Patterns, Swarms, and the Unreasonable Effectiveness of Mathematics
Speaker: Chad Topaz (Macalester College)
Wednesday, April 24, 2013
Abstract: From fish schools to zebra stripes to fluid waves, the world is full of patterns that form spontaneously. I will discuss natural pattern formation from the point of view of mathematical modeling, highlighting how minimal models can effectively -- and perhaps surprisingly -- describe real pattern-forming phenomena. As an extended example, I will discuss biological aggregations, which are arguably some of the most common and least understood patterns in nature. More specifically, I will present work performed with undergraduate students on modeling locust swarms with high-dimensional systems of nonlinear differential equations.
Natural Optimization: The Story of Farmer Ted
Speaker: Matt DeLong (Taylor University)
Wednesday, April 10, 2013
Abstract:The problem of minimizing the perimeter of a rectangle of a given area is familiar to all introductory calculus students. Its solution was not at all natural, however, to Farmer Ted, a fictitious character introduced in a 1999 Mathematics Magazine article. Farmer Ted required integer solutions to his farming needs. Three articles in the Magazine (two by first-year undergraduate authors) used elementary number theory to help Farmer Ted do his business naturally and efficiently. In this talk I will share the mathematics of, as well as the story behind, these cute problems. I will also discuss some lessons learned from directing undergraduate research, and tell you why my Erdös number is not exactly four.
Short bio: Matt is a visiting professor in the Department of Mathematics at Harvey Mudd College for 2012-2013, while on sabbatical from his roles as Professor of Mathematics and Fellow of the Center for Teaching and Learning Excellence at Taylor University, in Upland, IN. He is also one of the Associate Directors of the MAA’s Project NExT. Matt has a B.A. from Northwestern University and a Ph.D. from the University of Michigan. He was awarded the 2005 Alder Award and the 2012 Haimo Award for distinguished teaching from the MAA.
An Introduction to Surface Tension (Or Why Raindrops are Spherical)
Speaker: Andrew Bernoff (Harvey Mudd College)
Wednesday, March 20, 2013
Abstract: A common misconception is that raindrops take the form of
teardrops. In fact, they tend to be nearly spherical due to
surface tension forces. This is an example of how at small
scales the tendency of molecules to adhere to each other is the
dominant effect driving a fluid’s motion. In this talk we will
explain how surface tension arises from intermolecular forces. We
will also examine some examples of the behavior that can occur at
small scales due to the balance between fluid-fluid and fluid-solid
forces, with applications as varied as understanding how detergents
help clean clothes to designing fuel tanks in zero gravity
Are Umpires Racist?
Speaker: Jeff Hamrick (USF)
Wednesday, March 6, 2013
Abstract: We investigate the racial preferences of Major League Baseball umpires as they evaluate both pitchers and hitters from 1989-2010, including the 2002-2006 period in which "QuesTec" electronic monitoring systems were installed in some ball parks. We find limited, and sometimes contradictory, evidence that umpires unduly favor or unjustly discriminate against players based on their race.
Variables including attendance, terminal pitch, the absolute score differential, and the presence of monitoring systems do not consistently interact with umpire/pitcher and umpire/hitter racial combinations. Most evidence that would first appear to support racially-connected behaviors by umpires vanishes in three-way interaction models. Overall, in contrast with some other literature on this subject, our findings fall well short of convincing evidence for racial bias.
Why Nature Rarely Assembles into Spheres
Speaker: David Uminsky (USF)
Wednesday, February 20, 2013
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.
Tic-Tac-Toe and the Topology of Surfaces
Speaker: Linda Green (Dominican University)
Wednesday, February 06, 2013
Abstract: Informally, two objects have the same topology if the first object can be deformed to look like the second by bending and stretching it, without making any violent changes like tearing or fusing. In this talk, we'll represent 2-dimensional surfaces as "gluing diagrams" of polygons whose edges are identified in pairs. We'll develop techniques to decide if two gluing diagrams represent surfaces with the same topology. By generalizing these ideas to 3-dimensional spaces, we can gain an understanding of possible shapes for the universe. Along the way, we'll build our intuition for unusual surfaces by playing familiar games like tic-tac-toe ... with a twist.
Where does the railroad track go?
Speaker: Shirley Yap (CSU - East Bay)
Wednesday, November 14, 2012
Abstract: Throughout history, artists have derived inspiration from mathematics. But mathematicians have also derived inspiration from art. In this talk, I will discuss a specific intersection of math and art that will help you see art in all its three-dimensional splendor.
Twin Peaks, Crater Lake, and Earthquakes : Interactive Multivariable Calculus and Linear Algebra on the Internet
Speaker: Thomas Banchoff (Brown University)
Friday, November 2, 2012
Abstract: What happens to geographical landmarks when the ground under them shifts? Interactive computer graphics demonstrations and animations provide striking illustrations of examples from multivariable calculus and linear algebra, the two courses that naturally lead in to differential geometry of curves and surfaces. This talk will feature computer renditions of graphs of families of functions of two variables as well as parametric curves in the plane and in three-space, concentrating on changes in critical points and contour lines. Interactive demonstrations on the Internet will illustrate the presentation.
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, 2012Abstract:
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, 2012Abstract
: 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, 2011Abstract:
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, 2011Abstract:
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, 2011Abstract:
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.
Speaker: Ellen Veomett
(Saint Mary's College)
Wednesday, September 7, 2011Abstract:
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.
- Bennequin surfaces & links
Speaker: Yi (Owen) Xie and Xuanchang (Carl) Liu
When: May 11, 2011, 3:45pm
Where: Harney Science Center, Room 232
Abstract: It's here.