The Department of Mathematical Sciences at Lakehead University runs about 5 to 6 colloquiums a year, on an irregular schedule.
TUESDAY, MARCH 13, 2018
Dr. Xiaowen Zhou, Professor,
Department of Mathematics & Statistics
"Extinction, Explosion and Coming Down from Infinity for Nonlinear
Continuous-State Branching Processes"
Date: Tuesday, March 13, 2018
Time: 3:30 - 4:30
Room: RB 1023
Abstract: A continuous-state branching process can be identified as the unique
nonnegative solution to a SDE driven by a Brownian motion and a compensated Poisson random measure; see Bertoin and Le Gall (2006) and Dawson and Li (2012). By adapting this SDE, we can introduce a continuous-state branching process with nonlinear branching mechanism. Intuitively, the solution to the modified SDE is a branching process with branching rates depending on the current population size.
Using a martingale approach, we study its survival/extinction behaviors and find respective sufficient conditions on the branching rate functions under which the process either survives with probability one or dies out with a positive probability, respectively. Similarly, we can also discuss the explosion and the coming down from infinity behaviors of the continuous-state nonlinear branching process. We will show
that those conditions are quite sharp.
This talk is based on joint work with Peisen Li and Xu Yang.
FRIDAY, MARCH 16, 2018
ENERGY DRIVEN SYSTEMS FROM LIQUID CRYSTALS AND EPITAXY
Dr. Xin Yang Lu, Assistant Professor
Department of Mathematical Sciences
Friday, March 16, 2018
Abstract: Epitaxy is a process in which a thin film is grown above a much thicker substrate. Even in the simplest case, with no deposition, and purely elastic interactions, such growth leads to a nonuniform film thickness since the film and the substrate can have different rigidity constants. The resulting system is thus an energy driven one, but quite irregular. Similarly, the evolution of nematic liquid crystals, systems is modeled by a highly complex energy driven system. In this talk I will present some recent results about the regularity of solutions to several equations arising from nematic liquid crystals and epitaxy.