Department Seminars & Colloquia
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Wavelets are introduced as an alternative to the classical Fourier analysis in late 80s, and since then, they have been used in various applications including signal and image processing. In this talk, I will review some of basics and challenges of wavelets, especially from the point of view of wavelet constructions in multidimensional setting. I will then present some new methods of construction.
We consider the dynamical system of Sinai billiards with a single cusp where two walls meet at the vertex of a cusp and have zero one-sided curvature, thus forming a flat point at the vertex. For Holder continuous observables, we show that properly normalized Birkhoff sums, with respect to the billiard map, converge in law to a totally skewed alpha-stable law.
A quantum walk is a (rather imperfect analog) of a random walk on a graph.
They can be viewed as gadgets that might play a role in quantum computers, and have been
used to produce algorithms that outperform corresponding classical procedures. Physical
questions about these walks lead to problems in spectral graph theory, and they also provide
interesting new graph invariants. In my talk I will present some of the background,
and some of the many open problems that they have given rise to.
In this talk I will start by describing a certain subset of real numbers which contain all the numbers which are of interest to arithmeticians. These numbers are called periods, and they form a countable set and in principle are much more easy to handle than a general real number. Then I will specialize to a certain subset of periods which are of mixed Tate type. The ones which have good reduction for all primes have periods called multi-zeta values, which were first defined by Euler. The remainder of the talk will be about a p-adic version of these numbers called p-adic multi-zeta values.
There are p-adic periods of the unipotent fundamental group of the thrice punctured line. They turn out to give all the p-adic periods of mixed Tate motives over Z. I will give an explicit series representation of these values in all depths. The new tool is a certain regularization trick for p-adic series.
Synchronization of oscillators denotes a phenomenon for the adjustment of rhythms among weakly coupled oscillators, andis one of the collective modes appearing in oscillatory complex systems such as ensembles of Josepson junctions, pacemaker cells and fireflies etc. In this talk, I will briefly discuss some challenging mathematical problems for synchronization via the Kuramoto and Lohe models, andpresent a survey of mathematical developments for these models in recent years.