Events

Title: Shorter Zero-Knowledge Proofs from MPC

Abstract:

In this talk I will review the MPC-in-the-head approach to constructing zero-knowledge proofs, then talk about some recent research results to make the proofs shorter.

In a zero-knowledge proof system, a prover wants to convince a verifier that they know a secret value, without revealing it. A common case involves a one-way function, where the prover wants to convince a verifier that they know a secret input corresponding to a public output.

Title: The (3+1)-free conjecture of chromatic symmetric functions

Abstract:

The chromatic symmetric function, dating from 1995, is a generalization of the chromatic polynomial. A famed conjecture on it, called the Stanley-Stembridge (3+1)-free conjecture, has been the focus of much research lately. In this talk we will be introduced to the chromatic symmetric function, the (3+1)-free conjecture, new cases and tools for resolving it, and answer another question of Stanley of whether the (3+1)-free conjecture can be widened. This talk requires no prior knowledge.

Title: Switching Equivalence on the Grassmannian

Abstract:

When constructing configurations of subspaces with desirable properties, one might ask if the configuration is indeed "new.''  It has been known for about 50 years that Gram matrices of equiangular vectors in real Euclidean space correspond to finite simple graphs via the Seidel adjacency matrix, and the collections of such vectors which span the same lines correspond to switching equivalence classes of graphs.

Title: Quantum Distributed Complexity of Graph Diameter and Set Disjointness

Abstract:

In the Congest model, a network of p processors cooperate to solve some distributed task. Initially, each processor knows only its unique label, the labels of its neighbours, and a polynomial upper bound on p, the size of the network. The processors communicate with their neighbours in rounds. In each round, a processor may perform local (quantum) computation, and send a short message to each of its neighbours. How many rounds of communication are required for some processor to compute the diameter of the network?

Title: Fractional decompositions and Latin square completion

Abstract:

It was shown recently by Delcourt and Postle that any sufficiently large graph $G$ of order $n$ with minimum degree at least $0.827n$ has a fractional triangle decomposition, i.e. an assignment of weights to the triangles in $G$ such that for every edge $e$, the total of all weights of triangles containing $e$ is exactly one.

Title: Warped Proximal Iterations for Multivariate Convex Minimization in Hilbert Spaces

Abstract:

We propose a multivariate convex minimization model which involves a mix of nonsmooth and smooth functions, as well as linear mixtures of the variables. This formulation captures a wide range of concrete scenarios in the literature. A limitation of existing methods is that they do not achieve full splitting of our problem in the sense that each function and linear operator is activated separately. To circumvent this issue, we propose a novel approach, called warped proximal iterations, for solving this problem.

Title: On the Laplacian spectra of token graphs

Abstract:

We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph F_k(G)of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this talk, we give a relationship between the Laplacian spectra of any two token graphs of a given graph.

Title: A New Graph Polynomial from the Chromatic Symmetric Function

Abstract:

The chromatic symmetric function X_G of a graph generalizes the chromatic polynomial by distinguishing proper n-colourings by how many times each colour is used. Furthermore, many other natural graph polynomials also arise from specializations of X_G;

Title: Quantum walks do not like bridges

Abstract:

In this talk we consider graphs with two cut vertices joined by a bridge, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex.

Title: Edge-Disjoint Linkage in Infinite Graphs

Abstract:

In 1980 Thomassen conjectured that, for odd k, an edge-connectivity of k is enough for a graph to be weakly k-linked, meaning any k pairs of terminals can be linked by k edge-disjoint paths. The best known result to date for finite graphs is from 1991, by Andreas Huck, and assumes an edge-connectivity of k+1 for odd k.