Applied dynamical system seminar

Speaker: Junping Shi (College of William & and Mary)

"Modelling Phytoplankton-Virus Interactions: Phytoplankton Blooms and Lytic Virus Transmission"

Time: 12:30

Room: MC 204

A dynamic reaction-diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyilytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment. This is a joint work with Yawen Yan and Jimin Zhang.

Colloquium

Speaker: Janusz Adamus (Western)

"Introduction to Arc-analytic Geometry."

Time: 15:30

Room: MC 107

Abstract: Arc-analytic geometry is a fairly new branch of real analytic and algebraic geometry, inspired by John Nash's questions about the role of arcs in geometry. It studies the so-called arc-analytic functions and arc symmetric sets. In the algebraic setting, it provides the most satisfactory real counterpart of Zariski topology over an algebraically closed field. In the analytic setting, in contrast, it consists at present mostly of tough open problems. I will give a brief history of the subject with an overview of classical results from the late 80's and the 90's, and discuss both the recent progress and questions. The talk should be accessible to senior math undergrads.

Colloquium

Speaker: Junping Shi (College of William & Mary, VG, USA)

"Reaction-diffusion models for animal movement with spatial memory and nonlocal advection"

Time: 15:30

Room: MC 107

Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Spatial memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements: (i) reaction-diffusion-advection model with time-delayed memory-based movement; and (ii) reaction-diffusion-advection model with a non-local advection term driven by a cognitive map representing memory of past animal locations embedded in the environment. The well-posedness of models and bifurcation of spatiotemporal patterns will be discussed.

Transformation Groups Seminar

Speaker: Kumar Shukla (Western)

"Reisner's criterion"

Time: 14:30

Room: MC 108

TBD