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BEGIN:VEVENT
DTSTART:20240419T210000Z
UID:179412@events.unl.edu
DTSTAMP:20240221T162401Z
ORGANIZER;CN=Adam Larios:
SUMMARY:Adam Larios\, University of Nebraska - Lincoln
STATUS:CONFIRMED
DESCRIPTION:Partial Differential Equations (PDEs) lie at the heart of nearl
y every area of science. Einstein's theory of general relativity\, quantum
mechanics\, complex weather patterns\, the spread of disease\, the turbul
ent flow of blood in the heart\, the growth of tumors\, the stability of b
ridges\, the erratic patterns of stock options\, the pulsing of electromag
netic waves\, the flow of oceans and rivers\, the flocking patterns of bir
ds\, the growth of bones as we develop\, the spots of cheetahs\, and the s
tripes of zebras\, are all modeled by PDEs. Moreover\, PDEs arise within m
athematics itself\, in areas such as differential geometry (the minimal su
rface equation)\, complex analysis (the Cauchy-Riemann equations)\, and ha
rmonic functions (Laplace's equation). Two of the seven famous $1\,000\,00
0 Clay Millennium Prize problems are directly about PDEs\, and a third pro
blem was solved by using PDEs as the major proof tool.\n\nI will give many
examples of PDEs\, and then give you a tool to be able to understand much
of the basic behavior of PDEs at a glance. We will see many visual demons
trations\, and by the end\, you will be able to understand some of the und
erlying dynamics of several important PDEs\, including the 3D Navier-Stoke
s equations\, and also the chaotic "flame" equation known as the Kuramoto-
Sivashinsky equation. We will discuss the problem of singularities for the
se equations\, that is\, the question of whether solutions to the equation
can become unphysical over time. Most of the talk should be accessible to
students who have taken calculus.
LOCATION:Avery Hall Room 115
URL://events.unl.edu/math/2024/04/19/179412/
DTEND:20240419T220000Z
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