__January 17__

__Speaker__- Ben Polletta

__Title__- What Is Curvature, and Does Your iTunes Library Have It?What does it mean for a higher-dimensional space to be curved? How can we compute the curvature of a graph or a set of data points? The curvature of a Riemannian manifold, an important tool in subjects including dynamical systems and general relativity, is central to the study of geometric flows, an area of much recent activity. At the same time, there is an increasing awareness that statistical data may lie on curved manifolds. Consequently, we'd like to compute quantities associated with curvature on simplicial complexes, which may arise as data sets or approximations to abstract manifolds. Ideally, we'd like a discrete measure of curvature which approaches classical curvature as our simplicial complex gets fine. In this talk, I will give an elementary introduction to curvature, and I will describe one approach to computing scalar curvature on simplicial complexes. Time permitting, I will show how in two dimensions, this discrete curvature approaches classical scalar curvature in an appropriate limit.

__January 24__

__Speaker__- John Kerl

__Title__- The Householder transformation, Swiss-Army knife of numerical linear algebraIn this talk I will define the Householder transformation, then immediately put it to work in several ways:

- To illustrate the usefulness of geometry to elegantly derive and prove seemingly algebraic properties of the transform,
- To demonstrate an underappreciated use of the Householder transform for numerical linear algebra,
- To show how geometric notions of determinant and matrix norm can be used to easily understand round-off error in Householder and Gaussian-elimination methods,
- To prove that not only the applied grads can have fun with numerical techniques, and
- To give an application of Householder transforms to dumb on-board processors, subtitled "What I did over the winter break while the rest of you were having a real vacation."

__January 31__

__Speaker__- Grethe Hystad

__Title__- The Srong Szego Limit TheoremIn this talk, I will sketch the proof of the Szego limit theorem on the asymptotics of Toeplitz determinants. The Potts-Ward formula calculates the two point spin correlations of the Ising model as a Toeplitz determinant. I will show how to derive the Onsager-Yang formula for the spontaneous magnetization by applying the Szego limit theorem to the Potts-Ward formula.

__February 7__

__Speaker__- Cameron McLeman

__Title__- Pointless TopologyEven at first glance, there is a striking parallel between Galois theory and covering space theory. They both use a group (the Galois group and fundamental group, respectively) to classify the (nice) intermediate extensions of a given extension/covering. It's not hard to make this analogy more precise using the language of categories and functors, but it's tempting to leave the story there -- as a compelling analogy. The goal of the talk will be to provide an interpretation under which these two constructions (and many more) are in fact the

*same*notion, using the idea of a*Grothendieck topology*. By analogy, a topological space is a set equipped with a distinguished collection of subsets (the open ones) that behaves nicely under unions and intersections. A Grothendieck topology is just a topology equipped with a pair of quotation marks: A ''set'' with a specified collection of ''subsets'' which behaves nicely under ''unions'' and ''intersections.'' The talk will make this last sentence precise.__February 14__

__Speaker__-No Speaker

__Title__-__February 21__

__Speaker__-No Speaker

__Title__-__February 28__

__Speaker__- Daniel Champion

__Title__-Polyhedral Manifolds and Pseudo-ManifoldsThis talk will be an introductory exploration of several intriguing and historically rich 3-manifolds. In particular, we will be focusing on manifolds (and pseudo-manifolds) obtained from polyhedra via identification of faces, or from quotients by their isometry groups. Of particular interest will be the local geometry, homotopy, and homology groups. In the least, you will be introduced to a number of 3-manifolds (including lens spaces) and learn how to draw an excellent dodecahedron or icosahedron freehand.

__March 7__

__Speaker__- Yuliya Gorlina

__Title__- Symplectic Geometry and Polygon Moduli SpacesEveryone hears about symplectic geometry, but few people actually know that much about it. In this talk, I will attempt to give you an idea about what symplectic geometry is. For those familiar with Lie algebra, I will give an introduction to the moment map and symplectic reduction. At the end, we will see how all of this relates to polygons.

__March 21__

__Speaker__-Chantel Blackburn

__Title__- The Hausdorff Metric Geometry: 19 is Just...Missing!The Hausdorff metric gives a way to measure the distance between non-empty compact subsets of n-dimensional Euclidean space. A configuration defines two sets (infinite or finite) for which it is possible to have a finite number of elements at each location between the sets. One of the intriguing properties of the geometry imposed by this metric is that no finite configuration exists with 19 elements at each location between two sets. This talk addresses 1) whether any such infinite configuration exists and 2) an interesting application of the finite result to graph theory.

__March 28__

__Speaker__- Casey Warmbrand

__Title__- Poker Models, Best-Responses, and BluffingIn this talk I will present the two most famous poker models developed by Emile Borel and John von Neumann. Both models greatly simplify the game of poker; they are both two player games where each player's "hand" is simply an independent uniformly distributed random variable between 0 and 1. Both games only allow one round of betting with limited options. Using the techniques of game theory, I will present a thorough analysis of both models, presenting best-responses to any possible strategy. We will see the benefit to occasional bluffing in the von Neumann model of poker.

__April 4__

__Speaker__- Alex Petrov

__Title__- Algebraic TangentsWe all know what a tangent line is from Calculus. In this talk I will define the concept of a tangent line to an algebraic curve via the tools of commutative algebra. After we have gone through the definitions, I will prove that I have defined exactly the usual tangent line that we are all familiar with. In the end I will give an example that I hope will convince everyone that the new definition has its merits.

__April 11__

__Speaker__-Justin Miller

__Title__-p-adic Continued Fractions of Quadratic IrrationalsI will discuss the classical theorems about real continued fractions and attempts to create p-adic analogues.

__April 18__

__Speaker__- Ryan Smith

__Title____April 25__

__Speaker__- Grant Peterson

__Title__- What is the molecular clock, and what should we expect from it on short time scales?Observational studies tell us that closely related but evolutionarily distinct lineages evolve at a constant rate through time. This idea gives rise to the molecular clock. However, a difficulty arises on short time scales when we actually try to estimate how long two lineages have been distinct. In this talk I will explain what the molecular clock is, the difficulties with it on short time scales, and how we can see what we should expect taking a computational approach.

__May 2__

__Speaker__- Arlo Caine

__Title__- Illustrating MathematicsIf a picture can be worth a thousand words, then a movie can be worth a million. Ongoing improvements in computer technology and graphics manipulation software are opening new pathways for communicating mathematics. In this talk I will show some illustrations of mathematics that I created using POV Ray. The Persistence Of Vision Raytracer (POVRay) is free software (available for both MSWindows and Linux platforms) that can be used to create very detailed 3d images. I'll show you how to get started using POVRay and some other readily available programs to make animations. We'll illustrate a cyclic subgroup of the loop group of SU(2), geodesics in the 3-sphere, alignment of symmetric space embeddings with group decompositions, and finish with what could be a new Disney theme park ride: "The Hopf Fibration Experience."