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
| Simpson Agonistes: The Crisis of Donut | Communism is Soviet power plus the yassification of the whole country | 10 | 0 | 0 | 10 |
| I'd prefer to have the team name be Christensen et al. than anything that Erik cooks up | Tensei Shitara Flashcard Data Ken | 10 | 0 | 0 | 10 |
| as rational as the square root of two power bottoms | Moderator Can't Neg me While in Alpha | 10 | 0 | 0 | 10 |
| Ryan Wesley Routh's 10 000 NATO-trained Afghan Quizbowlers | She Dicer On My Argonaute Till I RNA Interfere | 10 | 0 | 0 | 10 |
| The Only Existing Manuscript from A Clockwork Orange | You cannot go to Aarhus to see his peat-brown head / With eyes like ripening fruit | 10 | 10 | 10 | 30 |