Richard Gejji Presents Mathematical Biology Research
 
Richard Gejji gave a poster presentation entitled, "Analysis of a Continuous Limit Equation Modelling Chemotactic Cells with Volume Exclusion" at the Math Biology Workshop at University of Utah in Salt Lake City on May 15 and 16, 2009. The purpose of the conference was to bring together early career researchers who have an interest in sharing their research and discussing the challenges of building a research career that crosses the disciplines of mathematics and biology.

Gejji is pursuing a Ph.D. in Mathematics under the guidance of Mark Alber, the Notre Dame Chair in Applied Mathematics and director of the Interdisciplinary Center for the Study of Biocomplexity at the University of Notre Dame. Alber and Pavel Lushnikov, associate professor in the Department of Mathematics and Statistics at the University of New Mexico, have derived a model from local cell-cell interactions to describe their collective motion under the assumption that the cells do not overlap. From this model, they have derived a continuous limit equation that is a very good approximation of the discrete model. At this conference, Gejji presented his research with Alber and Bogdan Kazmierczak, from the Polish Academy of Sciences, Institute of Fundamental Technological Research, on proving the boundedness of solutions to the equation Alber and Lushnikov derived as well as the group’s results on the existence of patterns that form. This shows that the solution does not blow-up in finite time and that under certain parameter ranges the solution is capable of producing increasingly complex patterns.

Later this summer, Gejji will be participating in the 2009 Summer Graduate Program of the Mathematical Biosciences Institute on a topic in biology with mathematical applications. This year's theme is on developmental biology and mathematical ecology and evolution. He will spend the first week on tutorials about evolutionary ecology and adaptive dynamics and the following two weeks on a team project where he will participate with a team to work on one of the following topics:
1. Maintenance of variation in mate choice and mate quality
2. Sanctions and cooperative behavior
3. Evolution of dispersal in heterogeneous landscapes
4. Evolution of virulence.