Pure Maths Colloquium: Can one hear the shape of a triangle?
1 December 2014 16:00 in CM221
Everything is known about triangles … or is it? Consider the problem:
Do area, perimeter and sum of reciprocals of the angles of a triangle determine the triangle uniquely?
In the talk I will answer this question and show how this provides an answer to the question in the title. This amounts to studying the eigenvalues of the Laplacian on triangles as functions of the triangle. I will sketch the history of the general problem 'Can one hear the shape of a drum?' from inverse spectral theory and explain some of the techniques used in its analysis. Finally I will discuss some recent results on a singular adiabatic limit problem which arises when studying the asymptotics of eigenvalues on a degenerating family of triangles or similar geometric setups.
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