Dynamics on your screen

a zoom mini-conference

August 3-6, 2020




The online conference ``Dynamics on your screen" will cover a broad range of topics in dynamical systems and will feature 3 talks each day using the platform zoom. All are welcome to participate. The invitations to zoom talks will be distributed by email to registered participants. Available slides and lecture notes will be posted on this page after the conference concludes. However, we don't plan to video record the lectures.

Organizers: Livio Flaminio (Lille), Andrey Gogolev (Ohio State), Federico Rodriguez Hertz (Penn State)

Registration

We ask all participants to register and use their real names while participating in the conference. Registration is free. Please follow this link to register.

Invited speakers

Danijela Damjanovic (KTH Royal Institute of Technology)
Giovanni Forni (University of Maryland)
Catalina Freijo (Federal University of Minas Gerais)
Colin Guillarmou (Paris-Saclay University)
Asaf Katz (University of Chicago)
Wenyu Pan (University of Chicago)
Olga Paris-Romaskevich
Yakov Pesin (Pennsylvania State University)
Jana Rodriguez Hertz (Southern University of Science and Technology)
Çağrı Sert (University of Zurich)
Michele Triestino (University of Burgundy)
Kurt Vinhage (Pennsylvania State University)

Daily schedule (Monday to Thursday)

First talk 9:00-9:55am (New York time) = 3:00-3:55pm (Paris time)
Second talk 10:05-10:50am (New York time) = 4:05-4:50pm (Paris time)
Coffee/tea break 11:00-11:15am (New York time) = 5:00-5:15pm (Paris time)
Third talk 11:15-12:00am (New York time) = 5:15-6:00pm (Paris time)

Schedule
  Monday 8/3 Tuesday 8/4 Wednesday 8/5 Thursday 8/6
First talk Yakov Pesin Danijela Damjanovic Jana Rodriguez Hertz Colin Guillarmou
Second talk Çağrı Sert Michele Triestino Asaf Katz Wenyu Pan
Coffee/tea break
Third talk Olga Paris-Romaskevich Catalina Freijo Kurt Vinhage Giovanni Forni
 
2-3pm/8-9pm Open problem session


Open problem session

David Fisher
Classification of smooth group actions with uniform hyperbolicity

Miaohua Jiang
Does the entropy functional of an Anosov map on a torus with respect to its SRB measure have any non-trivial local extrema?

Clark Butler
Classification problem for Anosov diffeomorphisms in dimension 6

Alistair Windsor
Smooth realization of a gaussian process

Abstracts

Danijela Damjanovic
Global rigidity of some partially hyperbolic abelian actions (slides)
I will discuss global rigidity theme for abelian actions in the context of partially hyperbolic higher-rank actions and present several results and challenges in this direction.This is joint work with Amie Wilkinson and Disheng Xu.

Giovanni Forni
On decay of correlations for parabolic flows (slides)
I will survey recent progress and open questions on mixing, decay of correlations and spectral properties for several classes of smooth parabolic flows given by time-changes of homogeneous unipotent flows and translation flows. In particular, I will discuss joint work on speed of mixing of smooth time-changes of horocycle flows (with Ulcigrai) of Heisenberg nilflows (with Kanigowski), on mixing of smooth time-changes of general ergodic nilflows (with Avila, Ravotti and Ulcigrai) and on the countable Lebesgue spectral type of a class of Kochergin flows (with Fayad and Kanigowski).

Catalina Freijo
Lyapunov exponents for non-uniformly fiber-bunched cocycles (slides)
We consider a fixed hyperbolic dynamic in the base and study how the Lyapunov exponents vary as functions of the cocycle. In this context, Backes, Brown and Butler have proved that the Lyapunov exponents are continuous when restricted to the cocycles with both stable and unstable uniform holonomies. A conjecture of Marcelo Viana states that this condition on the holonomies can be relaxed asking only for an holonomy that variates continuously with the cocycle. We provide evidence that the conjecture is true by proving some partial results in this direction over non- uniformly fiber-bunched cocycles. This is a joint work with Karina Marin (UFMG).

Colin Guillarmou
The Ruelle-Taylor joint spectrum for Anosov actions (slides)
We define a notion of joint spectrum for Anosov R^k actions using Koszul complexes (and the so-called Taylor spectrum) on certain functional spaces called anisotropic Sobolev spaces. We show that this joint spectrum is an intrinsic discrete subset of C^k and study the particular value $\lambda=0$. This leads to some new SRB type measures and the question of mixing can be interpreted spectrally using this theory. Joint work with Bonthonneau, Hilgert and Weich.

Asaf Katz
Measure rigidity of Anosov flows via the factorization method (slides)
Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a negatively curved surface. In the talk we will introduce those flows and their dynamical behavior. Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows. Using this adaption, we show that for a quantitatively non-integrable Anosov flow, every generalized u-Gibbs measure is absolutely continuous with respect to the whole unstable manifold. In the talk I will discuss the factorization method, the relations to previous works (Eskin-Mirzakhani, Eskin-Lindenstrauss) and the result together with some examples and applications.

Wenyu Pan
Exponential mixing of geodesic flow for geometrically finite manifolds with cusps (slides)
Let $\mathbb{H}^n$ be the hyperbolic $n$-space and $\Gamma$ be a geometrically finite discrete subgroup in $\operatorname{Isom}_{+}(\mathbb{H}^n)$ with cusps. In the joint work with Jialun Li, we establish exponential mixing of the geodesic flow over the unit tangent bundle $T^1(\Gamma\backslash \mathbb{H}^n)$. Previously, such results were proved by Stoyanov for convex cocompact discrete subgroups and Mohammadi-Oh and Edwards-Oh for $\Gamma$ with large critical exponent. We obtain our result by constructing a nice coding for the geodesic flow and then prove a Dolgopyat-like spectral estimate for the corresponding transfer operator. In the talk, I am planning to explain the construction of the coding, which is partly inspired by the works of Lai-Sang Young and Burns-Masur-Matheus-Wilkinson. I will also discuss the application of obtaining a resonance-free region for the resolvent on $\Gamma\backslash \mathbb{H}^n$.

Olga Paris-Romaskevich
Slow holomorphic dynamics and polynomial entropy (slides)
The maps with chaotic dynamics represent a great interest and have been studied in detail, in various contexts. In this talk, I will be interested in the maps living on the opposite edge of the spectrum — maps with the dynamics of low complexity. They can be defined, for example, as those that have zero topological entropy. To quantify the complexity of such maps, one can consider a slower, polynomial entropy. I will give an introduction to polynomial entropy, with a focus on the low complexity holomorphic dynamics, following my recent work with Serge Cantat.

Yakov Pesin
The Smooth Realization Problem: Area Preserving Diffeomorphisms with Polynomial Decay of Correlations (slides)
Given any smooth compact connected and oriented surface, I present a construction of an area preserving diffeomorphism with non-zero Lyapunov exponents, which is Bernoulli and has polynomial decay of correlations, satisfies the Central Limit Theorem and has the Large Deviation Property. In addition, this diffeomorphism possesses a unique hyperbolic Bernoulli measure of maximal entropy with respect to which it has exponential decay of correlations. This is a joint work with Samuel Senti and Farruh Shahidi.

Jana Rodriguez Hertz
Stable ergodicity beyond partial hyperbolicity (slides)
The first known mechanism implying stable ergodicity of the volume measure is hyperbolicity. It took time to obtain new examples: partially hyperbolic diffeomorphisms. Pugh and Shub conjectured that partial hyperbolicity generically implied stable ergodicity, a conjecture that was proved by Avila, Crovisier and Wilkinson. Non-partially hyperbolic stably ergodic diffeomorphisms were also known to exist, but so far all the known examples were DA-diffeomorphisms. We will discuss different mechanisms other than partial hyperbolicity that could generically imply stable ergodicity with respect to the volume measure. In fact, we conjecture that very little hyperbolicity, namely, positive metric entropy, generically implies stable ergodicity. While this conjecture still seems far to be solved, we show new examples of stably ergodic diffeomorphisms. For instance, in 3-dimensional manifolds, there is a stably ergodic non-partially hyperbolic diffeomorphism in the isotopy class of each partially hyperbolic diffeomorphism. In particular, there are such examples in 3-manifolds other than the 3-torus. On the other hand, we conjecture that the existence of a minimal invariant expanding foliation generically implies stable ergodicity. We have proven this conjecture for 3-dimensional manifolds, and there are some advances for higher dimensional manifolds. This is part of different joint works with G. Núñez and D. Obata.

Cagri Sert
Equilibrium measures of affine fractals (slides)
We will start by giving an overview of dimension theory and equilibrium measures of similarity and affine fractals making connections with repellers of expanding maps. In a second part, we will explain a dimension gap result yielding in particular a sort of converse to a classical result of Hutchinson: under an irreducibility assumption, an affine fractal admitting a Bernoulli equilibrium measure with maximal dimension is a similarity fractal. In the last part, I will explain some ways to turn around this gap by consideration of subsystems. Based on joint works with Ian Morris.

Michele Triestino
Actions of locally moving groups of homeomorphisms of the real line (slides)
In a recent project in collaboration with Joaquín Brum, Nicolás Matte Bon, and Cristóbal Rivas, we investigate the structure of the space of actions on the real line of locally moving groups. A group of homeomorphisms of the real line is locally moving if, for every open interval, there exists a subgroup acting on it without global fixed points, and acting trivially in restriction to its complement. Classical examples are provided by Thompson's group F, but even by large groups, such as the group of compactly supported homeomorphisms of the real line. As a consequence of classical work of Rubin, every isomorphism between two locally moving groups is realized by a homeomorphism, and in particular every locally moving group admits a unique locally moving action. What about the other actions?

Kurt Vinhage
Complete classification of transitive, totally Cartan actions (slides)
I will discuss recent progress in rigidity theory for actions of abelian groups. After several results on local rigidity of lattice and abelian group actions in the 80s and early 90s, Katok and Spatzier conjectured that in fact *all* hyperbolic actions without rank one factors are smoothly conjugate to an algebraic model. We verify the conjecture for all transitive, totally Cartan actions: ones for which there are many hyperbolic elements, and for which a dynamical splitting is simple. This is the first time the conjecture can be proven without strong ergodicity or perturbative assumptions. We furthermore classify all transitive, totally Cartan actions, even those with rank one factors. They are all built from direct products of Anosov flows and diffeomorphisms and homogeneous actions. Joint with Ralf Spatzier.

Participants

  1. Aaron Brown
  2. Adam Abrams
  3. Adam Kanigowski
  4. Adrian Perez Bustamante
  5. Adriana da Luz
  6. Adriana Sánchez
  7. Agnieszka Zelerowicz
  8. Albert Artiles
  9. Alejandro Kocsard
  10. Alejo García
  11. Alena Erchenko
  12. Alessandro Arsie
  13. Alex Furman
  14. Alex Zamudio
  15. Alexander Arbieto
  16. Alexander Cantoral Vilchez
  17. Alexander Gorodnik
  18. Alfonso Artigue
  19. Ali Tahzibi
  20. Alisson Pereira
  21. Alistair Windsor
  22. Alp Uzman
  23. Amie Wilkinson
  24. Amin Talebi
  25. Ana Carolina Ramos
  26. Anastasios Stylianou
  27. Anders Karlsson
  28. Andre Oliveira
  29. Andreas Wieser
  30. Andrés Bellei
  31. Andres Koropecki
  32. Angel Pardo
  33. Anibal Velozo
  34. Anindya Chanda
  35. Aritro Pathak
  36. Artem Dudko
  37. Asgar Jamneshan
  38. Aygul Galimova
  39. Barak Weiss
  40. Bárbara Núñez
  41. Benedict Sewell
  42. Benjamin Call
  43. Bernardo Carvalho
  44. Biao MA
  45. Boris Hasselblatt
  46. Boris Kalinin
  47. Boris Kruglikov
  48. Brayan Mauricio Rodriguez
  49. Bruce Peckham
  50. Bruno Yemini
  51. C Cheng
  52. Cagri Sert
  53. Carllos Eduardo Holanda
  54. Carlos H. Vasquez
  55. Carlos Matheus
  56. Carsten Peterson
  57. Cássio Morais
  58. Cesar Romero Mora
  59. Changguang Dong
  60. Charles Walkden
  61. Christoforos Neofytidis
  62. Christophe Golé
  63. Clark Butler
  64. Cláudia Ferreira
  65. Connor Jackman
  66. Constantin Kogler
  67. Corinna Ulcigrai
  68. Cristina Lizana
  69. Cristóbal Rivas
  70. Daniel Alvey
  71. Daniel Ingebretson
  72. Daniel Reis de Oliveira
  73. Danijela Damjanovic
  74. Danny Stoll
  75. Danyu Zhang
  76. Daren Wei
  77. Dave Constantine
  78. Davi Obata
  79. David Fisher
  80. Débora de Oliveira
  81. Deniel Correa
  82. Deokwon Sim
  83. Dhiraj Ghadage
  84. Diaaeldin Taha
  85. Diego Lugo
  86. Dmitri Scheglov
  87. Dong Chen
  88. el Houcein el Abdalaoui
  89. Elias Rego
  90. Elizabeth S Flores
  91. Elon Lindenstrauss
  92. Elmer Beltran
  93. Emilio Corso
  94. Erez Nesharim
  95. Eric Albers
  96. Eric Cabezas
  97. Erwan Lanneau
  98. Fabrizio Bianchi
  99. Feliks Przytycki
  100. Ferrán Valdez
  101. Farruh Shahidi
  102. Fernando Lenarduzzi
  103. Fernando Micena
  104. Filiz Dogru
  105. Francois Ledrappier
  106. Frank Trujillo
  107. Freddy Castro
  108. Freddy Vicente
  109. Gerhard Knieper
  110. Gil Astudillo
  111. Grace Work
  112. Greg Davis
  113. Guido Marinoni
  114. Habibeh Pourmand
  115. Hector Sanchez
  116. Hellen de Paula
  117. Henrik Kreidler
  118. HeSam Rajabzadeh
  119. Hiba Fayoumi
  120. Homin Lee
  121. Hongkun Zhang
  122. Hugo Araújo
  123. Hugo Carrillo
  124. Ibai Aedo
  125. Inti C. Diaz
  126. Ivan Gonzalez
  127. Jack Burkart
  128. Jacob Mazor
  129. Jacqueline Warren
  130. Jade Ventura
  131. Jairo Bochi
  132. Jamerson Bezerra
  133. Jana Rodriguez Hertz
  134. Jane Hawkins
  135. Jaqueline Siqueira
  136. Javier Saenz
  137. Jean Lafont
  138. Jennyffer Bohorquez
  139. Jialun LI
  140. Jianlong Liu
  141. Jiaqi Yang
  142. Jieun Seong
  143. Jimi Daniel Gomez
  144. Jimmy Santamaria
  145. Jimmy Tseng
  146. Jing Zhou
  147. Jiyoung Hanv
  148. Joan Gimeno
  149. Joao Rijo
  150. João Lopes Dias
  151. Joaquín brum
  152. Joaquin Delgado
  153. Joaquín Lejtreger
  154. Joaquín Lema Perez
  155. John Hynes
  156. Jon Chaika
  157. Jonathan DeWitt
  158. Jorge Gonzalez
  159. Josh Southerland
  160. Juan Carlos Morelli Ramírez
  161. Juan Carlos Salcedo Sora
  162. Juan Paucar
  163. Juan Tolosa
  164. Kari Kuester
  165. Karin Reinhold
  166. Karina Marin
  167. Karl Petersen
  168. Keith Burns
  169. Keivan Mallahi-Karai
  170. Kelly Yancey
  171. Khadim War
  172. Kiho Park
  173. Konstantin Khanin
  174. Kriti Sehgal
  175. Kursat Yilmaz
  176. LASSALLE Philippe
  177. Lautaro Cilenti
  178. Lin Shu
  179. Lei Yang
  180. Leonardo Dinamarca
  181. Leydiane Campos
  182. Luciana Salgado
  183. Mahdi Teymuri Garakani
  184. Mahesh Nerurkar
  185. Maheshan Ekanayaka
  186. Maisam Hedyehloo
  187. Manfred Denker
  188. Manuel Jesús Saavedra Jiménez
  189. Manuel Stadlbauer
  190. Marco López
  191. María Isabel Cortez
  192. Mark Bell
  193. Mark Pollicott
  194. Marlies Gerber
  195. Martha Łącka
  196. Martin Leguil
  197. Martyna Górska
  198. Mary He
  199. Mauricio Genta
  200. Mauro Artigiani
  201. Meysam Nassiri
  202. Miaohua Jiang
  203. Michael Jakobson
  204. Michele Triestino
  205. Mihajlo Cekić
  206. Minsung Kim
  207. Mitul Islam
  208. Nattalie Tamam
  209. Nawaf Alansari
  210. Nayana Wanasingha
  211. Nelda Jaque
  212. Nestor Nina
  213. Nguyen-Thi Dang
  214. Nicolás Alvarado
  215. Nicolas Monod
  216. Nikolai Edeko
  217. Noy Soffer Aranov
  218. Nyima Kao
  219. Odylo Costa
  220. Olga Paris-Romaskevich
  221. Olga Lukina
  222. Osama Khalil
  223. Ozkan Demir
  224. Pablo D. Carrasco
  225. Pallavi Panda
  226. Paulo Varandas
  227. Peng Sun
  228. Philipp Kunde
  229. Ping Ngai (Brian) Chung
  230. Polina Vytnova
  231. Porfirio Toledo
  232. Predrag Punosevac
  233. Rachel McEnroe
  234. Radu Saghin
  235. Rafael de la Llave
  236. Rafael Pereira
  237. Rafael Potrie
  238. Rainer Nagel
  239. Ralf Spatzier
  240. Raul Ures
  241. Renato Velozo
  242. Reza Mohammadpour
  243. Rhiannon Dougall
  244. Richard Buckalew
  245. Richard Montgomery
  246. Richard Sharp
  247. Robert Leek
  248. Robert Niemeyer
  249. Rodrigo Andrade
  250. Rodrigo Bissacot
  251. Rodrigo Treviño
  252. Roland Gunesch
  253. Roland Prohaska
  254. Ruxi Shi
  255. Salman Siddiqi
  256. Sam Dodds
  257. Samuel Everett
  258. Santiago Martinchich
  259. Santiago Montouliu
  260. Satbir Malhi
  261. Saúl Quispe
  262. Sebastian Burgos
  263. Sebastian Hurtado
  264. Sebastian Ramirez
  265. Sébastien Labbé
  266. Sejal babel
  267. Seth Chaiken
  268. ShengYuan ZHAO
  269. Shilpak Banerjee
  270. Shrey Sanadhya
  271. SHREYASI DATTA
  272. Simion Filip
  273. Simon Baker
  274. Sinisa Slijepcevic
  275. Sixu Liu
  276. Siyuan Tang
  277. Solly Coles
  278. Sonia Pinto-de-Carvalho
  279. Stefano Luzzatto
  280. Steve Hurder
  281. Sumana Kundu
  282. Svetlana Katok
  283. Tanja Eisner
  284. Tejbir Lohan
  285. Thang Nguyen
  286. Thomas Barthelmé
  287. Thomas Richards
  288. Tsviqa Lakrec
  289. Tulio Ferreira
  290. Valéria Santos
  291. Victor Castillo
  292. Victor Kleptsyn
  293. Victor Vilaça Da Rocha
  294. Victoria Sadovskaya
  295. Vincent Delecroix
  296. Vincent Pecastaing
  297. Weisheng Wu
  298. Welington Cordeiro
  299. Wenyu Pan
  300. Yakov Pesin
  301. Yang Yang
  302. Yi PAN
  303. Ying Sue Huang
  304. Yu-Wei Fan
  305. Yulia Meshkova
  306. Yun Yang
  307. Yuping Ruan
  308. Yuting Fang
  309. Zahra Reshadat
  310. Zemer Kosloff
  311. Zhe Zhou
  312. Zhijing Wang