Events

Title: Minimal relations for an algebra inspired by algebraic graph theory

Abstract:

The balanced algebra has two generators, R and L, and its defining relations are that any pair of balanced words commutes. For example, RL and LR are balanced (contain the same number of both generators), so in the balanced algebra, (RL)(LR)=(LR)(RL).

Title: A Matching Theoretic Flat Wall Theorem

Abstract:

One of the key theorems in Graph Minors is the Flat Wall Theorem which asserts the existence of a large wall under certain conditions. In this talk, we discuss about graphs with perfect matchings and their relationship with digraphs. Our main focus is on a matching theoretic analogue of the Flat Wall Theorem for bipartite graphs excluding a fixed matching minor.

Title: Random Self-reducibility of Ideal-SVP via Arakelov Random Walks

Abstract:

Fixing a number field, the space of all ideal lattices, up to isometry, is naturally an Abelian group, called the *Arakelov class group*. This fact, well known to number theorists, has so far not been explicitly used in the literature on lattice-based cryptography. Remarkably, the Arakelov class group is a combination of two groups that have already led to significant cryptanalytic advances: the class group and the unit torus.

Title: Springer fibers and the Delta Conjecture at t=0

Abstract:

Springer fibers are a family of varieties that have remarkable connections to combinatorics and representation theory. Springer used them to geometrically construct all of the irreducible representations of the symmetric group (Specht modules). Moreover, they give a geometric meaning to Hall-Littlewood symmetric functions.

Title: Traveling Salesman Problems: Approximation Algorithms and Black-Box Reductions

Abstract:

We survey the recent progress on approximation algorithms and integrality ratios for variants of the traveling salesman problem, with a focus on black-box reductions from one problem to another. In particular, we explain recent results for the Path TSP and the Capacitated Vehicle Routing Problem, which are joint works with Vera Traub and Rico Zenklusen and with Jannis Blauth and Vera Traub.

Title: Hadamard diagonalizable graphs of small order

Abstract:

A graph whose Laplacian matrix has a full set of eigenvectors with entries in {1,-1} is said to be Hadamard diagonalizable (i.e. there exists a Hadamard matrix which diagonalizes the Laplacian matrix). We demonstrate that the only diagonalizable graphs on n=8k+4 vertices are K_n and K_{n/2,n/2}.

Title: Strong components of the directed configuration model

Abstract:

We study the behaviour of the largest components of the directed configuration model in the barely subcritical regime. We show that with high probability all strongly connected components in this regime are either cycles or isolated vertices and give an asymptotic distribution of the size of the kth largest cycle. This gives a configuration model analogue of a result of Luczak and Seierstad for the binomial random digraph.

Title: Semidistrim Lattices

Abstract:

This talk will introduce semidistrim lattices, which generalize semidistributive lattices and trim lattices; these two families, in turn, generalize distributive lattices. We will discuss structural, topological, and dynamical properties of semidistrim lattices. In particular, we will see how one can define a certain bijective operator on a semidistrim lattice called rowmotion; this definition unifies the definition that Barnard gave for semidistributive lattices and the definition that Thomas and Williams gave for trim lattices.

Title: The Problem Landscape of SIDH

Abstract:

The Supersingular Isogeny Diffie-Hellman protocol (SIDH) has recently been the subject of increased attention in the cryptography community. Conjecturally quantum-resistant, SIDH has the feature that it shares the same data flow as ordinary Diffie-Hellman: two parties exchange a pair of public keys, each generated from a private key, and combine them to form a shared secret.

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.