IPM Calendar 
Friday 1 July 2022   Today  
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.

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           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 ...