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Mathematics Colloquium Schedule
----------------------------| Fall 2013 |----------------------------
December 6, 2013 (2-3pm, F03-200A), Professor Sam Nelson, Department of Mathematics, Claremont McKenna College
Title: Augmented Birack Homology
Abstract: Augmented biracks are algebraic structures related to knots and links. In this talk we will see a homology theory associated to finite augmented biracks and define knot and link invariants associated to elements of the second cohomology of a quotient complex we call $N$-reduced cohomology.
November 15, 2013 (2-3pm, F03-200A), Nen Huynh, Department of Mathematics and Statistics, CSULB
Title: A Generalized Left-to-Right (GLR) parser for Tree-Adjoining Grammars (TAG) using Matrices
Abstract: Ever since the introduction of tree-adjoining grammars (TAG), there has been a push to discover efficient parsing algorithms for such grammars. Different approaches have been attempted most of them come from parsing paradigms present for context-free grammars. However, there is currently a lack in a matrix-centered approach to the problem. This is surprising because the grammar employs trees and it is then natural to parse such grammar using a tree traversal. Hence, matrices are involved since they are known to perform graph (and, hence, tree) traversals optimally. We present a generalized left-to-right parser to demonstrate the advantage of the matrix approach.
November 8, 2013 (12:30 -1:30 pm, F03-200A), Professor Jim Hoste, Department of Mathematics
Title: Involutory Quandles of Knots.
Abstract: Associated to every knot or link is its quandle, an algebraic invariant with a long history dating back to the 1940's. The knot quandle is more sensitive than the fundamental group of the complement of a knot. In fact it is a complete knot invariant. Not surprisingly, knot quandles, like knot groups, are difficult to analyze. Passing to the less sensitive involuntary quandle provides a more manageable invariant that is easier to compute and compare between knots. In this talk I will define the knot quandle and describe the involuntary quandle associated to several classes of knots and links such as 2-bridge links, pretzel links, and torus links.
October 25, 2013 (2 -3 pm, F03-200A), Kristen Hendricks, Department of Mathematics
University of California, Los Angeles
Title: Categorification and the Alexander polynomial
Abstract: In the past fifteen years, low dimensional topologists have become interested in invariants of 3- and 4-manifolds (and knots and surfaces within them) which refine the information of certain classical invariants. We say these modern invariants are categorifications of their classical counterparts. I'll explain what categorification is, and talk about the relationship of a classical invariant of knots, the Alexander polynomial, and its categorified version, Heegaard Floer knot homology, introduced by Ozsvath-Szabo and Rasmussen in the early 2000s.
October 11, 2013 (1 -2 pm, LA5-149), Professor David Bachman, Department of Mathematics
Title: From soap films to the shape of space.
Abstract: I will give a pseudo-historical account of the field of "minimal surfaces," which was originally motivated by trying to find the shape of the soap bubble film that spans a given twisted loop of wire. This story culminates with the recent influence this theory has had on topologists studying 3-manifolds: possibilities for the shape of our universe.
October 4, 2013 (12 -1 pm, FO3-200A), Professor John dePillis, Department of Mathematics
University of California, Riverside
Title: An Illustrated Approach to Special Relativity and Its Paradoxes.
Abstract: A BASIC ASSUMPTION of special relativity (SR) is that the speed of light in a vacuum is the same for all
observers regardless of their speeds or the speed of the light source. Consequences of this simple axiom are profound. For example, rods in
motion shrink in the direction of motion, and clocks in motion always run slower than stationary clocks.
We analyze these properties and paradoxes of SR through the geometry of Minkowski diagrams which also allow for a novel linear-algebraic derivation
of the Lorentz transformation.