USF Math Colloquium Archive 2010–2012

Past talks (2011–2012)

 

  • 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, 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.

  • 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.

 

  • The mathematics of Rubik's cube
    Speaker:      Dr. Philip Matchett Wood (Stanford)
    When:  April 6, 2011, 4:00pm
    Where:  Harney Science Center, Room 127
    Abstract:  In the past 30 years, the Rubik's Cube has been one of the world's best selling toys and most engaging puzzles. This talk will aim to cover some of the mathematics that has been inspired by the Rubik's Cube. There are many mathematical questions one might ask, for example:
  • How many different configurations are there for a Rubik's Cube?
  • What is the hardest configuration to solve
  • What about generalizations of the Rubik's Cube?

    The talk will introduce the idea of a mathematical group along with ideas from algorithms and optimized computing.  The main goal will be a hands-on demonstration of how the mathematics of the Rubik's Cube can be applied to something that everone is interested in: having fun!

 
 

  • Noncomputable functions and undecidable sets
    Speaker:      Dr. Russell Miller (Queens College – City University of New York)
    When:  March 30, 2011, 4:00pm
    Where:  Harney Science Center, Room 127
    Abstract:  Intuitively, a function f is computable if there is a computer program which, when given input n, runs and eventually stops and outputs f(n). This notion was made precise by Alan Turing, in his definition of the machines which came to be known as Turing machines. Without going too far into the formalism, we will investigate how one might arrive at such a definition, and how that definition can be used to show that a particular function cannot be computed by any such machine. Such a function is said to be noncomputable, and if the characteristic function of a set is noncomputable, then the set is undecidable.

  • The dynamics of group actions on the circle
    Speaker:      Anne McCarthy (Fort Lewis College)
    When:  March 9, 2011, 4:00pm
    Where:  Harney Science Center, Room 127
    Abstract:  We will investigate how functions can be viewed as transformations of the circle. The basic notions of dynamical systems and group actions will be introduced. We will then give a classification of how one particular group acts on the circle by discussing the dynamics of the actions. Lots of pictures and examples will be provided.

  • The curious mascot of the fusion project — Meditations on Flexing, Dualizing Polyhedra
    Speaker:      Dr. Benjamin Wells (USF)
    When:  February 15, 2011, 4:30pm
    Where:  Harney Science Center, Room 127
    Abstract:  The Fusion Project (FP) is a research program at the University of San Francisco that seeks to bring 7th grade math classes to the art of the de Young Museum (and vice versa). We also have our eye on the opportunities of new media for teaching middle school math. The Hoberman Switch-Pitch™ is the project’s mascot (I looked it up—it can be an object!). After an introduction to FP, we’ll explore the static and dynamic symmetry of this curious, ancient shape. We’ll also visit with other wild shapes in and out of cages.

  • Eigencircles of 2x2 matrices
    Speaker:  Graham Farr (Monash University)
    When:  January 27, 2011, 4:30pm
    Where:  Harney Science Center, Room 127
    Abstract:  An Eigenvalue of a square matrix A is a number k such that Ax = kx for some nonzero vector x, and the corresponding x is called its Eigenvector. Eigenvalues and Eigenvectors have applications throughout mathematics and science. We show how to associate, to any 2-by-2 matrix A, a circle (the     Eigencircle) that can be used to illustrate and prove many properties of Eigenvalues and Eigenvectors using well-known results from classical geometry.


     

Past talks (2010)

  • The History of “Gaussian” Elimination
    Speaker:      Joseph Grcar
    When:  November 17, 2010, 4pm
    Where: Harney Science Center, Room 232 
    Abstract:  Gaussian elimination is universally known as “the” method for solving simultaneous linear equations. As Leonhard Euler remarked in 1771, it is “the most natural way” of proceeding. The method was invented in China about 2000 years ago, and then it was reinvented in Europe in the 17th century, so it is surprising that the primary European sources have not been identified until now. It is an interesting story in the history of computing and technology that Carl Friedrich Gauss came to be mistakenly identified as the inventor of Gaussian elimination even though he was not born until 1777.
     
    The European development has three phases. First came the “schoolbook” method that began with algebra lessons written by Isaac Newton; what we learn in high school or precalculus algebra is still basically Newton's creation. Second were methods that professional hand computers used to solve the normal equations of least squares problems; until comparatively recently the chief societal use for Guassian elimination was to solve normal equations for statistical estimation. Third was the adoption of matrix notation in the middle of the last century; henceforth the schoolbook lesson and the professional algorithms were understood to be related in that all can be interpreted as computing triangular decompositions.

  • Making sports as fun doing your taxes: How statistical analysis is used to build teams, plan for opponents and give fans more to argue about
    Speaker:     Benjamin Alamar (Menlo College, Director of Basketball Analytics and Research at Oklahoma City Thunder)
    When: October 20, 2010, 4pm
    Where: Harney Science Center, Room 232
    Abstract:  As soon as sports are invented, statistics are created to help us understand who won and how well each team/individual played. Coaches, managers and fans have gotten used to discussing their sports within the context of certain numbers, but the numbers that are most frequently discussed are often misleading or incomplete. Good statistical analysis can help process the data that is available in more informative ways and suggest which types of information would be most useful to begin to collect.
     
    With each new advance in the field of sports statistics, however, comes further push-back from groups of fans and executives that do not see the utility of the new analysis. This sets up the additional challenge for the sports statistician of not only pioneering new techniques, but effectively communicating their analysis to the relevant audience, so that the work is not wasted. When communicated effectively though, advanced statistical analysis is used regularly in the front offices and coaching rooms of MLB, the NBA and the NFL.
     
     
  • Matroids as a theory of independence
    Speaker:     Federico Ardila (San Francisco State University)
    When: October 6, 2010, 4pm
    Where: Harney Science Center, Room 232
    Abstract:      Consider the following three questions:
    • If each person in a town makes a list of people that they are willing to marry, what is the largest possible number of marriages that could take place?
    • Let a=x2+y2, b=x3+y3, and c=x5+y5. Is there a polynomial equation with constant coefficients satisfied by a, b, and c?
    • How do we build the cheapest road system connecting all the cities in a country, if we know the cost of building a road between any two cities?

    To answer these questions, mathematicians in very different areas were led to the discovery of "matroids". My talk will give a brief introduction to these objects.
     

  • Quaternion numbers: history and applications
    Speaker:     Alon Amit (Facebook, Inc.)
    When: September 23, 2010, 4pm
    Where: Harney Science Center, Room 232
    Abstract: Quaternions are a strange and wonderful system of numbers which includes, but vastly extends, the complex numbers. Complex numbers correspond to pairs of real numbers, and so to points in the plane; the quaternions correspond to quadruples of real numbers and to points in 4-dimensional space. We will talk about why and how they were discovered (this has to do with physics), why we have a number system in 2 and 4 but not 3 dimensions (this has to do with topology) and what they are good for (this has to do with number theory and computer animation).
     
  • A knotty problem
    Speaker:     Radmila Sazdanovic (MSRI)
    When: April 14, 2010, 4pm
    Where: Harney 232
    Abstract: We will define knots and talk about tools (invariants) mathematicians use to better understand and distinguish knots, which is a very knotty and still open problem. Therefore, mathematicians keep inventing better and better invariants: starting with numerical ones, such as the unknotting number or 3-colorings, through polynomials all the way to most recent, homology theories. This heavy mathematical machinery can be used outside mathematics: in physics, quantum computing, DNA studies and protein folding.
     
  • Unsolvability in mathematics
    Speaker: Jennifer Chubb (USF)
    When: March 31, 2010, 4pm
    Where: Cowell Hall, Room 413
    Abstract: David Hilbert said that in mathematics, "there is no ignorabimus," and, in a way, he was right (though not in the way he'd hoped). If a problem is solvable, we should be able work out a solution, and if it's not, well, then we should be able to prove that. If we want to show a problem is solvable, we know what to do... find the solution! Showing that a problem is unsolvable is trickier. One way is to show that being able to solve that problem would make it possible for us to solve another problem that's already known to be unsolvable. We will discuss the Alan Turing's Halting Problem and see why it is unsolvable. With this example in hand, we will discuss other famous problems, including Hilbert's 10th Problem, and see their connections to the Halting Problem.
     
  • Finding a Classical Needle in a Quantum Haystack: An introduction to quantum algorithms
    Speaker: Michael Nathanson (Dept. of Mathematics and Computer Science, St. Mary's College of California)
    When: February 24, 2010, 4:30pm
    Where: Harney, Room 510
    Abstract: Quantum computing attempts to redesign hardware at the atomic scale to take advantage of the strange effects of quantum mechanics, and there are growing numbers of physicists, computer scientists, and mathematicians who work on these problems. It has been shown that, in theory, a quantum computer could accomplish certain tasks (such as factoring) much faster than the best-known algorithms for classical computers. This talk will introduce quantum computing by exploring the quantum search algorithm. The algorithm is beautifully geometric and can be visualized in a plane. Since the search problem is well understood, it is easy to compare the efficiency of the quantum algorithm against the best possible classical one.