SMRI Seminar: Pedit -- Minimal Lagrangian surfaces of high genus in $CP^2$

SMRI Seminar: 
’Minimal Lagrangian surfaces of high genus in $CP^2$’ 
Franz Pedit (University of Massachusetts, Amherst) 

Thursday 24th August, 1:00-2:00pm (AEST) 
Carslaw 375 & online via Zoom (register/join - https://uni-sydney.zoom.us/j/88338253103) 

Abstract: The study of properties of surfaces in space has historically been a fertile
ground for advances in topology, analysis, geometry, Lie theory, and mathematical
physics.  The most important surface classes are those which arise form variational
problems, for example, minimal surfaces which are critical points of the area
functional.  The Euler Lagrange equations are PDEs which serve as model cases for
developments in geometric analysis.  Often these equations exhibit large (sometimes
infinite dimensional) symmetry groups which puts the theory into the realm of
“integrable systems”, that is, PDEs which allow for an infinte hierarchy of
conserved quantities.  This theory has been studied extensively over the past 40 years
and led to significant advances in the classification of (minimal, constant mean
curvature, Willmore etc.)  surfaces of genus one.  The higher genus case has been more
illusive and examples are usually constructed using non-linear perturbation theory and
gluing techniques.  

In this talk I will explain how one can use ideas from integrable systems to construct
examples of high genus minmal Lagrangian surfaces without recourse to hard analysis.  

This approach is more explicit than PDE existence results and one is able to obtain more
quantitative information about the constructed examples, for instance, asymptotic
area/energy estimates.  I will also give a brief overview of the historical developments
and the significance of minimal Lagrangian surfaces in mathematical physics.  

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Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on
the SMRI Terrace (accessed through A14-04-L4.36) 

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