Geometry of Points and Lines in the Plane: Combinatorial and Algebraic Perspectives

The next talk in the La Trobe University Department of Mathematics and Statistics Colloquium Series will be given by Dr Michael Payne.

Seminar Abstract:

Mathematicians have studied the geometry of points and lines in the plane since ancient times. Over the last century or so, combinatorial questions regarding incidences between points and lines have gained increasing attention. For example, Sylvester asked in 1893 whether a finite non-collinear set of points must necessarily determine a line with just two points, and bounding the minimum number of such lines remained an open problem until Tao and Green provided an (asymptotic) solution in 2012.

At the same time, the algebraic view of geometry flourished and algebraic geometry was developed into a deep and highly abstract theory. Researchers in combinatorial geometry initially found few uses for this theory, but recently more and more links are being discovered. In this talk I will discuss this history in the context of some combinatorial problems that particularly interest me, and give a gentle introduction to some of the links with algebraic geometry that are being uncovered.

Host University: La Trobe University

Seminar Convener: Dr Michael Payne

How to participate in this seminar

1. Book your university’s Access Grid Room, or a university or APAC etc. Access Grid Room that you are able to use, and

2. Send an email to the seminar convener at La Trobe University (Michael Payne) to advise that you will be attending the seminar.