Speaker: Bram Petri, Max Planck Institute, Bonn Title: The length spectrum of a random surface

Speaker: Zur Luria (ETH) Title: Hamiltonian spheres in random hypergraphs Abstract: Hamiltonian cycles are a fundamental object in graph theory, and combinatorics in general. A classical result states that in the random graph model G(n,p), there is a sharp threshold for the appearance of a Hamiltonian cycle. It is natural to wonder what happens in higher dimensions - that is, in random uniform hypergraphs?

Title: Gaussian Random Links Abstract: A model for random links is obtained by fixing an initial curve in some n-dimensional Euclidean space and projecting the curve on to random 3 dimensional subspaces. By varying the curve we obtain different models of random knots, and we will study how the second moment of the average crossing number change as a function of the initial curve. This is based on work of Christopher Westenberger.

Speaker: Thilo Weinert, BGU Title: The Ramsey Theory of ordinals and its relation to finitary combinatorics Abstract: Ramsey Theory is a branch of mathematics which is often times summed up by the slogan “complete disorder is impossible”. An important branch of finitary Ramsey Theory lies in the determination of Ramsey Numbers. Infinitary Ramsey Theory on the other hand is an important branch of set theory. Whereas the Ramsey Theory of the Uncountable often times features independence phenomena, the Ramsey Theory of the Countably Infinite provides many interesting combinatorial challenges.

Speaker: Ehud Fridgut (Weizmann Institute) Title: Almost-intersecting families are almost intersecting-families. Abstract: Consider a family of subsets of size k from a ground set of size n (with k < n/2). Assume most (in some well defined sense) pairs of sets in the family intersect. Is it then possible to remove few (in some well defined sense) sets, and remain with a family where every two sets intersect? We will answer this affirmatively, and the route to the answer will pass through a removal lemma in product graphs.

Speaker: Elon Lindenstrauss (HU) Title: On the spectral gap of Cayley graphs for the group of affine transformations Abstract: Joint work with P. Varju. One of the most important open questions regarding spectral gap of Cayley graphs is the dependence of the gap on the choice of generators.

Title: The Theta Number of Simplicial Complexes Abstract: The celebrated Lovász theta number of a graph is an efficiently computable upper bound for the independence number of a graph, given by a semidefinite program. This talk presents a generalization of the theta number to simplicial complexes of arbitrary dimension, based on real simplicial cohomology theory, in particular higher dimensional Laplacians.

Speaker: Yinon Spinka (TAU) Title: Long-range order in random colorings and random graph homomorphisms in high dimensions Abstract:

Title: Labeling and Eliminating Geometric Realization Spaces Abstract: I will introduce a Moduli-space of Shapes of Polyhedra, and show how they may be eliminated by labeling their underlying combinatorial data. I discuss how this relates to geometric realization problems and in particular to flexibility of polyhedra.

Speaker: Amitay Kamber, HU Title: Lp Expander Complexes. Abstract: In recent years, several different notions of high dimensional expanders have been proposed (which in general are not equivalent), each with its own goal and motivation. The goal of this talk is to propose another generalization, based on ideas from the representation theory of p-adic groups. By comparing a complex to its universal cover, we show how to define Lp-expanders and in particular L2-expanders, which are Ramanujan complexes, generalizing the notions of expander graphs and Ramanujan graphs.

Speaker: Andrew Thomason, Cambridge Title: Hypergraph containers Abstract: A collection of containers for a (uniform) hypergraph is a collection of subsets of the vertex set such that every independent set lies inside a container. It has been discovered (Balogh, Morris, Samotij, and Saxton) that it is always possible to find such a collection for which the containers are not big (close to independent) and the size of the collection itself is quite small. This basic, if surprising, fact has many applications, and allows easy proofs of some theorems that were previously difficult or unknown.

Title: Counting lattice points inside a d-dimensional polytope via Fourier analysis Abstract: Given a convex body $B$ which is embedded in a Euclidean space $R^d$, we can ask how many lattice points are contained inside $B$, i.e. the number of points in the intersection of $B$ and the integer lattice $Z^d$. Alternatively, we can count the lattice points inside B with weights, which sometimes creates more nicely behaved lattice-point enumerating functions.

Speaker: Adam Sheffer, CalTech Title: Geometric Incidences and the Polynomial Method Abstract: While the topic of geometric incidences has existed for several decades, in recent years it has been experiencing a renaissance due to the introduction of new polynomial methods. This progress involves a variety of new results and techniques, and also interactions with fields such as algebraic geometry and harmonic analysis.