| Date: | 09/24/08 |
|---|---|
| Speaker: | George Jennings and Wai Yan Pong |
| Title: | Open Source Software for Computation |
| Abstract: | We will illustrate the basics of SAGE and Octave. |
| Date: | 05/07/08 |
| Speaker: | Alfonso Carriazo (University of Sevilla, SPAIN) |
| Title: | Submanifolds associated with graphs. |
| Abstract: |
Given an almost Hermitian manifold, the study of its submanifolds attending to their behaviors with respect to the ambient almost complex structure is a main topic in complex Riemannian geometry. In this sense, complex submanifolds, totally real submanifolds and CR submanifolds are well-known, and some other kinds of submanifolds have been introduced later as their natural generalizations: slant, semi-slant, quasi-slant, etc... All these submanifolds have something in common: they can be associated with graphs. Basically, we first construct a graph related to the tangent space at an arbitrary point of the submanifold, and then, we extend it differentiably to every point, in a certain way. In this talk, we show some advances on this idea, including general results on the structures of the associated graphs, characterizations of some kinds of submanifolds and some classifications in dimensions 4 and 6. We think that this association will provide us with new tools to study the general problem of classification of submanifolds, by establishing some nice relationships between two traditionally remote research areas: Differential Geometry and Discrete Mathematics. |
| Date: | 04/23/08 |
| Speaker: | Marek Suchenek (CSUDH) |
| Title: | On REALLY big numbers |
| Abstract: |
Mathematicians and other children often play the following game: We take turns naming numbers, and see who can name the largest one. [Kenneth Kunnen, 1977]
It is amazing, and very entertaining, to learn how incredibly large numbers (or sizes of infinity, if you will) one can conceive. In this talk, mostly intended for undergraduate students, I will scratch the surface of elegant and deceitfully simple theory that lies behind the above game. (For those familiar with the subject, that theory comes essentially from Kelley-Morse theory of classes and Zermelo-Fraenkel set theory with Axiom of Choice.) |
| Date: | 03/19/08 |
| Speaker: | Shandy Hauk (University of Northern Colorado) |
| Title: | Developing Video Cases of College Math Instruction |
| Abstract: | A national cooperative of universities is developing a collection of videos of college math classes for helping college math instructors as they develop their teaching skills. Still in the first year of a 3-year project, we have some draft video and text materials and are seeking input about the materials from college math instructors. The purpose of this meeting is to share some of these materials and get feedback about how to shape and re-develop the materials. |
| Date: | 03/05/08 |
| Speaker: | Chi-Lung Chang (CSUDH) |
| Title: | Is there life after Venn? |
| Abstract: | A Venn diagram is the result of partitioning the universe at hand by means of a circle or circles. A C-diagram, on the other hand, is the result of partitioning the same universe by means of lines, vertical or horizontal, into subsets which are "cells". There has been a quiet experimentation ongoing to replace the Venn diagram with the C-diagram in my elementary mathematics classes. The concept of the C-diagram was first introduced in my talk of 10/24/07, Teaching Probability using Event Grids. The purpose of this talk or, more appropriately, workshop is to exchange ideas on how best to use the C-diagram from the perspective of elementary mathematics students and teachers in such tasks as depicting sets,verifying set identities or counting with sets. The emphasis will be on the nuts and bolts of C-diagrams rather than theory. After my imminent departure from CSUDH, it is my hope that some teachers may want to continue this "movement". In addition, the subject may also have the potential of being an investigative Math Ed topic to confirm or reject the hitherto positive anecdotal evidence. Virtually no math background is needed to understand the talk. |
| Date: | 02/07/08 |
| Speaker: | Andrew Nevai (Mathematical Biosciences Institute, Ohio Sate University) |
| Title: | Spatial problems in mathematical ecology |
| Abstract: | In this talk, I will introduce two spatial problems in theoretical ecology together with their mathematical solutions. The first part of the talk concerns competition between plants for sunlight. In it, I use a mechanistic Kolmogorov-type competition model to connect plant population vertical leaf profiles (or VLPs) to the asymptotic behavior of the resulting dynamical system. For different VLPs, conditions can be obtained for either competitive exclusion to occur or stable coexistence at one or more equilibrium points. The second part of the talk concerns the spatial spread of infectious diseases. Here, I use a family of SI-type models to examine the ability of a disease, such as rabies, to invade or persist in a spatially heterogeneous habitat. I will discuss properties of the disease-free equilibrium and the behavior of the endemic equilibrium as the mobility of healthy individuals becomes very small relative to that of infecteds. The family of disease models consists variously of systems of difference equations (which I will emphasize), ODEs, and reaction-diffusion equations. |
| Date: | 02/04/08 |
| Speaker: | Rene Schipperus (University of Calgary) |
| Title: | An introduction to Ramsey Theory |
| Abstract: | We give some of the history and first theorems in the subject known as Ramsey theory. There will be some simple and elegant proofs accessible to everyone. Near the end of the talk the speaker will discuss some of his own contributions to the Ramsey theory of ordinal numbers. |
| Date: | 01/31/08 |
| Speaker: | Sam Nelson (Pomona College) |
| Title: | An algebraic approach to Knot Theory |
| Abstract: | Quandles are an algebraic category similar to groups but with axioms dervied from the Reidemeister moves. Quandle theory is a rich source for invariants of knots and links as well as invariants of related objects such as braids, tangles, welded and virtual knots, knotted surfaces in S^4, 3-manifolds, etc. In this talk we will see the basics of quandle theory, meet several examples of quandle structures found in groups, modules, and vector spaces, and see a sampling of some recent results in quandle theory obtained in joint work with my research students. |
| Date: | 01/29/08 |
| Speaker: | Bruce Shapiro (Caltech) |
| Title: | Computational Modeling of the Shoot Apical Meristem |
| Abstract: | The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to five hundred cells that range from five to ten microns in diameter. These cells are organized into several distinct zones that maintain their topological and functional relationships throughout the life of the plant. As the plant grows, organs (primordia) form on its surface flanks in a phyllotactic pattern that develop into new shoots, leaves, and flowers. The central region contains pluripotent stem cells that continue to divide and differentiate into mature tissue throughout the life of the plant. In the computable plant project we observe several cell type-specific markers for growth and differentiation in live Arabidopsis plants with a dedicated confocal laser scanning microscope. These markers are affixed to various gene products or promoter regions using green fluorescent protein (GFP) variants that flouresce when they are illuminated within the microscope by a laser. This allows us to observe various meristem and floral primordial features, such as membranes and nuclei, and to track specific cell lineages over time. By fitting mathematical and computational models to these spatiotemporal expression patterns, we can infer how primordial cells are progressively specified and organs develop. From this we develop forward simulations and visualizations of the growing SAM. The talk will survey the modeling techniques and tools used and the modeling results produced in this project. |
| Date: | 01/22/08 |
| Speaker: | Jianlin Xia (UCLA) |
| Title: | Superfast solvers for some large structured matrix problems |
| Abstract: | This talk discusses superfast solvers for some large matrix problems which are rank structured. Examples of these structured problems include some large discretized PDEs, Toeplitz systems, certain low-rank updated eigenproblems (e.g. companion matrices), and others. Our superfast solvers use certain semiseparable rank structured matrices. I will first briefly show an example of a quadratic cost companion matrix eigensolver. Then I will focus on a fast multifrontal type direct solver for large sparse discretized PDEs. Mesh ordering and node elimination schemes are discussed. Semiseparable matrices are used to approximate dense intermediate matrices in the factorization. A new linear time factorization algorithm for semiseparable matrices is presented. The overall sparse solver has nearly linear complexity and linear storage, and has good potential for parallelization. It can also work as an effective preconditioner. Numerical results will be shown. This is joint work with Shiv Chandrasekaran, Ming Gu, Alan Laub, and Xiaoye Li. |