Question
With Richard Palais, this mathematician co-names a lemma that states that, near a critical point, a function on a Hilbert space locally resembles a quadratic form. For 10 points each:
[10h] Give this mathematician who names functions whose critical points all have a nonsingular Hessian. This mathematician’s namesake theory uses differentiable functions to study the topology of a manifold.
ANSWER: Marston Morse [accept Morse functions; accept Morse-Palais lemma; accept Morse theory]
[10m] In Morse theory, this word refers to the number of negative eigenvalues of the Hessian at a critical point. For a group G and a normal subgroup H, this word denotes the number of cosets of H in G.
ANSWER: index [accept Morse index]
[10e] The Morse index is strictly between zero and n at precisely these critical points, which are neither local minima nor local maxima.
ANSWER: saddle points [accept minimax points]
<Nageswaran, Other Science>
Summary
| 2024 ESPN @ Stanford | 03/09/2024 | Y | 2 | 30.00 | 100% | 100% | 100% |
Data
| Free Agents | Berkeley B | 10 | 10 | 10 | 30 |
| Berkeley A | Stanford | 10 | 10 | 10 | 30 |