12/10/2018 1:00 PMArts One Lecture Theatre, Mile End CampusBehrang Noohi & Abhishek SahaWhat is derived geometry? / Bounding the heights of peaks of vibration modes on hyperbolic membranes
Behrang Noohi: What is derived geometry?
You may have heard of "derived/higher geometry" and wondered what it is. A brainchild of Alexander Grothendieck, it is more of a "new viewpoint in mathematics" rather than being a specific subject. A recent flurry of activities, aiming to set up the right foundations, has seen the subject transform enormously, resulting in spectacular applications to algebraic geometry,
symplectic geometry, topology, physics, computer science, etc. Despite the daunting technical apparatus involved, the main ideas are simple (at least some of them!). In this talk I will try to illustrate some of these ideas using simple examples.
Abhishek Saha: Bounding the heights of peaks of vibration modes on hyperbolic membranes
I will give a gentle introduction to the "sup-norm problem" in a setting where number theory plays a key role. The sup-norm problem asks for non-trivial bounds on the sup-norms of eigenfunctions of the Laplacian on Riemannian manifolds. In the special case when the manifold is a surface of constant negative structure, and isconstructed from "quaternion algebras", a famous result of Iwaniec and Sarnak improves upon the trivial bound using number-theoretic techniques. I will explain this result, and then talk about recent progress on an analogous question where the underlying surface is itself allowed to vary.
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