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Thesis defences

PhD Oral Defence - Kelvin Lagota, Mathematics and Statistics

Green function and self-adjoint Laplacians on polyhedral surfaces

Date & time

Monday, November 25, 2019
10 a.m. – 12 p.m.


This event is free


School of Graduate Studies


J.W. McConnell Building
1400 De Maisonneuve Blvd. W. Room LB 912

Wheelchair accessible


When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.


Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface X and compute the S-matrix of X at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian on a compact polyhedral surface of genus two with a single conical point. It turns out that the behaviour of the S-matrix at the zero value of the spectral parameter is sensitive to the geometry of the polyhedron.

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