Joint equidistribution of arithmetic orbits, joinings, and rigidity of higher rank diagonalizable actions II

Elon Lindenstrauss
Hebrew University of Jerusalem
March 4, 2015
An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept in the study of dynamical systems, and allow detection of "hidden common denominator" of two (or more) dynamical systems. While one parameter diagonalizable actions on homogenous spaces have lots of joinings, for two parameter actions any measurable joining can be provided to be in fact of a very precise algebraic kind.

On random walks in the group of Euclidean isometries

Elon Lindenstrauss
Hebrew University of Jerusalem
March 6, 2015
In contrast to the two dimensional case, in dimension $d \geq 3$ averaging operators on the $d-1$-sphere using finitely many rotations, i.e. averaging operators of the form $Af(x)= |S|^{-1} \sum_{\theta \in S} f(s x)$ where $S$ is a finite subset of $\mathrm{SO}(d)$, can have a spectral gap on $L^2$ of the $d - 1$-sphere. A result of Bourgain and Gamburd shows that this holds, for instance, for any finite set of elements in $\mathrm{SO}(3)$ with algebraic entries and spanning a dense subgroup.

The American Plate: A Culinary History in 100 Bites

Libby O'Connell
Chief Historian for History Channel
March 6, 2015
Dr. Libby O'Connell, chief historian for History Channel, will
discuss American culinary history and food traditions in this
talk drawn from her new book The American Plate: A Culinary
History in 100 Bites. Dr. O'Connell's lecture explores key moments
in U.S. history through the lens of food, from indigenous food
preparation to immigrant journeys to 20th century food fads,
to describe how and why food can be a central through-line for
understanding American history and culture.

Science Talk for Families- Jo Bovy

Jo Bovy, Member
John N. Bahcall Fellow, School of Natural Sciences
March 7, 2015
Jo Bovy, John N. Bahcall Fellow in the School of Natural Sciences, talks about stars, planets, and gases that make up galaxies, the dark matter that holds them together, and the history of our own Milky Way galaxy in this talk geared for children and families.

Strong contraction and influences in tail spaces

Elchanan Mossel
University of Pennsylvania
March 9, 2015
Various motivations recently led Mendel and Naor, Hatami and Kalai to study functions in tail spaces - i.e. function all of whose low level Fourier coefficients vanish. I will discuss the questions and conjectures that they posed and our recent work which resolves some of these questions and conjectures. Based on a joint work with Steven Heilman and Krzysztof Oleszkiewicz.