| Friday 19 April 2024 | |
| Events for day: Wednesday 15 June 2022 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Expander Graphs: Intrinsic Structures School MATHEMATICS Expander graphs have been extensively studied in recent decades due to their important applications in different areas of mathematics and computer sciences. Due to high connectivity of expanders, explicit construction of these graphs has been of great theoretical and applied importance in the literature. In this talk, we focus on finding special simple structures such as trees and cycles in expander graphs and we show how these observations can be exploited in Ramsey Theory. To get more information about the Combinatorics and Computing Weekly Seminar and webinars Zoom link, join the following google group: https://groups ... 16:00 - 17:30 Geometry and Topology Seminar - online Some Generic Statistical Properties of Dynamical Systems School MATHEMATICS In this talk we aim to introduce a basic observation about relation between statistical properties of a map and its perturbations, which holds Baire generically in any family of dynamics. Roughly speaking, the relation is that any statistical behavior that is exhibited by small perturbations of a map, is exhibited by the map itself. This observation can be applied in two different category of maps. The first category is formed by those families of maps that the existence of time averages for is guaranteed for almost every point, such as conservative systems or mostly contracting partially hyperbolic diffeomorphisms. Here we present ... 17:30 - 18:30 Mathematical Logic Weekly Seminar O-minimal Version of the Elekes-Szabo Theorem School MATHEMATICS Erdos and Szemeredi observed the following sum-product phenomenon: there is some c>0 such that for any finite set A of reals, max{|A+A|, |A*A|} > |A|^{1+c}. Later, Elekes and Ronyai generalized this by showing that for any polynomial f(x,y) we must have |f(A*A)|>|A|^{1+c}, unless f is either additive or multiplicative (i.e. of the form g(h(x) + i(y)) or g(h(x) * i(y)) for some univariate polynomials g,h,i respectively). A remarkable theorem of Elekes and Szabo provides a conceptual generalization, showing that for any polynomial F(x,y,z) such that its set of zeroes has dimension 2, if F has a maximal possible number of zeroes n^2 on finite n ... |