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SUMMARY:Quantum Unique Ergodicity and the number of nodal domains of autom
 orphic forms
DTSTART:20180704T134500
DTEND:20180704T144500
DTSTAMP:20260922T014117Z
UID:1ee3c6ecdd3fbb5a38679301a843889e343b21d463496c61fccbd6d0
CATEGORIES:Conferences - Seminars
DESCRIPTION:Junehyuk Jung (Texas AM)\nIt has been known for decades that o
 n a flat torus or on a sphere\, there exist sequences of eigenfunctions ha
 ving a bounded number of nodal domains. In contrast\, for a manifold with 
 chaotic geodesic flow\, the number of nodal domains of eigenfunctions is e
 xpected to grow with the eigenvalue. In this talk\, I will explain how one
  can prove that this is indeed true for the surfaces where the Laplacian i
 s quantum uniquely ergodic\, under certain symmetry assumptions. As an app
 lication\, we prove that the number of nodal domains of Maass-Hecke eigenf
 orms on a compact arithmetic triangles tends to $+\\infty$ as the eigenval
 ue grows. I am going to also discuss the nodal domains of automorphic form
 s on $SL_2(\\mathbb{Z})\\backslash SL_2(\\mathbb{R})$. Under a minor assum
 ption\, I will give a quick proof that the real part of weight $k\\neq 0$ 
 automorphic form has only two nodal domains. This result captures the fact
  that a 3-manifold with Kaluza--Klein metric never admits a chaotic geodes
 ic flow. This talk is based on joint works with S. Zelditch and S. Jang.
LOCATION:MA A3 31 https://plan.epfl.ch/?room=MAA331
STATUS:CONFIRMED
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