#### Contact Info

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

Monday, August 28, 2023 11:30 AM EDT

**Title: **Sandpile groups of cones over trees

Speaker: |
Dorian Smith |

Affiliation: |
University of Minnesota Twin Cities |

Location: |
Please contact Sabrina Lato for Zoom link |

**Abstract: **The sandpile group K(G) of a graph G is a finite abelian group, isomorphic to the cokernel of the reduced graph Laplacian of G. We study K(G) when G = Cone(T) is obtained from a tree T on n vertices by attaching a new cone vertex attached to all other vertices. For two such families of graphs, we will describe K(G) exactly: the fan graphs Cone(P_n) where P_n is a path, and the thagomizer graph Cone(S_n) where S_n is the star-shaped tree. The motivation is that these two families turn out to be extreme cases among Cone(T) for all trees T on n vertices.

Wednesday, August 23, 2023 11:30 AM EDT

**Title: **Chasing Positive Bodies

Speaker: |
Niv Buchbinder |

Affiliation: |
Tel Aviv University |

Location: |
MC 5417 |

**Abstract: **We study the problem of chasing positive bodies in \ell_1: given a sequence of bodies K_t\subset R^n revealed online, where each K_t is defined by a mixed packing-covering linear program, the goal is to (approximately) maintain a point x_t \in K_t such that \sum_t \|x_t - x_{t-1}\|_1 is minimized. This captures the fully-dynamic low-recourse variant of any problem that can be expressed as a mixed packing-covering linear program and thus also the fractional version of many central problems in dynamic algorithms such as set cover, load balancing, hyperedge orientation, minimum spanning tree, and matching.

Monday, August 14, 2023 2:30 PM EDT

**Title: **URA Presentations

Speakers: |
Benjamin Wong, Rick Lyu, and Yen-Kang Fu |

Affiliation: |
University of Waterloo |

Location: |
MC 5479 |

**Abstract: **A series of presentations by a group of Spring 2023 Undergraduate Research Assistants. The topics of each presentation are detailed below.

Thursday, August 10, 2023 1:00 PM EDT

**Title: **From the Upper Bound Conjecture to Gorenstein linkage

Speaker: |
Patricia Klein |

Affiliation: |
Texas A&M |

Location: |
MC 5501 |

**Abstract: **In 1957, Motzkin conjectured that the maximum number of faces possible for a polytope on n vertices in d-space is achieved by the convex hull of n points on the moment curve in d-space. This conjecture, called the Upper Bound Conjecture, was proved by McMullen in 1970 and generalized by Stanley in 1975. On the road to Stanley's proof, a correspondence between squarefree monomial ideals and simplicial complexes was born. That correspondence is called the Stanley--Reisner correspondence. It has come to occupy a central place in combinatorial algebraic geometry.

Tuesday, August 8, 2023 2:30 PM EDT

**Title: **URA Presentations

Speakers: |
Michael Xu, Yundi Duan, Thomas Snow |

Affiliation: |
University of Waterloo |

Location: |
MC 5479 |

**Abstract: **A series of presentations by a group of Spring 2023 Undergraduate Research Assistants. The topics of each presentation are detailed below.

Friday, August 4, 2023 3:30 PM EDT

**Title:** Rigidity of Simplicial Complexes

Speaker: | Bill Jackson |

Affiliation: | Queen Mary University of London |

Location: | MC 5501 |

**Abstract:** A *simplicial k-cycle* is an abstract simplicial k-complex in which every (k-1)-face belongs to an even number of k-faces. A *simplicial k-circuit* is a minimal simplicial k-cycle (in the sense that none of its proper subcomplexes are simplicial k-cycles).

Thursday, August 3, 2023 1:00 PM EDT

**Title:** Specializations of Macdonald polynomials using multiline queues and multiline diagrams

Speaker: |
Jerónimo Valencia |

Affiliation: |
University of Waterloo |

Location: |
MC 5501 |

**Abstract: **Multiline queues were introduced by Ferrari and Martin to model the stationary states of the TASEP, a 1D non-equilibrium particle model. Later, Corteel, Mandelshtam, and Williams gave a formula for the Macdonald polynomial using a (X,q,t)-weighted version of multiline queues. This talk aims to develop the combinatorics of such objects in the t=0 case.

Combinatorics & Optimization

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext 33038

PDF files require Adobe Acrobat Reader.

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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 co-ordinated within the Office of Indigenous Relations.