|
|
|
|
|
| REU at Cornell University ( June 19 - August 11, 2000 (8 weeks) ) |
 | Deadline: February 24, 2000 |
| Summary: |
| Undergraduates will work on research projects under the direction of Cornell University Mathematics Department members and visitors. The three specific projects and faculty members directing them follow. |
| PROJECT 1: ANALYSIS ON FRACTALS (ROBERT STRICHARTZ) Students in this project will study properties of functions defined on fractals. For a certain class of self-similar fractals, including the familiar Sierpinski gasket (also called the Sierpinski triangle,) there is now a theory of "differential equations." One of the goals of this project is to obtain more information about solutions of these fractal differential equations, following up on work that has been done over the past 3 summers by REU students. (See the web site http://mathlab.cit.cornell.edu/~gibbons for a sample of this work.) |
| PROJECT 2: MATH PROBLEMS FROM BIOLOGY (RICK DURRETT) Ecology and genetics are a source of many interesting problems in mathematics. Among the problems we will consider are the following: |
| Evolving predator prey systems. In the 60's Paine demonstrated that a predator can cause the coexistence of species that would not coexist in its absence. How many species can coexist in this way? What happens when new species are introduced by mutation or immigration. |
| Transposable elements are like computer viruses in our DNA. The availability of complete genomic sequence for yeast and for fruit flies (to be released in Feb 2000) makes it possible to ask questions about the number of distinct families of TE's and when they entered the genome. |
| Genome rearrangement. Our DNA evolves not only by small local changes but also by large inversions within a chromosome or exchange between two chromosomes. The 15 October 1999 issue of Science magazine gives a fairly complete picture for mammals but many questions remain about the relationship between plant genomes. |
| BACKGROUND: Students should have some experience in programming. No knowledge of biology is required but an undergraduate course in probability would be useful. |
| PROJECT 3: ALGEBRAIC COMBINATORICS (RICHARD EHRENBORG AND MARGARET READDY) Algebraic combinatorics links many different areas of mathematics including polytopes, algebra, discrete geometry and partially ordered sets, to name a few. In this REU project we will explore different interactions between these areas. The planned projects include: |
| Exploring flag vectors of polytopes starting with zonotopes and hyperplane arrangements. Extending classical permutation statistics, such as descent set, excedance set and inversions, to set-valued ones. |
| Finding appropriate enumerative properties of classes of matrices, such as alternating signed matrices and their analogues. |
| BACKGROUND: Some programming experience is desirable, and a course in abstract algebra or group theory would be helpful, but neither is required. |
|
![[Up]](/images/up.gif)
![[Feedback]](/images/feedback.gif)
