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Please note: The University of Waterloo is closed for all events until further notice.

Monday, August 31, 2020 — 11:30 AM EDT

**Title:** Scaffolds

Speaker: | William J. Martin |

Affiliation: | Worcester Polytechnic Institute |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

Building on the work of various authors who have used tensors in the study of association schemes and spin models, I propose the term "scaffold" for certain tensors that have been represented by what are sometimes called "star-triangle diagrams" in the literature. The main goal of the talk is to introduce and motivate these objects which somewhat resemble partition functions as they appear in combinatorics. (The exact definition is too cumbersome to include here.)

Friday, August 28, 2020 — 3:30 PM EDT

**Title:** Pure pairs

Speaker: | Sophie Spirkl |

Affiliation: | University of Waterloo |

Zoom: | Please email Emma Watson. |

**Abstract:**

A pure pair in a graph G is a pair of subsets A and B of the vertex set such that between A and B, either all edges or no edges are present in G. This concept was first introduced in connected with the Erdos-Hajnal conjecture, but has since developed a life of its own. I will give an overview of results and open questions on pure pairs.

Based on joint work with Maria Chudnovsky, Jacob Fox, Alex Scott, and Paul Seymour.

Monday, August 24, 2020 — 11:30 AM EDT

**Title:** Laplacian Quantum Fractional Revival On Graphs

Speakers: |
Bobae Johnson, August Liu, Malena Schmidt, Neo Yin |

Affiliation: | York University |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

Given a set of quantum bits, we can model their interactions using graphs. The continuous-time quantum walks on a graph can be viewed as the Schrödinger dynamics of a particle hopping between adjacent vertices. In this talk, the transition matrix of the continuous-time quantum walk is given by $e^{-itL}$, where $L$ is the graph’s Laplacian matrix.

Friday, August 21, 2020 — 3:30 PM EDT

**Title:** An Algorithmic Reduction Theory for Binary Codes: LLL and more

Joint work with Thomas Debris-Alazard and Wessel van Woerden

Speaker: | Léo Ducas |

Affiliation: | Centrum Wiskunde & Informatica (CWI) |

Zoom: | Please email Emma Watson |

**Abstract:**

Lattice reduction is the task of finding a basis of short and somewhat orthogonal vectors of a given lattice. In 1985 Lenstra, Lenstra and Lovasz proposed a polynomial time algorithm for this task, with an application to factoring rational polynomials. Since then, the LLL algorithm has found countless application in algorithmic number theory and in cryptanalysis.

Monday, August 17, 2020 — 11:30 AM EDT

**Title:** State transfer and the size of the graph

Speaker: | Gabriel Coutinho |

Affiliation: | Universidade Federal de Minas Gerais |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

If there is perfect state transfer between two vertices at distance d, how small can the graph be compared to d? This question is motivated by the fact that the known infinite families of graphs admitting state transfer at increasingly large distances are all obtained from graph products, thus their sizes grow exponentially compared to their diameter.

Friday, August 14, 2020 — 3:30 PM EDT

**Title:** Constructing broken SIDH parameters: a tale of De Feo, Jao, and Plut's serendipity.

Speaker: | Chloe Martindale |

Affiliation: | University of Bristol |

Zoom: | This event has been cancelled. |

**Abstract:**

This talk is motivated by analyzing the security of the cryptographic key exchange protocol SIDH (Supersingular Isogeny Diffie-Hellman), introduced by 2011 by De Feo, Jao, and Plut. We will first recall some mathematical background as well as the protocol itself. The 'keys' in this protocol are elliptic curves, which are typically described by equations in x and y of the form y^2 = x^3 + ax + b. Of importance in this talk will be 'endomorphisms' associated to elliptic curves: these are functions that map an elliptic curve to itself which also satisfy some nice properties.

Monday, August 10, 2020 — 11:30 AM EDT

**Title:** What do graph planarity and homomorphism counts have to do with quantum mechanics?

Speaker: | David Roberson |

Affiliation: | Technical University of Denmark |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

I will introduce the notion of quantum isomorphisms of graphs. These are defined in terms of a game in which two cooperating players attempt to convince a referee that two given graphs are isomorphic.

Thursday, August 6, 2020 — 2:30 PM EDT

**Title: **Subdivergence-free gluings of trees

Speaker: | Jordan Long |

Affiliation: | University of Waterloo |

Zoom: | Contact Karen Yeats |

**Abstract:**

Motivated by questions in quantum field theory, we introduce a purely combinatorial problem of counting subdivergence-free gluings of trees. We present closed-form expressions counting subdivergence-free gluings for four different families of trees, as well as an algorithm to count subdivergence-free gluings of arbitrary pairs of trees. This is joint work with Clair Dai and Karen Yeats.

Thursday, August 6, 2020 — 2:30 PM EDT

**Title:** Counting the $c_2$ invariant on the circulant family of graphs

Speaker: | Mushegh Shahinyan |

Affiliation: | University of Waterloo |

Zoom: | Contact Karen Yeats |

**Abstract:**

The algebro-geometric invariant on Feynman Diagrams called the $c_2$ invariant is a useful tool for detecting properties of Feynman periods. We present this identity on graphs that originate from the scalar $\phi_4$-theory with a purely combinatorial perspective and go over some strategies for computing it. We will further narrow our focus onto the circulant family of graphs and present some explicit results.

Thursday, August 6, 2020 — 2:30 PM EDT

**Title:** Abelian covering graphs and their properties

Speaker: | Olha Silina |

Affiliation: | University of Waterloo |

Zoom: | Contact Karen Yeats |

**Abstract:**

A covering graph is a structure obtained from a graph by ‘replacing’ every vertex with a coclique of size $r$. The main focus of this talk is connections between (spectral) characteristic of a cover and properties such as being walk- or distance- regular.

Monday, August 3, 2020 — 11:30 AM EDT

**Title:** Decomposing discrete quantum walks into continuous quantum walks

Speaker: | Harmony Zhan |

Affiliation: | York University |

Zoom: | Contact Soffia Arnadottir |

**Abstract:**

The Grover walk is a discrete quantum walk inspired by Grover's search algorithm. It takes place on the arcs of a graph, and alternates between "coin flips" and "arc reversal". In this talk, I show that for a distance regular graph X with diameter d and intertible A(X), the Grover walk on X can be "decomposed" into at most d "commuting" continuous quantum walks.

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