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DTSTAMP:20250812T194158Z
DESCRIPTION:Title: Nodal sets of monochromatic waves from a deterministic a
 nd random point of view\n\nAbstract:\n\nIn this talk we present recent res
 ults on the nodal set (i.e.\, the zero level set) of monochromatic waves (
 i.e.\, solutions of the Helmholtz equation) on the Euclidean space. Follow
 ing the breakthrough\n\nwork of F. Nazarov and M. Sodin\, a growing litera
 ture gives us powerful probabilistic results for the number of connected c
 omponents of the nodal set of random monochromatic waves. The aim of this 
 talk is to explore the properties of these standard random monochromatic w
 aves and\, consequently\, define a more general class of random monochroma
 tic waves depending on a parameter $s\in\mathbb{R}$\, which includes the s
 tandard definition as a particular case. This parameter\n\ncontrols some r
 egularity (of the Fourier transform) and decay properties of these waves. 
 Given that\, we study the structure of the nodal set depending on that par
 ameter from a deterministic and from a\n\nrandom point of view. Finally\, 
 we show how to construct deterministic realizations or examples of monochr
 omatic waves satisfying the probabilistic Nazarov-Sodin volumetric growth 
 for the number of\n\nconnected components of the nodal set and similarly f
 or the volume of the nodal set. This is a joint work with A. Enciso\, D. P
 eralta-Salas and A. Sartori.\n\nZoom link: https://umontreal.zoom.us/j/817
 06136500?pwd=UVFZeXhWd1RpY29GeE1nS2RkK0V3Zz09\n\nMeeting ID: 817 0613 6500
 \n\nPasscode: 872949\n
DTSTART:20220520T183000Z
DTEND:20220520T193000Z
SUMMARY:Álvaro Romaniega (Instituto de Ciencias Matemáticas)
URL:/mathstat/channels/event/alvaro-romaniega-institut
 o-de-ciencias-matematicas-339604
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