פעילויות השבוע
Jerusalem - Be'er Sheva Algebraic Geometry Seminar
Derived quotients of Cohen-Macaulay rings
ינו 6, 15:00—16:30, 2021,
מרצה
Liran Shaul (Charles University, Prague )
תקציר
It is well known that if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is an $A$-regular sequence, then the quotient ring $A/(a_1,\dots,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by deriving the quotient operation, if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is any sequence of elements in $A$, the derived quotient of $A$ with respect to $(a_1,\dots,a_n)$ is Cohen-Macaulay. As an application, we generalize the miracle flatness theorem to derived algebraic geometry. As another application, given a morphism $f:X\to Y$ from a Cohen-Macaulay scheme to a nonsingular scheme, we show that the homotopy fiber of $f$ at every point is Cohen-Macaulay.
BGU Probability and Ergodic Theory (PET) seminar
Amenability, proximality, and higher order syndeticity Online
ינו 7, 11:10—12:00, 2021, Online
מרצה
Guy Salomon (Weizmann Institute)
תקציר
An action of a discrete group G on a compact Hausdorff space X is called proximal if for every two points x and y of X there is a net g_i in G such that lim(g_i x)=lim(g_i y), and strongly proximal if the action of G on the space Prob(X) of probability measures on X is proximal. The group G is called strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point.
In this talk, I will present a correspondence between (strongly) proximal actions of G and Boolean algebras of subsets of G consisting of certain kinds of “large” subsets. I will use these Boolean algebras to establish new characterizations of amenability and strong amenability. Furthermore, I will show how this machinery helps to characterize “dense orbit sets” answering a question of Glasner, Tsankov, Weiss, and Zucker.
This is joint work with Matthew Kennedy and Sven Raum.