DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Bjorn Sandstede, Brown University

**Title: ***
Geometry and analysis of localized structures
*

**Abstract:**
Spatially localized patterns arise in many natural processes: buckled
shells, spots in autocatalytic chemical reactions, crime hotspots,
localized fluid structures, and vegetation spots are prominent
examples. Despite appearing on vastly different scales, spatially
localized structures often share similar features and properties, and
mathematical techniques can help identify the origins of such patterns
across different systems. In bistable systems, the profiles associated
with localized patterns are often close to the second nontrivial
bistable state over a large bounded region, and this region increases
as a system parameter is varied. In this talk, I give an overview of
this phenomenon and discuss the existence and stability of localized
patterns from geometric and analytical perspectives.

**Time:** Friday, February 15, 2019, 1:30-2:30pm

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491