Research Group "Stochastic Algorithms and Nonparametric Statistics"

Research Seminar "Mathematical Statistics" WS 2021/2022

  • Place: The seminar will be hybrid and realized via Zoom. Please note that the so-called ``3G rule" applies at Weierstrass Institute. Our lecture room ESH has according to hygiene recommendations only a capacity of 16 people. If you intend to participate you must register for our mailinglist with Andrea Fiebig ( Prior to each talk a doodle will be created where it is mandatory to sign in for attendance in person. Therefore, it is mandatory for those who want to participate in person to register (put your name in the list) using the doodle link sent by e-mail before the lecture. Please follow the streamed talk at , if 16 guests have already registered
  • Time: Wednesdays, 10.00 a.m. - 12.30 p.m.


03.11.2021 Evgeny Stepanov (Russian Academy of Sciences, St. Petersburg)
The story of a fish in a turbulent ocean: How to survive and how to return home
Can a fish with limited velocity capabilities reach any point in the (possibly unbounded) ocean? In a recent paper by D. Burago, S. Ivanov and A. Novikov, ''A survival guide for feeble fish", an affirmative answer has been given under the condition that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This brilliant result extends some known point-to-point global controllability theorems though being substantially non constructive. We will give a fish a different recipe of how to survive in a turbulent ocean, and show how this is related to structural stability of dynamical systems by providing a constructive way to change slightly a divergence free vector field with vanishing mean drift to produce a non dissipative dynamics. This immediately leads to closing lemmas for dynamical systems, in particular to C. Pugh's closing lemma, saying also that the fish can eventually return home. Joint work with Sergey Kryzhevich (St. Petersburg).






last reviewed: October 21, 2021 by Christine Schneider