Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Quenched local limit theorem for ergodic random conductance model
Abstract: We prove an almost sure local limit theorem for a symmetric random walk in an ergodic random environment. The proof is based on the parabolic Harnack inequality, which holds under some moment conditions on the conductances and the quenched invariance principle.
Playing with Subshifts
Abstract: We study the class of word-building games, where two players pick letters from afinite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player A) or not (a win for player B). We focus on symbolic dynamical games, where the target set is a subshift. We investigate the relation between the target subshift and the set of turn orders for which A has a winning strategy.
Block Maps between Primitive Uniform and Pisot Substitutions
Abstract: We prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift. This result is proved using a common generalization of block maps and substitutions, which we call dill maps.
Pricing Variance Swaps on Time-Changed Markov Processes
ABSTRACT We prove that the variance swap rate is just the price of a co-terminal European-style contract when the underlying is modeled as an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process. The payoff function of the European contract that prices the variance swap satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. We present examples of Markov processes whose...
Optimal shape of an open mining pit
Abstract: Given a vein of ore in the ground, which is to be extracted by open-pit mining, what is the shape which will maximize profit? This problem is often treated by discretization, but we present a new way to handle directly the continuous case. We set it up as an optimal transportation problem, which we solve using Kantorovitch duality. This is joint work with Maurice Queyranne
On extensions of Kenderov’s single-valuedness result for monotone maps
Abstract: One of the most famous single-valuedness results for set-valued maps is due to Kenderov and states that a monotone set-valued operator is single-valued at any point where it is lower semi-continuous. This has been extended in Christensen-Kenderov to monotone maps satisfying a so-called property. Our aim in this work is twofold: First, to prove that the property assumption can be weakened; second to emphasize that these classical single-valuedness results for monotone operators can be obtained, in very simple way, as direct...
Slope and Geometry in Variational Mathematics
Abstract: Various notions of the “slope” of a real-valued function pervade optimization and variational mathematics more broadly. In the semi-algebraic setting—an appealing model for concrete variational problems — the slope is particularly well-behaved. This talk sketches a variety of surprising applications, illustrating the unifying power of slope. Highlights include error bounds for level sets, the existence and regularity of steepest descent curves in complete metric spaces (following Ambrosio et al.), transversality and the...
Asymptotic behaviour of solutions to relativistic Schrödinger equation and its applications.
Abstract: We will discuss about sharp asymptotic behaviour of solutions to relativistic Schrödinger equation together with it’s applications to unique continuations properties (weak, strong, from sets of postive meassure) and sharp essentially self-adjointness of relativistic Schrödinger equation with Coulomb potential.”
Boundedness and regularity of isoperimetric sets with density
Abstract: We show that every isoperimetric set in $\R^N$ with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the other hand, the present assumption is sharp, as we show with an explicit example. To obtain our result, we observe that the main tool which is often used, namely a classical “$\epsilon-\epsilon$” property already discussed by Allard, Almgren and Bombieri, admits a weaker...
