Mathematics Plenary Speaker (Sunday,
10:15-11:45 a.m.)
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Chris Cosner is Professor of
Mathematics at the Department of Mathematics and Computer Science
of the University of Miami. He did his undergraduate work at the
University of California, San Diego, and received a PhD in
Mathematics from the University of California, Berkeley; his
advisor was Murray Potter. He was Assistant Professor at Texas A&M
prior to joining the University of Miami in 1982. He was a
visiting member of the Institute for Advanced Study and a visiting
faculty member at the University of Tennessee. His research
interests are elliptic and parabolic equations and systems, in
particular, reaction-diffusion systems and their application to
mathematical biology. He is co-author of "Spatial Ecology via
Reaction-Diffusion Equations", Wiley Series in Mathematical and
Computational Biology, 2003, and has authored or co-authored more
than 80 research papers in these fields, several of them in
biology journals. He is a member of the editorial board of
Advanced Nonlinear Studies.
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Some population models
with conditional dispersal.
Traditional spatial models in ecology often assume that
organisms disperse randomly by simple diffusion or similar processes.
In some cases, however, organisms may respond to their surroundings or
the presence of other organisms.McPeek and Holt introduced the terms
"unconditional" and "conditional" , respectively, to describe those
two types of dispersal. This talk will present some recent results
and work in progress on some models with conditional dispersal. The
models are based on partial differential equations that are similar to
reaction-diffusion equations, but incorporate advection, density
dependence in the diffusion coefficient, or density dependent boundary
conditions. The models arise as descriptions of the effects of
conditional dispersal on population dynamics and on competition
between species. Their analysis involves the use of methods from
partial differential equations and from continuation/bifurcation
theory. Those methods sometimes lead to linear eigenvalue
problems for elliptic operators with nonclassical boundary conditions.
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