Title: Algebraic structure of the Hopf algebra of double posets
|Zoom:||Contact Karen Yeats|
A Hopf algebra of double posets was introduced by Claudia Malvenuto and Christophe Reutenauer in 2011, motivated by the study of pictures of tableaux as defined by Zelevinsky. Starting from the correspondence between top-cones in the braid arrangement and partial orders, we investigate several properties of the Hopf algebra of double posets as the image of a Hopf monoid (via the Fock functor). In particular, we obtain a non-cancellative formula for the antipode. A description of the primitive space is also discussed.
Title: A proof of the Erdős–Faber–Lovász conjecture
|Affliliation:||University of Birmingham|
|Zoom:||Contact Emma Watson|
The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. We prove this conjecture for every sufficiently large $n$. This is joint work with Dong Yeap Kang, Daniela Kühn, Abhishek Methuku, and Deryk Osthus.