Logunov's SISSA Mathematical Colloquium -- reminder

[Antonio Lerario]

 Dear All,

this is to remind next SISSA Mathematical Colloquium, scheduled for
tomorrow.

Speaker: Aleksandr Logunov (Princeton)
Title: Zero sets of Laplace eigenfunctions
When: Monday, January 25, at 4pm Rome
Where: remotely at this link https://sissa-it.zoom.us/j/86560206823

Abstract: In the beginning of 19th century Napoleon set a prize for the
best mathematical explanation of Chladni’s resonance experiments. Nodal
geometry studies the zeroes of solutions to elliptic differential equations
such as the visible curves that appear in these physical experiments. We
will discuss geometrical and analytic properties of zero sets of harmonic
functions and eigenfunctions of the Laplace operator. For harmonic
functions on the plane there is an interesting relation between local
length of the zero set and the growth of harmonic functions. The larger the
zero set is, the faster the growth of harmonic function should be and vice
versa. Zero sets of Laplace eigenfunctions on surfaces are unions of smooth
curves with equiangular intersections. Topology of the zero set can be
quite complicated, but Yau conjectured that the total length of the zero
set is comparable to the square root of the eigenvalue for all
eigenfunctions. We will start with open questions about spherical harmonics
and will explain some methods to study nodal sets.

Everyone is welcome!

Best,
Antonio

-- 
*http://people.sissa.it/~lerario <http://people.sissa.it/~lerario>*