ACMD Seminar: Boundary-degenerate elliptic equations, theory and applications

Brian Weber
ShanghaiTech University

CANCELLED

Tuesday, March 31, 2020, 3:00–4:00 PM
Building 101, Lecture Room C
Gaithersburg

Tuesday, March 31, 2020, 1:00–2:00 PM
Building 1, Room 1107
Boulder

Host: Justyna Zwolak

Abstract: Boundary-degenerate PDEs have attracted lots of recent attention, motivated by applications in financial mathematics, Kähler geometry, transport phenomena, and other applications. We study solutions to degenerate-elliptic equations of the form

y(f_xx +f_yy) + B₁(x,y)f_x + B₂(x,y)f_y + C(x,y)f = 0 

on the upper half-plane. Such solutions model a remarkably wide range of phenomena, from European-style options prices in finance, to scalar-flat metrics in toric Kähler geometry, and the boundary front of a fluid diffusing through a porous medium, among numerous other applications. We explore some recent work in the boundary- specification problem, and powerful constraints on solutions including a new Liouville- type theorem on entire solutions.

Bio: After receiving a Ph.D. in Mathematics from UW-Madison, specializing in differential geometry, Brian Weber received postdoc appointments at Stony Brook, NYU, and a professorship at the University of Pennsylvania. He currently lives and works in Shanghai, where he is a professor at ShanghaiTech University.

Note: Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.

This talk will be broadcast on-line using BlueJeans.  Contact acmdseminar [at] nist.gov (acmdseminar[at]nist[dot]gov) for details.