Activities This Week
AGNT
TBA
Dec 29, 16:00—17:15, 2021, -101
Speaker
Amit Ophir (HUJI)
BGU Probability and Ergodic Theory (PET) seminar
Non-classifiability of ergodic flows up to time change Online
Dec 30, 11:10—12:00, 2021, -101
Speaker
Philipp Kunde (Universität Hamburg )
Non-commutative Analysis Seminar
Bratteli diagrams, dynamics, and classification beyond the minimal case (part 2)
Jan 4, 11:00—12:00, 2022, seminar room -101
Speaker
Paul Herstedt (BGU)
Abstract
Earlier this year, we discovered a new class of zero-dimensional dynamical systems, which we call “fiberwise essentially minimal”, that are of importance to operator algebras because of the nice properties, in particular K-theoretic classification, of the crossed product. Today, we discuss the Bratteli diagrams associated to these systems, and extend the K-theoretic classification to include a dynamical condition called “strong orbit equivalence”, extending the existing result in the minimal case due to Giordano-Putnam-Skau.
Colloquium
Finite determinacy of maps. Group orbits vs their tangent spaces
Jan 4, 14:30—15:30, 2022, Math -101
Speaker
Dmitry Kerner (BGU)
Abstract
A function at a non-critical point can be converted to a linear form by a local coordinate change. At an isolated critical point one has the weaker statement: higher order perturbations do not change the group orbit. Namely, the function is determined (up to the local coordinate changes) by its (finite) Taylor polynomial.
This finite-determinacy property was one of the starting points of Singularity Theory. Traditionally such statements are proved by vector field integration. In particular, the group of local coordinate changes becomes a ``Lie-type” group.
I will show such determinacy results for maps of germs of (Noetherian) schemes. The essential tool is the “vector field integration” in any characteristic. This equips numerous groups acting on filtered modules with the ``Lie-type” structure. (joint work with G. Belitskii, A.F. Boix, G.M. Greuel.)