Events

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: Optimizing sums of eigenvalues

Abstract:

In its original proof, Hoffman's well known lower bound to the chromatic number is obtained after replacing several terms of a sum of eigenvalues by the smallest eigenvalue of the graph.

Title: Counting planar maps, 50 years after William Tutte

Abstract:

Every planar map can be properly coloured with four colours. But how many proper colourings has, on average, a planar map with $n$ edges? What if we allow a prescribed number of "monochromatic" edges, the endpoints of which share the same colour? What if we have $q$ colours rather than four?

Title: Obstructions for matroids of path-width at most k and graphs of linear rank-width at most k

Abstract:

Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field $\mathbb F$, the list contains only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)].

Title: On the Security of the NIST lightweight Finalist Ascon

Abstract: 

The ongoing NIST lightweight cryptographic standardization project for the selection of ciphers which are suitable for constrained environments is in the final stage. The authenticated encryption algorithm Ascon, designed by Dobrauing et al., is one out of the 10 finalists. Ascon is also one of the winners of the CAESAR competition in the lightweight applications category.

Title: Bounded treewidth in hereditary graph classes

Abstract: A highlight of the superb graph minors project of Robertson and Seymour is their so-called Grid Theorem: a minor-closed class of graphs has bounded treewidth if and only it does not contain all planar graphs. Which induced-subgraph-closed graph classes have bounded treewidth?

Title: Box-ball systems, RSK, and Motzkin paths 

Abstract:  A box-ball system (BBS) is a discrete dynamical system whose dynamics come from the balls jumping according to certain rules. A permutation on n objects gives a BBS state by assigning its one-line notation to n consecutive boxes. After a finite number of steps, a box-ball system will reach a steady state. From any steady state, we can construct a tableau called the soliton decomposition of the box-ball system.

Title: An identity in the group algebra of the symmetric group

Abstract: Come with me on a magical journey into the mysterious world of inverse Wronskians.

Title: Stochastic Optimization

Abstract:  While deterministic optimization problems are very useful in practice, often times the assumption that all data is known in advance does not hold true. One possible way to relax this assumption is to assume that the data depends on random variables.

Title: Positivity and sums of squares in products of free algebras

Abstract: A noncommutative polynomial is said to be positive relative to some constraints if plugging matrices (or more generally, operators on a Hilbert space) satisfying the constraints into the polynomial always yields a positive operator. It is a natural problem to determine whether or not a given polynomial is positive, and if it is, to find some certificate of positivity. This problem is closely connected with noncommutative polynomial optimization, where we want to find matrices or operators that maximize the operator norm of some polynomial, subject to the constraint that some other polynomials in the operators are positive or vanish. When the algebra cut out by the constraints is a free algebra, free group algebra, or similar algebra, it's well-known that a polynomial is positive on operators satisfying the constraints if and only if it's a sum of Hermitian squares in the algebra.