Events

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: Two counterexamples related to chi-boundedness

Abstract:

This will be a joint talk with two parts.

Sophie Spirkl: I will present a counterexample to the following well-known conjecture: for every k, r, every graph G with clique number at most k and sufficiently large chromatic number contains a triangle-free induced subgraph with chromatic number at least r. 

Title: Rotational Differential-Linear Cryptanalysis of ARX Ciphers

Abstract:

The differential-linear attack, combining the power of the two most effective techniques for symmetric-key cryptanalysis, was proposed by Langford and Hellman at CRYPTO 1994. We further extend this framework by replacing the differential part of the attack by rotational differentials.

Title:  A curious identity between the orthogonal Brezin--Gross--Witten integral and Schur symmetric functions via b-deformed monotone Hurwitz numbers

Abstract:

This talk is intended for an algebraic combinatorial community and no prior knowledge is required. All the difficult words (Hurwitz numbers, KP hierarchy, HCIZ and BGW integrals, Jack symmetric functions, the b-conjecture) will be explained and gently introduced.

Title: On reverse mixing in quantum walks

Abstract:

A random walk on a connected undirected graph mixes to the principal eigenvector. We consider a continuous-time quantum walk to reverse this process: starting with the principal eigenvector, can we reach an arbitrary vertex if we were to place a loop on the target vertex?

Title: Homomorphism counts in robustly sparse graphs

Abstract:

For a fixed graph H and for arbitrarily large host graphs G, the number of homomorphisms from H to G and the number of subgraphs isomorphic to H contained in G have been extensively studied when the host graphs are allowed to be dense.

Title: Densest Subgraph: Supermodularity, Iterative Peeling, and Flow

Abstract:

The densest subgraph problem in a graph (DSG), in the simplest form, is the following. Given an undirected graph G = (V, E) find a subset S of vertices that maximizes the ratio |E(S)|/|S| where E(S) is the set of edges with both endpoints in S. DSG and several of its variants are well-studied in theory and practice and have many applications in data mining and network analysis.

Title: Packing and covering balls in planar graphs

Abstract:

The set of all vertices at distance at most r from a vertex v in a graph G is called an r-ball. We prove that the minimum number of vertices hitting all r-balls in a planar graph G is at most a constant (independent of r) times the maximum number of vertex-disjoint r-balls in G.

Title: Lineup polytopes and exclusion principles

Abstract:

The set of all possible spectra of 1-reduced density operators for systems of N particles on a d-dimensional Hilbert space is a polytope called hypersimplex and this is related to Pauli's exclusion principle. If the spectrum of the original density operators is fixed, the set of spectra (ordered decreasingly) of 1-reduced density operators is also a polytope.