Applied Math And Analysis Seminar
Tuesday, October 4, 2022, 3:15pm, Physics 119
Jeremy Louis Marzuola (UNC Chapel Hill)
Recent results on nodal sets for the Laplacian
Abstract:
In the first half of the talk, we will discuss some recent work on characterizing the number of nodal sets for an eigenfunction that was initiated with Graham Cox and Chris Jones, which has been further developed with Greg Berkolaiko, Yaiza Canzani and Graham Cox. This work gives an especially nice means of quantifying the number of nodal sets of an eigenfunction and the importance of a so-called two-sided Dirichlet-to-Neumann map in our analysis (this also has a graph analog and can be informative for analyzing equipartitions of a given domain). Then, in the second half of the talk, we will use these results as motivation to discuss more closely properties of nodal sets for low energy eigenfunctions on nearly rectangular domains that we looked at in joint work with Tom Beck, Yaiza Canzani and Marichi Gupta.

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