scale networks, from biological, to electrical, and to social. Various random graphs (and their not-so-random properties) have been connected to algorithms solving problems from community detection to matrix completion, coding theory, and various other statistics / machine learning fundamental questions; in the past decade, this research area has expanded to include random hypergraphs. One of these special properties is…

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Finding soap films in non-Euclidean geometry (Prof. David Bachman)

March 17 @ 4:15 pm - 5:30 pm

Title: Finding soap films in non-Euclidean geometry Abstract: In many computer graphics applications we approximate a smooth surface with one made up of tiny triangles. A common problem is to determine which way to move the vertices (the corners of the triangles), so that the total surface area decreases. If the boundary of the surface remains fixed, this allows us to find the soap film surface spanned by that boundary curve. In Euclidean geometry this leads to the famous “cotan-Laplace…

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Our muscles aren’t one-dimensional fibres (Prof. Nilima Nigam)

March 24 @ 4:15 pm - 5:30 pm

Title: Our muscles aren't one-dimensional fibres. Abstract: Skeletal muscles possess rather amazing mechanical properties. They possess an intricate structure, and behave nonlinearly in response to mechanical stresses. In the 1910s, A.V. Hill observed muscles heat when they contract, but not when they relax. Based on experiments on frogs he posited a mathematical description of skeletal muscles which approximated muscle as a 1-dimensional nonlinear and massless spring. This has been a remarkably successful model, and remains in wide use. Recently, we've…

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An ideal convergence: an example in noncommutative metric geometry (Prof. Konrad Aguilar)

March 31 @ 4:15 pm - 5:30 pm

Title: An ideal convergence: an example in noncommutative metric geometry Abstract: The ability to calculate the distance between sets (rather than just distance between points) has found applications in geometry and group theory as well as various branches of applied mathematics. The Hausdorff distance and the Gromov-Hausdorff distance are standard distances used in these applications. Moreover, a certain generalization of the Gromov-Hausdorff distance called the quantum Gromov-Hausdorff distance was built by M. A. Rieffel to answer some questions from physics…

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April 2021

Alexandria Volkening

April 7 @ 4:15 pm - 5:30 pm

Title: How do zebrafish get their stripes — or spots? Abstract: Many natural and social systems involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in fish. Because they are surprisingly similar to humans genetically, we…

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