The current schedule can be found here.

All talks are at 4:15 in HH229 unless otherwise noted.

To volunteer to give a talk, or for anything else regarding the seminar contact Megan Patnott.

Date | Speaker | Title |
---|---|---|

Monday, September 1 | David Galvin | The “Happy End Problem” — A Mathematical Love Story |

Monday, September 15 | Bonnie Smith | Monomial Ideals and the Core |

Monday, September 29 | Don Brower | The Random Graph is Simple |

Monday, October 27 | Tom Edgar | Rock the Vote or Vote The Rock |

Monday, November 10 | Steven Broad | Umbilics, Lines of Curvature and a Conjecture of Caratheodory |

Monday, December 1 | Richard Gejji | The Calculus on Time Scales |

Monday, January 26, 2009 | David Karapetyan | Well Posedness of the Camassa-Holm Equation on the Torus |

Monday, February 2 | CANCELED | |

Monday, February 16 | Stacy Hoehn | Manifolds and the Shape of the Universe |

Monday, April 6 | Josh Lioi | An Applied Mathematics Perspective on Blood Clotting |

Monday, April 20 | Ryan Grady | A Mathematical Introduction to Quantum Field Theory |

Monday, May 4 | TBD | (This is during finals week and may be canceled) |

**Speaker**- David Galvin
**Title**- The “Happy End Problem” — A Mathematical Love Story
**Abstract**-
Given any 5 points in the plane, no three collinear, some 4 of them must form the vertices of a convex quadrilateral. (Go ahead and convince yourself --- it's fairly easy).

Now let's try to generalize. Is there an f(n) such every set of f(n) points in the plane, no three collinear, contains n points that form the vertices of a convex n-gon?

This is the ``Happy End'' problem, posed in the early 1930's. Its solution touches on topics from graph theory, logic and analysis, as well as giving rise to a love story that spanned over seventy years and two continents.

**Speaker**- Bonnie Smith
**Title**- Monomial Ideals and the Core
**Abstract**- A monomial ideal in a polynomial ring R=k[X_1,..,X_d] is an ideal which can be generated by elements of the form X_1^{n_1}...X_d^{n_d}. Such an ideal J can be represented as a region in $d$-space, which in theory allows us to describe how to get from J to other monomial ideals associated to J in a very combinatorial manner. Two such associated ideals are the core of J and the $S_2$-ification of J. I will define these ideals, discuss them a bit, and show some results I have for a particularly nice class of ideals in k[x,y]. Pictures will abound.

**Speaker**- Don Brower
**Title**- The Random Graph is Simple
**Abstract**- There are many ways to define the random graph, but they all lead to the same, unique, structure. The first order theory of this structure gives a class of structures which "look like" the random graph. However, while there is a unique random graph, there are many, many look-a-likes in every uncountable cardinality. This talk will show how the many different look-a-likes come from the presence of a formula with the "independence property"; that the random graph is the simplest theory exhibiting this property; and, finally, survey other theories with this property. Also, the negation of having the independence property has its own, profound, consequences. All logic jargon will be explained, in patient, loving detail.

**Speaker**- Tom Edgar
**Title**- Rock the Vote or Vote The Rock
**Abstract**- Is it possible for Dwayne Johnson (aka The Rock) to get elected president of the United States? Who would he have to pay off? We give a talk investigating mathematical aspects of counting votes. We hope to come to the conclusion that it is very well possible that The Rock could be elected president if he gets to choose HOW to count the votes.

**Speaker**- Steven Broad
**Title**- Umbilics, Lines of curvature and a conjecture of Caratheodory
**Abstract**- We will introduce umbilics and discuss the structure of the lines
of curvature around generic isolated umbilics. We will also discuss a
conjecture attributed to Caratheodory which states that a smooth, convex
embedding of the 2-sphere into R^3 has at least two umbilics. Finally, we
will discuss the deep connection between the Caratheodory conjecture and
Loewner's conjecture about the index of the vector field (∂^2)ƒ
for C^2 functions ƒ : {|z| ≤ 1} to R.

(See abstract as pdf.)

**Speaker**- Richard Gejji
**Title**- The Calculus on Time Scales
**Abstract**- We know how to differentiate and integrate continuous functions, and we can apply difference and summation operations on discrete functions, but what can we say when the domain of the function is more complicated? Could we write down general product, chain, integration by parts and substitution rules independent of domain? How about inequalities and dynamical equations? All these questions and more will be answered in this whirlwind tour of Hilger's work towards unifying discrete and differential calculus.

**Speaker**- David Karapetyan
**Title**- Well-Posedness of the Camassa-Holm Equation on the Torus
**Abstract**- See abstract as pdf.

**Speaker**- Stacy Hoehn
**Title**- Manifolds and the Shape of the Universe
**Abstract**- An n-manifold is a topological space that locally just looks like n-dimensional Euclidean space. For example, the surface of the Earth is a 2-manifold since if I am standing on the Earth and look around me, it just looks like I am standing on a 2-dimensional plane. Meanwhile, the spatial universe in which we live appears to be a 3-manifold since every part of the universe that we have seen so far has locally looked like 3-dimensional Euclidean space. However, which 3-manifold is the universe? This question is not easy to answer, but recent experimental evidence suggests that there are only 10 possibilities.

**Speaker**- Josh Lioi
**Title**- An Applied Mathematics Perspective on Blood Clotting
**Abstract**- Hemostasis is the complex process by which the human body halts the loss of blood through clotting. The formation and eventual lysis (breaking up) of a clot is dictated by a multitude of factors, including chemical processes, cellular components, and the flow of blood through the vessel. By using a combination of differential equations and probabilistic approaches, we have begun to create a model which can allow us to better understand this biological phenomenon.

**Speaker**- Ryan Grady
**Title**- A Mathematical Introduction to Quantum Field Theory
**Abstract**- In this talk we describe field theories based on the axioms of Atiyah and Segal. Motivated by physics, field theories have become a valuable mathematical topic. Recently, Lurie, Stolz, Teichner and others have used field theories to study higher category theory as well as generalized cohomology theories. This talk will build up to this relation between field theories and cohomology.

MGSA - Math Department - University of Notre Dame