Speaker: Michael Krivelevich, Tel Aviv University Title: Embedding large minors in weak expanders and in sparse random graphs
ABSTRACT
A graph G on n vertices is called an alpha-expander if the external neighborhood of every vertex subset U of size |U|<=n/2 in G has size at least alpha*|U|.
In this talk we will study the so-called perturbed model which is a graph distribution of the form G \cup \mathbb{G}(n,p), where G is an n-vertex graph with edge-density at least d > 0, and d is independent of n.
We are interested in the threshold of the following anti-Ramsey property: every proper edge-colouring of G \cup \mathbb{G}(n,p) yields a rainbow copy of K_s. We have determined this threshold for every s.
Based on joint work with Elad Aigner-Horev, Oran Danon and Shoham Letzter.
Speaker: Bannai Eiichi (Kyushu University) Title: On unitary t-designs
Abstract:
The purpose of design theory is for a given space $M$ to find good finite subsets $X$ of $M$ that approximate the whole space $M$ well. There are many design theories for various spaces $M$. If $M$ is the sphere $S^{n-1}$ then such $X$ are called spherical designs. If $M$ is the unitary group $U(d)$, then such $X$ are called unitary designs.
Timo Krisam will speal about distal theories and the type decomposition theorem. . Title: Distal Theories and the Type Decomposition Theorem
Abstract: The class of NIP-Theories is an important subject of study in pure model theory. It contains many interesting examples like stable theories, o-minimal theories or algebraically closed valued fields.
Abstract: The Bernoulli convolution with parameter 1/2 < t < 1 is the distribution of the random variable (+/-)t + (+/-)t^2 + (+/-)t^3 + ..., where the sequence of signs +/- form an unbiased i.i.d. random sequence. This distribution has been studied since the 1930s, and the main problem is to characterize those parameters t for which the distribution is absolutely continuous, or has full dimension. In these talks I will review the history and recent developments, leading up to P. Varju's proof a little over a year ago, that for all transcendental parameters the dimension is 1.
Abstract: The Bernoulli convolution with parameter 1/2 < t < 1 is the distribution of the random variable (+/-)t + (+/-)t^2 + (+/-)t^3 + ..., where the sequence of signs +/- form an unbiased i.i.d. random sequence. This distribution has been studied since the 1930s, and the main problem is to characterize those parameters t for which the distribution is absolutely continuous, or has full dimension. In these talks I will review the history and recent developments, leading up to P.
