Events

Title: Data-Driven Sample-Average Approximation for Stochastic Optimization with Covariate Information

Abstract:

We consider optimization models for decision-making in which parameters within the optimization model are uncertain, but predictions of these parameters can be made using available covariate information.  We consider a data-driven setting in which we have observations of the uncertain parameters together with concurrently-observed covariates.  Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation.  We investigate a data-driven framework in which the outputs from a machine learning prediction model are directly used to define a stochastic programming sample average approximation (SAA). 

Title: Decomposing discrete quantum walks into continuous quantum walks

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.

Title: Abelian covering graphs and their properties

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.

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

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.

Title: Subdivergence-free gluings of trees

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.

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

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.

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

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.

Title: State transfer and the size of the graph

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.

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

Joint work with Thomas Debris-Alazard and Wessel van Woerden

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.

Title: Laplacian Quantum Fractional Revival On Graphs

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.