Sydney Dynamics Group Seminar: Nathan Duignan, University of Sydney -- Sydney Dynamics Group Seminar

Seminar : Sydney Dynamics group Seminar.  
Day/time : Thursday, September 24 at 4:00 PM 
Location : SMRI seminar room (A12 Macleay Room 301).  
Speaker : Nathan Duignan, University of Sydney 



Title: When is a PDE really an evolution equation? 


Abstract: Given an evolution equation, we know what data to prescribe: the values of the
dependent variables at an initial time.  For analytic equations and suitable analytic
initial data, the Cauchy–Kowalevski theorem then guarantees a local analytic
solution.  But most PDEs are not obviously evolution equations… or are they? 

In this talk, I will introduce the Cartan–Kähler formal theory of PDEs, developed
over the course of the 20th century.  It gives a geometric way of thinking about PDEs
together with an algorithmic machine that eats a system of equations and spits out what
freely specifiable data its local solutions can depend on.  Along the way, the machine
may uncover hidden compatibility conditions: additional equations that must hold before
a solution can exist.  

I will try to explain the main ideas through examples rather than formalism.  Time
permitting, I will finish with a recent application in which these ideas help constrain
the design and optimisation of stellarators, magnetic confinement devices used in fusion
research.