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The Birch and Swinnerton-Dyer conjecture concerns the number of rational solutions to equations defining these objects. For 10 points each:
[10m] Name these objects that when defined over the rationals are related to modular forms by the Taniyama–Shimura conjecture.
ANSWER: elliptic curves [prompt on partial answer; prompt on ECs; reject “ellipses”; reject “ellipsoid”]
[10e] The Taniyama–Shimura conjecture implies that this theorem is true. A proof of this theorem was released in 1994 by Andrew Wiles more than 350 years after its initial statement.
ANSWER: Fermat’s last theorem [prompt on Fermat’s theorem; prompt on FLT; reject “Fermat’s little theorem”]
[10h] The Taniyama–Shimura conjecture is a special case of a more general set of conjectures named after this mathematician. A group of conjectures named after this mathematician links automorphic forms and representation theory to Galois theory and has been called the “grand unified theory of mathematics.”
ANSWER: Robert Langlands [accept Langlands conjectures or Langlands program]
<Other Science>
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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Arizona StateColumbia B10101030MEH
Chicago AMichigan1010020ME
FloridaIowa State1010020ME
Georgia StateOhio State1010020ME
Georgia TechNorth Carolina B10101030MEH
Illinois ARIT1010020ME
MITIllinois B10101030MEH
MarylandVanderbilt1010020ME
MinnesotaColumbia A1010020ME
NorthwesternJohns Hopkins010010E
OttawaNorth Carolina A10101030MEH
Penn StateChicago B1010020ME
RutgersToronto C010010E
StanfordUCF10101030MEH
Toronto BBritish Columbia10101030MEH
UC Berkeley AWaterloo B10101030MEH
Virginia TechUC Berkeley B0101020EH
WUSTL ACornell B10101030MEH
WUSTL BWinona State1010020ME
Waterloo ACornell A1010020ME
YaleIndiana1010020ME

Summary

TournamentExact Match?HeardPPBEasy %Medium %Hard %
2025 ACF NationalsYes2122.86100%86%43%