Mathematical Sciences
Departmental Weekly Events
February 17 – February 14, 2025
AGENDA
Algebra Seminar, "Hyperplane Arrangements, Part 1: Combinatorics". Michael DiPasquale, NMSU. 12:30PM – 1:30PM. Zoom and SH 235. Link: 897 6549 4169.
Abstract: Arrangements of hyperplanes are unions of codimension one linear spaces in some vector space over a field. In this talk, I'll give a quick overview of some of the combinatorial aspects of hyperplane arrangements (including things like intersection lattices, characteristic/poincare polynomials, and chamber counting), and may also start to introduce some of the algebraic objects that I am interested in.
Abstract: Combinatorial topology traces its roots back to the Koenigsberg bridge problem of graph theory and the Euler characteristic. Differential and algebraic topology have roots in the interest of Poincare and others in problems of celestial mechanics. The two-body problem (of two masses moving under mutual gravitational attraction) is a handy vehicle in which physical concepts of angular momentum and total energy can be easily related to features of the geometry and topology of a solution space. One can go quite far into the discussion with a bit of advanced calculus, elementary physics, and analytic geometry.
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