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February 2021

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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Jennifer Taback

April 14 @ 4:15 pm - 5:30 pm

Title: Groups, Graphs and Trees Abstract: What do we mean by the geometry of a group? Groups seem like very abstract objects when we first study them, and it's natural to ask whether we can visualize them in some way. Given a group with a finite set of generators and relators, I will describe a canonical way to construct a geometric model of that group, called a Cayley graph. We will see many examples -- both standard and unusual --…

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Haydee Lindo

April 21 @ 4:15 pm - 5:30 pm

Title: Trace Ideals and Endomorphism Rings Abstract: In many branches of mathematics, the full set of "functions" between two objects exhibits remarkable structure; it often forms a group and in some special cases it forms a ring. In this talk, we will discuss this phenomenon in Commutative Algebra. In particular, we will talk about the endomorphism ring formed by the homomorphisms from a module to itself by first looking at commuting square matrices. I'll also introduce the trace ideal and…

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Jennifer Franko Vasquez

April 28 @ 4:15 pm - 5:30 pm

Title: Puzzling Permutations Abstract: Permutations are one of the most fundamental notions in mathematics. In this talk, we will discuss a visual representation of permutations and introduce some games one can play to help "see" different properties. These puzzling games can be used to provide insight into deeper mathematical content as well. Time permitting, we will explore connections to topology and biology. This talk is based on joint work with Steven Dougherty and Michael Allocca. Dr. Vasquez is a Professor…

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