Skip to content
# Events for 06/03/2020 from all calendars

## Groups and Dynamics Seminar

## Noncommutative Geometry Seminar

**Time: ** 12:00PM - 1:00PM

**Location: ** 940 9667 3668

**Speaker: **Andrew Marks, UCLA

**Title: ***Measurable realizations of abstract systems of congruence*

**Abstract: **In the last few years, several new results have been proved
with the unifying theme that the "paradoxical" sets in many classical
geometrical paradoxes can surprisingly be much "nicer" than one would
naively expect. For example, by the Banach-Tarski paradox any two
bounded subsets A and B of R^3 with nonempty interior are
equidecomposable. However, if A and B have the same Lebesgue measure,
then a recent theorem of Grabowski, M\'ath\'e and Pikhurko states that
A and B are equidecomposable using Lebesgue measurable pieces. So for
example, there is a Lebesgue measurable equidecomposition of a cube
and a ball in R^3 of the same volume
An abstract system of congruences describes a way of partitioning a
space into finitely many pieces satisfying certain congruence
relations. Examples of abstract systems of congruences include
paradoxical decompositions and n-divisibility of actions. We consider
the general question of when there are realizations of abstract
systems of congruences satisfying various measurability constraints.
We completely characterize which abstract systems of congruences can
be realized by nonmeager Baire measurable pieces of the sphere under
the action of rotations on the 2-sphere. This answers a question of
Wagon. We also construct Borel realizations of abstract systems of
congruences for the action of PSL_2(Z) on P^1(R). This is joint work
with Clinton Conley and Spencer Unger.

**Time: ** 1:00PM - 2:00PM

**Location: ** Zoom 942810031

**Speaker: **Paolo Antonini, SISSA

**Title: ***The Baum–Connes conjecture localised at the unit element of a discrete group*

**Abstract: **For a discrete group Γ we construct a Baum–Connes map localised at the group unit element. This is an assembly map in KK–theory with real coefficients leading to a form of the Baum-Connes conjecture which is intermediate between the Baum–Connes conjecture and the Strong Novikov conjecture.
A second interesting feature of the localised assembly map is functoriality
with respect to group morphisms. We explain the construction and we show that the relation with the Novikov conjecture follows from a comparison at the level of KKR-theory of the classifying space for free and proper actions EΓ with the classifying space for proper actions EΓ.
Based on joint work with Sara Azzali and Georges Skandalis.

**URL: ***Event link*