Matheus' Weblog
In 1966, M. Kac wrote a famous article asking whether Can one hear the shape of drum?: mathematically speaking, one wants to reconstruct (up to isometries) a domain from the knowledge of the spectrum of its Laplacian. In his article, M. Kac showed that one can hear the shape of a disk because of the following [ ]
Simion Filip, Curtis McMullen, Martin Moeller and I are co-organizing an online seminar called Billiards, Surfaces à la Teichmueller and Riemann, Online (BiSTRO). Similarly to several other current online seminars, the idea of BiSTRO arose after several conferences, meetings, etc. in Teichmueller dynamics were cancelled due to the covid-19 crisis. In any case, the first talk [ ]
Sinai billiards are a fascinating class of dynamical systems: in fact, despite their simple definition in terms of a dynamical billiard on a table given by a square or a two torus with a certain number of dispersing obstacles, they present some nasty features (related to the existence of grazing collisions) placing them slightly beyond the standard theory [ ]
Last January 8, 2020, Jialun Li gave the talk Decrease of Fourier coefficients of stationary measures on the circle in the flat seminar that I co-organize with Anton Zorich once per month. In this post, I ll transcript my notes of this nice talk (while taking full responsibility for any errors/mistakes in what follows). 1. Introduction 1.1. Stationary [ ]
Last time, we saw that if is a compact subset of reductive, real linear algebraic group such that the monoid generated by is Zariski dense in , then the Cartan projections and the Jordan projections associated to converge in the Hausdorff topology to the same limit , an object baptised joint spectrum of by Breuillard [ ]
Last November, I attended the beautiful conference Prime Numbers, Determinism and Pseudorandomness at CIRM. This conference was originally prepared to celebrate the 60th birthday of Christian Mauduit, but unfortunately a tragic event during the summer of 2019 made that this conference ended up becoming a celebration of the memory of Christian. The links to the titles, abstracts, slides and [ ]
In the previous post of this series, we gave the statements of some of the results of Breuillard and Sert on the definition and basic properties of the joint spectrum, and we promised to discuss the proofs in subsequent posts. Today, after a long hiatus, I ll try to accomplish part of this promise. More precise, I ll transcript [ ]
Yuri Lima asked me to announce in this blog the following opportunity for a post-doctoral position in Dynamical Systems and Ergodic Theory at Universidade Federal do Ceará (located in Fortaleza, Brazil): Serrapilheira Postdoctoral Fellowship UFC The Department of Mathematics at Universidade Federal do Ceará (UFC) invites applications for a Serrapilheira Postdoctoral Fellowship in dynamical [ ]
In this previous post here (from 2018), I described some back of the envelope calculations (based on private conversations with Scott Wolpert) indicating that some sectional curvatures of the Weil Petersson (WP) metric could be at least exponentially small in terms of the distance to the boundary divisor of Deligne Mumford compactification. Very roughly speaking, this heuristic computation went as…
The celebrated works of several mathematicians (including Poincaré, Denjoy, , Arnold, Herman, Yoccoz, ) provide a very satisfactory picture of the dynamics of smooth circle diffeomorphisms: each -diffeomorphism of the circle has a well-defined rotation number (which can be defined using the cyclic order of its orbits, for instance); is topologically semi-conjugated to the rigid rotation (i.e., for…