Japanese Ladders and the Braid Group
Speaker: Michael Alloca (Saint Mary's College)
Wednesday, October 17, 2012
Abstract: Japanese Ladders are a visual technique used to construct a
bijective map from a set to itself for purposes such as assigning grab bag gift
rules. They also entail a very enjoyable puzzle game. We will briefly explore
the rules of this game and slightly modified versions. We will also investigate
the underlying mathematics, which leads to fascinating generalizations of
permutations and of a well-known short exact sequence used with the braid
group.
Gauss' Theorema Egregium and modern geometry
Speaker: Lashi Bandara (visiting at Stanford University)
Wednesday, September 26, 2012
Abstract: In this talk, I will give a brief account the ideas of Gauss that led him to the Theorema Egregium, "Remarkable Theorem." I will then illustrate how Riemann looked upon these ideas as a seed which has now grown into the fruitful area known today as Riemannian geometry.
Two Parameter Families of Kernel Functions
Speaker: Casey Bylund (USF)
Wednesday, September 12, 2012
Casey presented work she did as part of a Research Experience for Undergraduates (REU) over the summer of 2012.
Sampling of Operators
Speaker: Goetz Pfander (Jacobs University)
Wednesday, May 2, 2012
Abstract: Sampling and reconstruction of functions is a central tool in science. A key result is given by the classical sampling theorem for bandlimited functions. We describe a recently developed sampling theory for operators. Our findings use geometric properties of so-called Gabor systems in finite dimensions. We shall briefly discuss these systems and include remarks on their potential use in the area of compressed sensing. Students with basic knowledge of calculus and linear algebra should be able to follow large portions of the talk.
The Art Gallery Theorem
Speaker: Emille Lawrence (University of San Francisco)
Wednesday, April 18, 2012
Abstract: Suppose you own a one-room art gallery whose floor plan is a simple polygon. Given that your collection of art is quite valuable, suppose further that you would like to place cameras in your gallery so that every point in the space is visible to at least one of the cameras. Additionally, to cut down on the cost of your security system and to be as unintrusive as possible to the gallery guests, you'd like to install as few cameras as possible. How many cameras would you need, and where would you decide to place them? This question, known as the Art Gallery Problem, was first posed in 1973 by Victor Klee, and has been extended by mathematicians in many directions over the years. We will answer this question, and discuss a proof via a 3-coloring argument. We will also discuss some interesting related problems in computational geometry.
Applying Markov Chains to NFL Overtime
Speaker: Chris Jones (St. Mary's College)
Wednesday, March 21, 2012
Abstract: The NFL recently changed its rules for games that go into overtime in the postseason. We will verify that the previous system provides a statistically significant bias to the team winning the toss and using Markov Chains we will show how the new rules appear to balance out that advantage. We will also look at other possible methods for deciding the winner in an overtime game that have been considered, and rejected.
The Graph Menagerie: Abstract Algebra meets the Mad Veterinarian
Speaker: Gene Abrams (University of Colorado at Colorado Springs)
Wednesday, March 7, 2012
Abstract: Click here.
Groups with Cayley graph isomorphic to a cube
Speaker: Rick Scott (Santa Clara University)
Wednesday, December 7, 2011
Abstract: Groups are algebraic objects that capture the notion of symmetry in mathematics. One way to study a group is from the geometric perspective of its Cayley Graph -- a collection of vertices and labeled edges that exhibits the symmetries of the group. In this talk we will consider groups whose Cayley graph is a cube. We will give a combinatorial characterization of these groups in terms of generators and relations and use it to describe a product decomposition. The talk with begin with a gentle introduction to groups and Cayley graphs, including definitions and lots of examples.
The Triumph of the One
Speaker: Benjamin Wells (USF Emeritus)
Friday, 11.11.11, at 1:11P.M.
Abstract: This talk discusses some interesting coincidences involving the number 1. It is not numerology, for there is no interpretation or inferred meaning. It is not mathematics, for no deductions are feasible. It is not computer science, for nothing is computed or scientific. It is not philosophy or psychology, for nothing depends on reflection, introspection, association, or the lower mind. No special claim is made of divine intervention. But it is math and art.
Continued Fractions and Geometry
Speaker: Paul Zeitz (University of San Francisco) (Also, he's on Wikipedia!)
Wednesday, November 2, 2011
Abstract: In this talk, we will look at a surprising connection between number theory and geometry that was discovered a few decades ago. There is a link between continued fractions, a topic in number theory, and hyperbolic geometry. The "glue" that links these two seemingly-unrelated subjects: complex numbers.
Shapes of spaces: 2- and 3-manifolds
Speaker: Marion Campisi (The University of Texas at Austin)
Wednesday, October 19, 2011
Abstract: If you took off in a faster than light rocket-ship and flew in a straight line forever, what would happen? Would you hit the edge of the universe? Would you keep going forever, always getting further away from home? Is there another possibility? Could the answer to these questions give us any clues about the shape of the Universe?
While we do not know what the actual shape of the universe is, mathematicians have been able to determine possible shapes a 3-dimensional universe could have. Before we try to understand these shapes, called 3-manifolds, we will build our intuition by considering the perspective of beings living in 2-dimensional universes, or 2-manifolds. We will consider possible 2-manifolds and develop tools that a being living in such a space could use to distinguish them. Finally, we will develop a picture of several different 3-manifolds and consider if there is any way to know whether any of them might be the shape of our own universe.
Isoperimetric Inequalities
Speaker: Ellen Veomett (Saint Mary's College)
Wednesday, September 7, 2011
Abstract: Suppose you had a closed loop, like a piece of string with both ends tied together. If someone asked you to place that loop on a sheet of paper so that it enclosed the largest possible area, what shape would you make? This kind of question gives rise to an isoperimetric inequality: an upper bound on the area of a set in the plane with fixed perimeter.
In this talk, we will discuss some very different types of isoperimetric inequalities. We will explore the Euclidean isoperimetric inequality, along with a geometric proof of that inequality using the Brunn-Minkowski Theorem. We will then consider a couple of discrete isoperimetric questions on two different but closely related graphs. We will see the interesting complications that arise when our graph has finitely many vertices, as opposed to infinitely many vertices.
