# Online talk: Daniel Bernstein

Monday, April 19, 3pm ET (8pm BST, 7am Tue NZST)
Daniel Bernstein, MIT
Rigidity of symmetry-forced frameworks

##### Abstract:

The fundamental problem in rigidity theory is to determine whether a given immersion of a graph into $\mathbb{R}^d$ can be continuously deformed, treating the edges as rigid bars that can move freely about their incident vertices. Rigidity is a generic property of each fixed graph $G$, in the sense that almost all immersions of $G$ into $\mathbb{R}^d$ are rigid, or almost all immersions are flexible. The graphs that are generically rigid in $\mathbb{R}^d$ are the spanning sets of a certain matroid. The main result of my talk will be about rigidity in the plane when the graphs and their immersions have certain symmetry constraints.

# Online talk: Daryl Funk

Monday, April 12, 3pm ET (8pm BST, 7am Tue NZST)
Daryl Funk, Douglas College
The class of bicircular matroids has only a finite number of excluded minors

##### Abstract:

We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the recently introduced class of quasi-graphic matroids. We show that if $N$ is an excluded minor of rank at least eight, then $N$ is quasi-graphic. Several small excluded minors are quasi-graphic. Using biased-graphic representations, we find that $N$ already contains one of these. We also provide an upper bound, in terms of rank, on the number of elements in an excluded minor, so the result follows.

# Online talk: Raphael Steiner

Monday, April 5, 3pm ET (8pm BST, 7am Tue NZST)
Raphael Steiner, TU Berlin
Directed graphs: Substructures and Coloring