Please advertise this talk at your home institution. Anyone is welcome to attend! 

YouTube recording: https://www.youtube.com/watch?v=aOpvWW1lBH8

Time: Wednesday, Nov 15 at 3pm ET
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Jim Geelen, University of Waterloo
Title: Average plane-size

Abstract: In 1941, Eberhard Melchior proved that the average line-length of a simple rank-3 real-representable matroid is less than three.  We discuss a long-overdue analogue of Melchior’s result that the average plane-size of a simple rank-4 real-representable matroid is bounded above by an absolute constant, unless the matroid is the direct-sum of two lines. This is joint work with Rutger Campbell and Matthew Kroeker.

Youtube recording: https://www.youtube.com/watch?v=hr17_7c2QSo

Please advertise this talk at your home institution. Anyone is welcome to attend! 

Time: Wednesday, Oct 18 at 3pm ET
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Kathryn Nurse, Simon Fraser University
Title: Seymour’s 6-flow theorem – a short proof

Abstract: Tutte conjectured in 1954 that every bridgeless graph has a nowhere-zero 5-flow. In 1982, Seymour showed that it is true when 5 is replaced with 6. In this talk, I present a short variation of Seymour’s proof. This work is joint with Matt DeVos.

YouTube recording: https://www.youtube.com/watch?v=zxNG3ksK76w

Please advertise this talk at your home institution. Anyone is welcome to attend! 

Time: Wednesday, Sep 20 at 3pm ET
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Nathan Bowler, Universität Hamburg
Title: The $K_4$ game

Abstract: Two players alternately claim edges of a complete graph on infinitely many vertices. The first to claim all edges of a $K_4$ wins. Can the first player force a win? I will explain the history of this question, why it is harder than it seems, and how to win this game.

YouTube recording: https://www.youtube.com/watch?v=qmlQeX5Oy0Q

Time: Thursday, July 20, 3pm ET
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Kevin Grace, Vanderbilt University
Title: Some generalizations of the class of spikes

Abstract: Spikes (also called tipless spikes in the matroid theory literature) form a well-known class of matroids that are important in the study of matroid connectivity. These matroids have the property that every pair of elements is contained in both a 4-element circuit and a 4-element cocircuit. We will present a family of generalizations of spikes, which we call (s, t)-spikes, with the property that every s-element subset of the ground set is contained in a 2s-element circuit and every t-element subset of the ground set is contained in a 2t-element cocircuit. We call this property the (s, 2s, t, 2t)-property. Our main result is that all sufficiently large matroids with the (s,2s, t, 2t)-property are (s, t)-spikes. This is joint work with Nick Brettell.