Question
On manifolds named for this person, the metric maps contravariant vectors to covariant vectors. For 10 points each:
[10e] Name this German differential geometer who also defined a namesake tensor describing the curvature of a manifold. This person’s namesake zeta function is central to a Millenium Prize problem.
ANSWER: Georg Frederic Bernhard Riemann [accept Riemannian manifolds; accept Riemann zeta function]
[10m] By defining a metric at every point in space, Riemannian manifolds define one of these contravariant vector spaces at every point on the manifold. An orthonormal basis is defined on these spaces by the partial derivatives of a coordinate chart.
ANSWER: tangent spaces [reject “cotangent” spaces]
[10h] This is the name of the canonical isomorphism induced by the metric between the cotangent bundle and the tangent bundle. This isomorphism is named in an analogy to how it raises and lowers indices in Einstein notation.
ANSWER: musical isomorphism (The “sharp” isomorphism raises a lowered index while the “flat” isomorphism lowers a raised one.)
<Science - Other Science - Math>
Summary
| 2024 ARGOS @ Brandeis | 03/22/2025 | Y | 3 | 13.33 | 100% | 33% | 0% |
| 2024 ARGOS @ Chicago | 11/23/2024 | Y | 6 | 13.33 | 100% | 17% | 17% |
| 2024 ARGOS @ Christ's College | 12/14/2024 | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2024 ARGOS @ Columbia | 11/23/2024 | Y | 3 | 10.00 | 100% | 0% | 0% |
| 2024 ARGOS @ McMaster | 11/17/2024 | Y | 5 | 14.00 | 100% | 20% | 20% |
| 2024 ARGOS @ Stanford | 02/22/2025 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2024 ARGOS Online | 03/22/2025 | Y | 3 | 13.33 | 100% | 33% | 0% |
Data
| CLEVELAND, THIS IS FOR YOU! | I wish it were possible to freeze time so I would never have to watch you retire | 10 | 0 | 0 | 10 |
| UBC | Thompson et al. | 10 | 0 | 0 | 10 |
| throw away your cards, rally in the streets | Aw we're so sorry to hear that maman died today, she gets five big booms | 10 | 10 | 0 | 20 |