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 @ Brown | 04/06/2024 | Y | 1 | 0.00 | 0% | 0% | 0% |
| 2024 ESPN @ Brown | 04/06/2024 | Y | 3 | 3.33 | 33% | 0% | 0% |
| 2024 ESPN @ Cambridge | 04/06/2024 | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2024 ESPN @ Chicago | 03/23/2024 | Y | 6 | 16.67 | 83% | 67% | 17% |
| 2024 ESPN @ Columbia | 03/23/2024 | Y | 6 | 16.67 | 100% | 33% | 33% |
| 2024 ESPN @ Duke | 03/23/2024 | Y | 2 | 10.00 | 50% | 50% | 0% |
| 2024 ESPN @ Online | 06/01/2024 | Y | 3 | 16.67 | 100% | 67% | 0% |