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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 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.
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: | Please email Emma Watson. |
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.
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.