Abstract: Arrow's impossibility theorem states that the only voting rule satisfying certain natural requirements is a dictatorship. Gil Kalai showed that even if we relax some of these requirements so that they only hold with high probability, we are not getting genuine new voting rules. Arrow's theorem is just one of many paradoxes in social choice theory.
Abstract: I'll discuss various "ratio mixing" properties of transformations preserving infinite measures e.g. "Krickeberg mixing" (based on the example in Hopf's 1936 book) & "rational weak mixing". I'll also introduce a new one connected to "tied down" renewal theory.
Contains joint works with Hitoshi Nakada, Dalia Terhesiu & Toru Sera
Hind Abu Saleh will speal about reducts of the real ordered field and strongly bounded structures. . Title: Reducts of the Real Ordered Field and Strongly Bounded Structures
Abstract: Let N =〈 A ;<,.. 〉 be an o-minimal structure and let A =〈 A ;.. 〉 be a reduct of N . The structure A is called strongly bounded if every A -definable subset of A is either bounded or co-bounded. In this talk we examine additive strongly bounded structures over R and as a corollary we identify all possible reducts of 〈 R ;+, ⋅ ,< 〉 , which expand the vector space
Until recently there was known an essentially unique way to resolve singularities of varieties of
characteristic zero in a canonical way (though there were different descriptions and proofs of correctness).
Recently a few advances happened --
1) The algorithm was extended to varieties with log structures and even to morphisms -- This requires to consider
more general logarithmic blow ups and results in a stronger logarithmic canonicity of the algorithms even for resolution
Until recently there was known an essentially unique way to resolve singularities of varieties of characteristic zero in a canonical way (though there were different descriptions and proofs of correctness).
Recently a few advances happened -- 1) The algorithm was extended to varieties with log structures and even to morphisms -- This requires to consider more general logarithmic blow ups and results in a stronger logarithmic canonicity of the algorithms even for resolution
Abstract: One of the first things we learn about a (proper) Gromov hyperbolic geodesic space X is the construction of the visual boundary of X. An ergodic theorist then learns that for a non-elementary discrete group of isometries G acting properly on X, there is an interesting family of \delta_G-quasi-conformal measures on the boundary. The parameter \delta_G is called the critical exponent of G, and is equal to the exponential growth rate of the orbit Gx in X.
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.
