Question

The behavior of reductions described by this word on quotient spaces determined by the momentum map is defined by the Marsden–Weinstein (“wine-stine”) theorem. This word describes the creed that “Everything is a Lagrangian (“luh-GRAHN-jee-an”) submanifold.” The Lie (“lee”) derivative of the top exterior power of mathematical objects described by (10[1])this word is always zero. On R-2n, the canonical choice for a mathematical object described by this word is the sum over i of: “dq-sub-i wedge dp-sub-i”. The cotangent bundle (-5[1])of a manifold (-5[1])always has (10[1]-5[1])the structure of this type of manifold. (10[2])The Liouville–Arnold (“l’YOO-vill-arnold”) Theorem (10[1])gives (-5[1])the sufficient conditions for a manifold described by this word to have action-angle coordinates. The action of a differential 2-form described by this word (10[1])defines the Poisson (“pwah-SAWN”) bracket. (-5[1])For 10 points, what word describes the branch of differential geometry that is the natural (-5[1])setting of Hamiltonian mechanics? (10[2])■END■ (10[4]0[11])

ANSWER: symplectic [accept symplectic geometry, symplectic manifolds, symplectic forms, symplectic creed, symplectic maps, or symplectic reductions; accept symplectomorphisms] (The sentence about Lie derivatives is a formulation of Liouville’s theorem.)
<Physics>
= Average correct buzz position

Summary

2023 ACF Nationals04/22/2023Y2157%0%29%111.33

Buzzes

PlayerTeamOpponentBuzz PositionValue
Swapnil GargUC Berkeley AColumbia A4510
Vivek SasseChicago BChicago A75-5
David BassVirginia ARutgers A78-5
Ricky LiMIT ANorthwestern A80-5
Vincent DuNorth Carolina AHarvard A8010
Tim MorrisonStanford AGeorgia Tech A8710
JD KrothIowa State AWUSTL B8710
Max ChemtovMcGill APenn State A9010
Simon GorbatyDuke AYale A91-5
Alex AkridgeIndiana ACornell B11510
Anson BernsBrown AFlorida A119-5
Jeya IyaduraiFlorida BRutgers B134-5
Kevin YeUC Berkeley BImperial A13810
Caleb KendrickMaryland AWUSTL A13810
Quynh PhungPurdue AHouston A1390
Adam FineChicago AChicago B13910
Andrew HannaVanderbilt AJohns Hopkins A1390
Maximillian NieburJohns Hopkins AVanderbilt A1390
Leo LawFlorida ABrown A13910
Noah ChenColumbia BMinnesota B13910
Todd MaslykMichigan ANYU A1390
Matthew SiffYale BPenn A1390
John BroussardHouston APurdue A1390
Roxanne TangOhio State ACornell A1390
Ameya PhadnisRutgers BFlorida B1390
Raul PassementTexas AChicago C13910
Halle FriedmanNYU AMichigan A1390
Geoffrey ChenCornell AOhio State A1390
Benjamin McAvoy-BickfordPenn AYale B1390