Department of Mathematical Sciences
Discrete Math Seminar
Tuesday, September 2nd, 2025
Olin Hall 126, 4:00PM- 4:50 PM
Speaker: Brigitte Servatius, WPI
Title: Infinitesimal Projective Transformations
Abstract: We are considering a projective plane configuration of points, $P_1 = (x_1,y_1)$, $P_2$ \ldots and lines $L_1 = (a_1,b_1)$, $L_1$ \ldots, with a point/line incidence recorded by $P_n \cdot L_m = -1$.
The derivative of the constraint system is an $|I|\times 2(|P|+|L|)$ matrix with columns indexed by the two projective coordinates of the points, followed by those of the lines; and whose rows correspond to incidences, with the $n$'th point with the $m$'th line incidence giving a row $$ \left [ 0, 0, \ldots, a_m, b_m \ldots, 0, 0; 0, 0, \ldots, x_n, y_n, \ldots, 0, 0 \right]$$ and we want to describe the 8 dimensional space of trivial projective motions with respect to this matrix.