Upcoming talks:
19 IV | Abdul Gaffar Khan (University of Delhi) On expansivity through pointwise dynamics Show abstract
In 1950, Utz introduced expansive homeomorphisms, a concept
widely acknowledged in current literature. Recently, there has been
notable progress in exploring this idea from a pointwise dynamics
perspective. This not only enhances existing theories but also reveals
insights not accessible through a global dynamics approach. This talk
focuses on two such notions: uniformly expansive points and minimally
expansive points. We will explore the presence of uniformly expansive
points in homeomorphisms on bounded intervals and their implications
for identifying expansive homeomorphisms on the unit circle.
Additionally, we will discuss how minimally expansive points
contribute to topological stability of a point by establishing a
pointwise form of Walters' stability theorem. We will discuss how this
result can be applied for homeomorphisms on intervals which is not the
case with other existing forms of Walters' stability theorem. This
talk is based on joint work with Tarun Das. |
19 IV | Dario Darji (University of Louisville) Introduction Prevalence and Applications Show abstract
Suppose we have a collection of objects such as such as the
group of homeomorphisms or diffeomorphisms. We choose an object from
this collection at “random”. What dynamical properties does this
object have? The usual notion of a “random” or a “large” collection is
that of generic or comeager, i.e., we show that the collection of all
objects with certain dynamical properties contain a countable
intersection of dense open sets. There is an alternate natural notion
of bigness called prevalence and its complement called shy sets or
Haar null sets. This notion of smallness often highlights different
properties than the usual notion of generic. In this introductory
talk, we give a background on prevalence, discuss a variety of results
involving prevalence and analysis, prevalence and automorphism groups
and state some open problems concerning prevalence and dynamics.
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The seminar takes place on Fridays
at 10.15-11.45 AM (Kraków time) - currently CEST (UTC+2) in the room 1016
of the Jagiellonian University
Department of Mathematics
and Computer Science
(ul. Łojasiewicza 6, Cracow).