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Friday, December 11, 2020 — 3:30 PM EST

**Title: **Sparse PSD approximation of the PSD cone

Speaker: | Santanu Dey |

Affiliation: |
H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology |

Zoom: | Please email Emma Watson |

**Abstract:**

While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One computational technique used to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller k × k principal submatrices — we call this the sparse SDP relaxation.

Thursday, December 10, 2020 — 1:00 PM EST

**Title:** Chromatic symmetric functions of Dyck paths and $q$-rook theory

Speaker: | Laura Colmenarejo |

Affiliation: | UMass Amherst |

Zoom: | Contact Karen Yeats |

**Abstract:**

Given a graph and a set of colors, a coloring of the graph is a function that associates each vertex in the graph with a color. In 1995, Stanley generalized this definition to symmetric functions by looking at the number of times each color is used and extending the set of colors to $\mathbb{Z}^+$. In 2012, Shareshian and Wachs introduced a refinement of the chromatic functions for ordered graphs as $q$-analogues.

Monday, December 7, 2020 — 11:30 AM EST

**Title:** Distinct Eignvalues and Sensitivity

Speaker: | Shahla Nasserasr |

Affiliation: | Rochester Institute of Technology |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

For a graph $G$, the class of real-valued symmetric matrices whose zero-nonzero pattern of off-diagonal entries is described by the adjacencies in $G$ is denoted by $S(G)$. The inverse eigenvalue problem for the multiplicities of the eigenvalues of $G$ is to determine for which ordered list of positive integers $m_1\geq m_2\geq \cdots\geq m_k$ with $\sum_{i=1}^{k} m_i=|V(G)|$, there exists a matrix in $S(G)$ with distinct eigenvalues ${\lambda_1,\lambda_2,\cdots, \lambda_k}$ such that $\lambda_i$ has multiplicity $m_i$.

Friday, December 4, 2020 — 3:30 PM EST

**Title: **Partial orders on the symmetric group

Speaker: | Oliver Pechenik |

Affiliation: | University of Waterloo |

Zoom: | Please email Emma Watson |

**Abstract:**

The symmetric group of permutations is naturally a poset in at least 4 different ways, the (strong) Bruhat order and three flavors of weak order. Stanley showed in 1980 that the Bruhat order is Sperner, essentially meaning that the obvious large antichains are in fact the largest possible. The corresponding fact for weak orders was open until last year, when it was established by Gaetz and Gao.

Thursday, December 3, 2020 — 1:00 PM EST

**Title:**** **Twisted Hopf algebras

Speaker: | Loïc Foissy |

Affiliation: | Université du Côte d'Opale |

Zoom: | Contact Karen Yeats |

**Abstract:**

A twisted Hopf algebra is a Hopf algebra in the category of linear species. The Fock functors allow to recover "classical" Hopf algebras from twisted ones. Numerous constructions and results can be lifted to the level of twisted bialgebras, such that cofreeness, shuffle and quasi-shuffles products, etc.

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The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.