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DTSTART;TZID=America/Los_Angeles:20210303T161500
DTEND;TZID=America/Los_Angeles:20210303T173000
DTSTAMP:20260514T180702
CREATED:20210204T003334Z
LAST-MODIFIED:20210221T214207Z
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SUMMARY:Ioana Dumitriu
DESCRIPTION:Title:  Spectral gap in random regular graphs and hypergraphs \nAbstract: 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 the spectral gap for graph-associated matrices; roughly speaking\, it means that the main eigenvalue(s) are well-separated from the bulk and it guarantees strong connectivity properties. This talk will take a look at the spectra of adjacency / Laplacian matrices for some random regular models\, explain how we know that the spectral gap is there\, and connect spectral properties to the aforementioned applications. It will cover joint work with Gerandy Brito\, Kameron Decker Harris\, and Yizhe Zhu.  \nIoana Dumitriu is a Professor of Mathematics at The University of California\, San Diego.
URL:https://colleges.claremont.edu/ccms/event/ioana-dumitru/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
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DTSTART;TZID=America/Los_Angeles:20210317T161500
DTEND;TZID=America/Los_Angeles:20210317T173000
DTSTAMP:20260514T180702
CREATED:20210204T003526Z
LAST-MODIFIED:20210312T000508Z
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SUMMARY:Finding soap films in non-Euclidean geometry (Prof. David Bachman)
DESCRIPTION:Title: Finding soap films in non-Euclidean geometry \nAbstract: 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 formula.” After reviewing this formula we will introduce spherical and hyperbolic space\, and discuss a solution to the same problem in those geometries.  \nDr. Bachman is Professor of Mathematics at Pitzer College and Director of the Claremont Center for the Mathematical Sciences.
URL:https://colleges.claremont.edu/ccms/event/david-bachman/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
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DTSTART;TZID=America/Los_Angeles:20210324T161500
DTEND;TZID=America/Los_Angeles:20210324T173000
DTSTAMP:20260514T180702
CREATED:20210204T004055Z
LAST-MODIFIED:20210312T000436Z
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SUMMARY:Our muscles aren't one-dimensional fibres (Prof. Nilima Nigam)
DESCRIPTION:Title: Our muscles aren’t one-dimensional fibres. \nAbstract: 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 realized that skeletal muscle is three dimensional\, has mass\, and fairly complicated structure. I’ll present some work on a mathematical model which captures some of this complexity. \nDr. Nilima Nigam is Professor at Simon Fraser University.
URL:https://colleges.claremont.edu/ccms/event/nilima-nigam/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
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DTSTART;TZID=America/Los_Angeles:20210331T161500
DTEND;TZID=America/Los_Angeles:20210331T173000
DTSTAMP:20260514T180702
CREATED:20210204T004224Z
LAST-MODIFIED:20210312T000546Z
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SUMMARY:An ideal convergence: an example in noncommutative metric geometry (Prof. Konrad Aguilar)
DESCRIPTION:Title: An ideal convergence: an example in noncommutative metric geometry \nAbstract:  \nThe 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 about operator algebras\, which are generalizations of algebras of complex-valued square matrices. In another direction\, J.M.G. Fell introduced a notion of convergence of ideals of a given operator algebra. Can the quantum Gromov-Hausdorff distance also be used to establish convergence of the associated quotient algebras? We discuss this for certain operator algebras called approximately finite-dimensional (AF) C*-algebras\, which can be represented by infinite graphs called Bratteli diagrams where the ideals and quotients are represented by subgraphs. It is the movement of the quotient graphs with respect to the ideal graphs that motivates our question and its answer. The main example we discuss will be given by graph representations of irrational numbers built by their associated continued fractions.  (This talk contains joint work with Samantha Brooker\, Frédéric Latrémolière\, and Alejandra López). \nProfessor Konrad Aguilar is Assistant Professor at Pomona College.
URL:https://colleges.claremont.edu/ccms/event/konrad-aguilar/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
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