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UID:20251121T152636EST-1584Tgz8w4@132.216.98.100
DTSTAMP:20251121T202636Z
DESCRIPTION:Stine Marie-Berge\, Leibniz Universität Hannover (1/3)\, Antoin
 e Métras\, Université de Montréal (2/3)\, Theo McKenzie\, UC Berkeley (3/3
 )\n\n(1/3) Title: Convexity Properties for Harmonic Functions on Riemannia
 n Manifolds\n	\n	Abstract: In the 70’s Almgren noticed that for a harmonic r
 eal-valued function defined on a ball\, its L 2 -norm over a sub-sphere wi
 ll have an increasing logarithmic derivative with respect to the radius of
  mentioned sphere. We examined similar integrals over a more general class
  of parameterized surfaces by studying harmonic functions defined on compa
 ct subdomains of Riemannian manifolds. The integrals over spheres are also
  generalized to level sets of a given function satisfying certain conditio
 ns. If we consider the L 2 norms over these level sets parametrized by a g
 eneralization of the radius\, we again reproduce Almgren’s convexity prope
 rty. We will sketch the proof of this result and illustrate the usefulness
  of the convexity result by examining some explicit parameterized families
  of surfaces\, e.g. geodesic spheres and ellipses. (2/3) Title: Steklov co
 nformally extremal metrics in higher dimensions Abstract: Steklov extremal
  metrics on surfaces have been much studied due to their connection to fre
 e-boundary minimal surfaces found by Fraser and Schoen. In this talk\, I w
 ill present a characterization of higher dimensional Steklov conformally e
 xtremal metrics\, highlighting its similarities with the same problem for 
 Laplace eigenvalues. To this end\, I will answer the question of which nor
 malization to use and show how the Steklov problem with boundary density a
 ppears natural in this context. This is joint work with Mikhail Karpukhin.
  (3/3) Title: Many nodal domains in random regular graphs Abstract: If we 
 partition a graph according to the positive and negative components of an 
 eigenvector of the adjacency matrix\, the resulting connected subcomponent
 s are called nodal domains. Examining the structure of nodal domains has b
 een used for more than 150 years to deduce properties of eigenfunctions. D
 ekel\, Lee\, and Linial observed that according to simulations\, most eige
 nvectors of the adjacency matrix of random regular graphs have many nodal 
 domains\, unlike dense Erd˝os-R´enyi graphs. In this talk\, we show that f
 or the most negative eigenvalues of the adjacency matrix of a random regul
 ar graph\, there is an almost linear number of nodal domains. Joint work w
 ith Shirshendu Ganguly\, Sidhanth Mohanty\, and Nikhil Srivastava.\n\n \n
 \n \n\nVisite the Web site: https://archimede.mat.ulaval.ca/agirouard/Spec
 tralClouds/\n
DTSTART:20220321T160000Z
DTEND:20220321T170000Z
SUMMARY:Young researchers in spectral geometry IV
URL:/mathstat/channels/event/young-researchers-spectra
 l-geometry-iv-338514
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