Bonus

The Wigner (“VIG-ner”) surmise describes the self-repulsion of this set, which is the complement of a linear operator’s resolvent. For 10 points each:
[10m] Name this set that contains a complex number lambda if the matrix given by [read slowly] “A minus lambda times the identity” is not invertible. A theorem named for this set gives a way of finding an orthonormal basis from a normal linear operator.
ANSWER: spectrum [or spectra or spectral theorem; prompt on set of eigenvalues]
[10h] Wigner names this distribution, the limiting distribution of the normalized spectrum of a Gaussian ensemble as matrix size grows. This distribution’s sole parameter, R, describes its finite support.
ANSWER: Wigner semicircle distribution
[10e] The Wigner surmise applies to a two-by-two GOE (“G-O-E”) matrix whose entries satisfy particular relations for this quantity, the square of the standard deviation.
ANSWER: variance [prompt on sigma-squared]
<Other Science>
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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
British ColumbiaWinona State1001020ME
Chicago AMinnesota001010E
FloridaCornell B1001020ME
Georgia StateUC Berkeley B1001020ME
HarvardCornell A001010E
Illinois AToronto C1001020ME
Illinois BIndiana001010E
MITYale1001020ME
MichiganColumbia A001010E
North Carolina AVanderbilt1001020ME
OttawaMaryland1001020ME
Penn StateRIT001010E
RutgersChicago B1001020ME
StanfordOhio State10101030MHE
TexasColumbia B001010E
Toronto ANorth Carolina B1001020ME
Toronto BWUSTL B10101030MHE
UC Berkeley AArizona State1001020ME
VirginiaNYU001010E
Virginia TechUCF001010E
WUSTL AIowa State1001020ME
Waterloo ALSE1001020ME

Summary

TournamentExact Match?HeardPPBEasy %Medium %Hard %
2025 ACF NationalsYes2217.27100%64%9%