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

2018
Jun
07

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

2018
Jun
07

2018
May
31

4:00pm to 5:30pm

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

4:00pm to 5:30pm

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

4:00pm to 5:30pm

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

4:00pm to 5:30pm

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?

2018
Apr
26

4:00pm to 5:30pm

Math Hall 2

Expander graphs have been a topic of great interest in the last 50 years for mathematicians and computer scientists. In recent years a high dimensional theory is emerging. We will describe some of its main directions and questions.

2018
Mar
22

2017
May
25

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

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

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

4:00pm to 5:15pm

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

4:00pm to 5:15pm

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

4:00pm to 5:15pm

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.

2018
Jan
25

2017
May
11

4:00pm to 5:15pm

Ross 70

The Schmidt Subspace Theorem, its S-arithmetic extension by Schlickewei, and subsequent (rather significant) refinements are highlights of the theory of Diophantine applications and have many applications, some quite unexpected.