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DTSTART;TZID=America/Los_Angeles:20250923T121500
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DTSTAMP:20260519T073415
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UID:3783-1758629700-1758633000@colleges.claremont.edu
SUMMARY:Graphical designs: combinatorics and applications (Catherine Babecki\, Caltech)
DESCRIPTION:A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking\, that means a graphical design is a relatively small subset of graph vertices chosen to capture the global behavior of functions from the vertex set to the real numbers. We first motivate and define graphical designs for graphs with positive edge weights. Through Gale duality\, we exhibit a combinatorial bijection between graphical designs and the faces of certain polytopes associated to a graph\, called eigenpolytopes. This polytope connection implies a variety of beautiful consequences\, including a proof of existence\, an upper bound on the cardinality of a graphical design\, methods to compute\, optimize\, and organize graphical designs\, the existence of random walks with improved convergence rates\, and complexity results for associated computational problems.  We conclude with applications to the equitable facility location problem.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-catherine-babecki-caltech/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20250925T160000
DTEND;TZID=America/Los_Angeles:20250925T170000
DTSTAMP:20260519T073415
CREATED:20250915T214113Z
LAST-MODIFIED:20250915T215619Z
UID:3836-1758816000-1758819600@colleges.claremont.edu
SUMMARY:Analysis seminar: Geometric classification problems with the Bergman metric (John Treuer\, UCSD)
DESCRIPTION:Title: Geometric classification problems with the Bergman metric \nAbstract: One of the common problems in mathematics is the classification problem: When are two mathematical structures really the same? The classification problem appears throughout undergraduate mathematics courses in different forms. For example\, in an abstract algebra course\, one asks when are two groups isomorphic? In a geometry course\, one asks when are two surfaces isometric? In a discrete math course\, one asks when are two sets bijective? The version in complex analysis is when are two domains (open\, connected sets) biholomorphic to each other? \nIn this talk\, we will begin by defining the primarily studied functions in complex analysis\, the complex differentiable functions also known as the holomorphic functions. We will then study the classification problem through the Bergman kernel and the Bergman metric. Towards the end of the talk\, recent progress on classifying domains and complex manifolds with Bergman metrics of constant holomorphic sectional curvature will be presented.
URL:https://colleges.claremont.edu/ccms/event/analysis-seminar-john-treuer-ucsd/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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DTSTART;TZID=America/Los_Angeles:20250926T110000
DTEND;TZID=America/Los_Angeles:20250926T121500
DTSTAMP:20260519T073415
CREATED:20250917T194906Z
LAST-MODIFIED:20250922T185920Z
UID:3839-1758884400-1758888900@colleges.claremont.edu
SUMMARY:CCMS Colloquium: Robert Cass (CMC)
DESCRIPTION:CCMS Colloquium invites you to a talk by Assistant Professor of Mathematics Robert Cass of Claremont McKenna College:\n\n \nTitle: An introduction to the Langlands program\n \nAbstract: Class field theory\, which was established in the early 20th century\, has its origins in Gauss’s law of quadratic reciprocity. As such\, it allows one to determine whether certain integer polynomials have a root mod p. The Langlands program is a vast area of current research in number theory that can be viewed as a generalization of class field theory to all integer polynomials. In this talk\, I will give a leisurely introduction to this circle of ideas by way of some concrete examples. I will conclude with my own work\, which includes a result on the independence of the cohomology theory chosen in a geometric and categorical analogue of the Langlands program.\n \nBrief Bio: Robert Cass joined the Mathematical Sciences Department at CMC as an Assistant Professor of Mathematics this fall. He received his B.S. from the University of Kentucky and his Ph.D. from Harvard University. After that\, he was an NSF postdoctoral fellow at Caltech and the University of Michigan. He is interested in the Langlands program and arithmetic geometry\, as well as related problems in algebraic geometry and representation theory. He enjoys mathematical questions that are simple to state but whose solutions involve tools from multiple disciplines\, especially those with unexpected connections to geometry.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-robert-cass-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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