Question

According to Kirchhoff's theorem, the cofactors of a matrix representation of this operator count the number of spanning trees. In algebraic graph theory, the discrete form of this operator is the difference between the degree and adjacency matrices. Elliptic operators generalize this operator, whose kernel consists of functions that satisfy the maximum principle, meaning (15[1])they attain extrema on their boundary. A (15[1])function f is harmonic if this operator of f equals zero; that (15[1])(*) PDE is named after this operator’s namesake and is the homogeneous version of Poisson’s equation. (10[1])The divergence of the gradient gives this operator, which is (10[1])symbolized with a triangle or as del-squared. (10[1])For 10 points, give this differential operator named for a French mathematician who also has a namesake real-to-complex transform. ■END■

ANSWER: Laplacian [or Laplace operator; accept del-squared until read; accept Laplacian matrix; accept Laplace’s equation; prompt on harmonic until read by asking “what is the more common name of that operator?”]
<VD, Other Science>
= Average correct buzz position

Back to tossups

Buzzes

PlayerTeamOpponentBuzz PositionValue
Asha BasuMcGill AToronto Metropolitan A5315
Sky LiToronto AWaterloo Cloze6015
Liam KusalikWaterloo AspidistraToronto Chestnut Rice and Kamehameha7215
Caleb OttWaterloo BasicToronto Disband the Club 2k248710
Ethen SunToronto BCarleton A9710
Cranmer MGinnMcMaster ApocolocyntosisBidiiOttawa Absolomabsolomabsolom10410