Seminar

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: 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: 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: 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: The results of a search for small association schemes with noncyclotomic eigenvalues

Abstract:

Title: On complete classes of valuated matroids

Abstract:

Valuated matroids were introduced by Dress and Wenzel in 1992. They are a central object in discrete convex analysis, and play important roles in other areas such as mathematical economics and tropical geometry. Finding a constructive characterization, i.e., showing that all valuated matroids can be derived from a simple class by some basic operations has been a natural question proposed in various contexts.

Title: State transfer on graphs with twin vertices

Abstract:

In this talk, we discuss algebraic and spectral properties of graphs with twin vertices that are important in quantum state transfer. We give a characterization of strong cospectrality between twin vertices, and characterize some types of state transfer that occur between them.