Colloquium SeriesSpring 2013Unless otherwise noted, talks will be at 3:50 PM in O'Connor 103. Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM. Tuesday April 16th Speaker: Martin Weissman, UC Santa Cruz Title: The arithmetic of arithmetic hyperbolic Coxeter's groups. Abstract: In the 1990s, John Conway used a ternary regular tree to visualize the classical theory of binary quadratic forms. After covering some highlights of Conway's "topograph," I will introduce a more general framework of arithmetic Coxeter's groups. These yield more general "topographs" which have been used most recently by Savin and Bestvina to study binary Hermitian forms. This talk will require no familiarity with group theory or quadratic forms -- only addition, subtraction, and multiplication of integers will be used for the majority of the time.
Tuesday, April 30th Speaker: David Uminsky, University of San Francisco Title: On Why Nature Rarely Assembles into Spheres Abstract: Soap bubbles on their own naturally select a sphere as their preferred shape as it is the solution which best balances the desire to minimize surface area while capturing a fixed amount of volume. Despite their natural beauty Nature rarely selects empty shells, or spheres, as the preferred shape to assemble into especially when particles to talk to one another do so over different length scales. Two notable exceptions are virus self assembly and the spontaneous assembly of macro-ions into super molecular spherical structures call "Blackberries." In this talk we will show how mathematics is just the right tool to explain this phenomena and help us predict when spheres will be the favored structure. The same tools will allow us to design nano particles to assemble into a variety of spherical patterns.
Tuesday, May 14th Speaker: Corey Irving, Santa Clara University Title: Generalized Barycentric Coordinates: An Introduction and an Application to Algebraic Geometry Abstract: Barycentric coordinates allow one to express points of a polygon as convex combinations of the vertices. For triangles and simplices these coordinates are uniquely defined and well known. However, for n-gons with n>3, they are not unique and less well known. For the first part of the talk we discuss various ways to define barycentric coordinates for general n-gons. The second part will focus on one type of barycentric coordinates, Wachspress coordinates, which are rational functions on the polygon, and we examine the algebraic variety they define. The first part of the talk will only assume basic freshman mathematics knowledge. The second part will assume some abstract algebra and very basic algebraic geometry. This is a summary of dissertation work done at Texas A&M where my advisor was Frank Sottile.
Tuesday, May 28th Speaker: Tom Church, Stanford University Title: TBA Abstract: TBA
Tuesday, June 4th Speaker: Michael Miller, Santa Clara University Title: TBA Abstract: TBA
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Abstracts of previous talks are available here. |
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