Characteristic Polynomials of Hyperplane Arrangements via Enumerative Combinatorics and Finite Field Method
Host
Department of Applied Mathematics
Speaker
Joungmin Song
Gwangju Institute of Technology
https://college.gist.ac.kr/main/profile_en/elec/basic_sjm.html
Description
A hyperplane arrangement is a finite set of hyperplanes in the real affine space \(R^n\). In this talk, we are concerned with the hyperplane arrangement \(J_n\) consisting of the planes satisfying equations: \(x_i = 0\), \(x_j = 1\), and/or \(x_i + x_j = 1\), \(1\leq i, j\leq n\). The number of regions, i.e., the connected components of \(R^n\) after removing the hyperplanes in \(J_n\) is given by the characteristic polynomial of the arrangement \(J_n\). We formulate this via enumerative combinatorics and finite field method. We also discuss a possible direction forward generalizing this process to a multinomial arrangements of similar form.
Most geometric and algebraic concepts will be defined and discussed in the talk. Only the knowledge of vector spaces and basic linear algebra will be assumed.
Event Topic
Discrete Applied Math Seminar