Basic Notions

The Basic notions seminar meets on Thursdyas at 16:00 at room 70 in the Ross Building.
2018 May 31

Basic Notions: Mike Hochman - "Furstenberg's conjecture on transversality of semigroups and slices of fractal sets" Part I

4:00pm to 5:30pm

Location: 

Ross 70
In 1970, Furstenberg made a number of conjectures about the expansions of real numbers in non-comensurable bases, e.g. bases 2 and 3. The most difficult remains wide open, but several related problems, which can be stated in terms of the dimension theory of certain fractal sets, were recently settled. In the first talk I will try to describe the conjectures and some of what was known. In the second talk I will present Meng Wu's proof of the "slice conjecture" (it was also proved independently by Pablo Shmerkin, and I will try to also say a little about that proof too).
2018 May 17

Basic Notions - Benjamin Weiss: "All ergodic systems have the Weak Pinsker property" Part 2

4:00pm to 5:30pm

Location: 

Ross 70
Second part of the talk from last week: An ergodic system (X;B; μ; T) is said to have the weak Pinsker property if for any ε > 0 one can express the system as the direct product of two systems with the first having entropy less than ε and the second one being isomorphic to a Bernoulli system. The problem as to whether or not this property holds for all systems was open for more than forty years and has been recently settled in the affirmative in a remarkable work by Tim Austin. I will begin by describing why Jean-Paul formulated this prob-
2018 May 10

Basic Notions - Benjamin Weiss: "All ergodic systems have the Weak Pinsker property"

4:00pm to 5:30pm

Location: 

Ross 70
An ergodic system (X;B; μ; T) is said to have the weak Pinsker property if for any ε > 0 one can express the system as the direct product of two systems with the first having entropy less than ε and the second one being isomorphic to a Bernoulli system. The problem as to whether or not this property holds for all systems was open for more than forty years and has been recently settled in the affirmative in a remarkable work by Tim Austin. I will begin by describing why Jean-Paul formulated this prob- lem and its significance. Then I will give an aerial view of Tim's
2018 May 03

Basic Notions - Alex Lubotzky: "Group stability and approximation"

4:00pm to 5:30pm

Location: 

Ross 70
An old problem (Going back to Turing, Ulam and others) asks about the "stability" of solutions in some algebraic contexts. We will discuss this general problem in the context group theory: Given an "almost homomorphism" between two groups, is it close to a homomorphism?
2017 May 25

Basic notions: Ehud de Shalit - The Loxton - van der Poorten conjecture

4:00pm to 5:00pm

Abstract: Adamczewski and Bell proved in the 2013 the Loxton - van der Poorten conjecture. It says the following. Let f be a Laurent power series (with complex coefficients) and let \sigma_p be the operator substituting x^p for x in f. Suppose that f satisfies a homogenous polynomial equation in the operator \sigma_p with coefficients which are rational functions, and a similar equation in the operator \sigma_q where p and q are multiplicatively independent natural numbers. Then f is a rational function.
2017 May 18

Basic notions: Ehud de Shalit - The Loxton - van der Poorten conjecture

4:00pm to 5:00pm

Abstract: Adamczewski and Bell proved in the 2013 the Loxton - van der Poorten conjecture. It says the following. Let f be a Laurent power series (with complex coefficients) and let \sigma_p be the operator substituting x^p for x in f. Suppose that f satisfies a homogenous polynomial equation in the operator \sigma_p with coefficients which are rational functions, and a similar equation in the operator \sigma_q where p and q are multiplicatively independent natural numbers. Then f is a rational function.
2017 Apr 20

Basic notions: Raz Kupferman (HUJI) - A geometric framework for continuum mechanics

4:00pm to 5:15pm

Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
2017 Mar 23

Basic Notions: Benjy Weiss (HUJI) - What are amenable groups and why are groups non-amenable II

4:00pm to 5:15pm

Location: 

Ross 70
Title: What are amenable groups and why are groups non-amenable Abstract: I will give an introduction to amenable groups and explain the result of Kevin Whyte that a countable non-amenable group admits a "translation-like" action by a non-abelian free group. I will also discuss (without proof) a measure theoretic analogue of this result due to D. Gaboriau and R. Lyons.
2017 Mar 09

Basic Notions: Benjy Weiss (HUJI) - What are amenable groups and why are groups non-amenable

4:00pm to 5:15pm

Location: 

Ross 70
Title: What are amenable groups and why are groups non-amenable Abstract: I will give an introduction to amenable groups and explain the result of Kevin Whyte that a countable non-amenable group admits a "translation-like" action by a non-abelian free group. I will also discuss (without proof) a measure theoretic analogue of this result due to D. Gaboriau and R. Lyons.
2017 Mar 16

Basic Notions: Benjy Weiss (HUJI) - What are amenable groups and why are groups non-amenable

4:00pm to 5:15pm

Location: 

Ross 70
Title: What are amenable groups and why are groups non-amenable Abstract: I will give an introduction to amenable groups and explain the result of Kevin Whyte that a countable non-amenable group admits a "translation-like" action by a non-abelian free group. I will also discuss (without proof) a measure theoretic analogue of this result due to D. Gaboriau and R. Lyons.

Pages