Please contact Nishant Chandgotia (nishant.chandgotia@gmail.com) or Shilpak Banerjee (shilpak@iittp.ac.in) to be added to the mailing list.
This is a recurrent seminar but not necessarily periodic. The sessions will be on zoom (for the link please contact the organisers) and will depend on the speaker's and organiser's schedule. We will try to record the sessions if the speaker agrees.
Recorded videos will be posted on https://youtube.com/playlist?list=PLjIyCJaXNtwrp7XoiXH71GYS6wDh9BsRe&si=KVtJICs7-naEVhof
Speaker: Ángel González-Prieto (Universidad Complutense de Madrid)
Time: 2:30 PM, Tuesday , 23 September, 2025 Indian Standard Time (convert to your time zone: https://www.timeanddate.com/worldclock/converter.html)
Zoom link: https://zoom.us/j/98463954270?pwd=TPrp5b0fB3KUae3VDisHgjcefTBUl9.1
Meeting ID: 984 6395 4270
Passcode: 833478
Title: Turing universality in dynamical systems
Abstract: The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualisations of computation. Recently, this connection has gained renewed attention, fueled by T. Tao's program aiming to discover blowing-up solutions of the Navier-Stokes equations using an embedded computational model, and by the intriguing links between static solutions and contact structures. In this vibrant context, a series of groundbreaking works have shown that Turing machines can be simulated through the flow lines of certain remarkable dynamical systems.
In this talk, we will introduce a novel perspective on computability in dynamical systems, drawing inspiration from Topological Quantum Field Theory. We will demonstrate that any computable function can be realized through the flow of a volume-preserving vector field on a smooth bordism. This result not only provides a new computational model but also unveils compelling insights into the interplay between the topological characteristics of the flow, the existence of compatible contact-like geometric structures on the bordism, and the computational complexity of the function.
Joint work with E. Miranda and D. Peralta-Salas
Speaker: Nicanor Carrasco-Vargas (Jagiellonian University)
Time: 2:30 PM, Wednesday, 27 August, 2025 Indian Standard Time (convert to your time zone: https://www.timeanddate.com/worldclock/converter.html)
Video: https://youtu.be/1VcMTs3vZUk
Title: Topological slow entropy of some skew products
Abstract: This talk is about a family of skew products that naturally generalize the [T,T⁻¹] system, well studied in ergodic theory. We consider the analogous construction in the topological category. These systems are built by a subshift in the base, a continuous cocycle to the integers, and an arbitrary invertible system in the fiber. We are interested in the situation where the entropy of the skew product construction is independent of the entropy of the fiber system. In this case we have a large family of systems in which the invariant of topological entropy is constant and therefore does not provide much information. The main result states that under suitable conditions, the entropy of the fiber system can be recovered as the slow entropy of the skew product with a well-chosen scale. This result provides a topological analogous of existing results in the measurable category (Heicklen, Hoffman, & Rudolph; Ball; Austin), and the main novelty is that it covers some instances zero-entropy systems in the base.
The talk will be based on the recent preprint https://arxiv.org/abs/2506.17932
Speaker: Philipp Kunde (Oregon State University)
Video: https://youtu.be/pVDrmNwWeTs
Time: 4:00 PM, Thursday, 10th July, 2025 Indian Standard Time (convert to your time zone: https://www.timeanddate.com/worldclock/converter.html)
Title: Shrinking targets and eventually always hitting points
Abstract: The term shrinking target problems in dynamical systems describes a class of questions which seek to understand the recurrence behavior of typical orbits of a dynamical system. The standard ingredients of such questions are a probability measure preserving dynamical system (X, μ, T) and a sequence of targets {B_m}_{m∈N} with B_m ⊂ X and μ(B_m) → 0. Classical questions in this area focus on the set of points whose n-th iterate under T lies in the n-th target for infinitely many n. We study a uniform analogue of these questions, the so-called eventually always hitting points. These are the points whose first n iterates will never have empty intersection with the n-th target for sufficiently large n. We search for necessary and sufficient conditions on the shrinking rate of the targets for the set of eventually always hitting points to be of full or zero measure. In particular, I will present some recent dichotomy results for some interval maps obtained in collaboration with Mark Holland, Maxim Kirsebom, and Tomas Persson.
If time permits, I will also discuss another modification of the problem where we study points that return infinitely many times to a sequence of shrinking targets around themselves.
Speaker: Omri Sarig (Weizmann Institute)
Video: https://youtu.be/VY5I9axxlCA
Time: Monday, June 9, 4 PM - 5 PM Indian Standard time (convert to your time zone: https://www.timeanddate.com/worldclock/converter.html)
Title: Irregularities in Uniform Distribution
Abstract: : Suppose a is an irrational number. Weyl proved that na mod 1 is uniformly distributed on the unit interval. i.e., the frequency of visits of na mod 1 to a subinterval of [0,1] tends to the length of the subinterval. It has long been known that the error term in this limit theorem can exhibit strong bias, reflecting an “irregularity” in uniform distribution in the higher-order term. This bias depends on the fine number theoretic properties of a. For example, the square roots of two and three do not behave the same way (!) I will explain how infinite ergodic theory can shed light on this phenomenon, and describe some recent joint work with Dmitry Dolgopyat on the equidistribution of the error term. There are amusing connections to the geometry of translation surfaces with infinite genus, and to local limit theorems of inhomogeneous Markov chains.
Speaker: Daren Wei (National University of Singapore)
Video: https://youtu.be/ivGlXDthiwg
Time: 11:30 AM, Thursday, 29 May, 2025 Indian Standard Time
Title: Time Change Rigidity of Unipotent Flows
Abstract: Two non-isomorphic ergodic measure preserving flows can become isomorphic if one of the systems undergoes an appropriate time change. In this case we will say that these flows are Kakutani equivalent to each other. We say that an ergodic flow is loosely Kronecker if it is Kakutani equivalent to the straight line flow on (say) a two torus in an irrational direction (the exact direction is immaterial as these are all equivalent to each other). Landmark work of Ratner from the late 70s (that paved the way to her even more famous results on orbit closures and equidistribution of unipotent flows) establishes that 1) the horocycle flow on any finite area surface of constant negative curvature is loosely Kronecker. 2) the product of two such flows is not loosely Kronecker. It remained an open problem whether e.g. products of two horocycle flows are Kakutani equivalent to each other. We show unipotent flows are very rigid under time changes, and indeed unless the flows are loosely Kronecker, two unipotent flows are Kakutani equivalent if and only if they are isomorphic as measure preserving flows. This is a joint work with Elon Lindenstrauss.
Speaker: Barak Weiss (Tel Aviv University)
Video: https://youtu.be/wYua18NGy3o
Time: 2 PM, Tuesday, 22 March, 2025 Indian Standard Time
Title: The Illumination problem
Abstract: The illumination problem, formulated by Straus in the 1950’s and solved by Tokarsky in the 1990’s, is whether there is a polygonal “hall of mirrors", containing two points that do not illuminate each other. In recent years it has been found that the possible examples are special and significantly restricted. Progress in understanding the illumination problem has relied on deep results in ergodic theory, probability and geometry, including results of Mirzakhani that were part of her 2014 Fields medal citation. I will briefly describe the history of the problem, state recent results, and sketch the relation to dynamics.
Speaker: Jakub Konieczny (University of Oxford)
Video: https://www.youtube.com/watch?v=PY5J2GKilmE
Slides: https://drive.google.com/open?id=1LUNEA05TZkOLZbfNrT-PVFLrw22UIthW&usp=drive_fs
Time: 5 PM, Tuesday, 18 March, IST
Title: Arithmetical subword complexity of automatic sequences
Abstract: It is well-known that the subword complexity of an automatic sequence grows at most linearly, meaning that the number of length-l subwords which appear in a given automatic sequence a = (a(n))_n is at most Cl for a constant C dependent only on a. In contrast, arithmetic subword complexity measures the number of subwords which appear along arithmetic progressions, and can grow exponentially even for very simple automatic sequences. Indeed, the classical Thue-Morse sequence has arithmetic subword complexity 2^l, which is the maximal possible complexity for {0,1}-valued sequence.
Together with Jakub Byszewski and Clemens Müllner we obtained a decomposition result which allows us to express any (complex-valued) automatic sequence as the sum of a structured part, which is easy to work with, and a part which is pseudorandom or uniform from the point of view of higher order Fourier analysis. We now apply these techniques to the study of arithmetic subword complexity of automatic sequences. We show that for each automatic sequence a there exists a parameter r --- which we dub "effective alphabet size" --- such that the arithmetic subword complexity of a is at least r^l and at most (r+o(1))^l.
Speaker: Dominik Kwietniak (Jagiellonian University)
Video: https://youtu.be/2F7sY_x8kmA
Time: 3 PM, Friday, 31st January
Title: Bowen's Problem 32 and complexity of the conjugacy problem for systems with specification
Abstract: We show that Bowen's Problem 32 on the classification of symbolic systems with specification does not admit a solution that would use concrete invariants. To this end, we construct a class of symbolic systems with specification and show that the conjugacy relation on this class is too complicated to admit such a classification. More generally, we gauge the complexity of the classification problem for symbolic systems with specification. Along the way, we also provide answers to two question related to complexity of pointed systems with specification: to a question of Ding and Gu related to the complexity of pointed Cantor minimal systems and to a question of Bruin and Vejnar on the complexity of the classification of pointed transitive Hilbert cube systems.
This is joint work with Konrad Deka, Bo Peng and Marcin Sabok, see arXiv:2501.02723 https://doi.org/10.48550/arXiv.2501.02723