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.
The k-Yamabe flow and its solitons.
Abstract: The Yamabe problem is a classical question in conformal geometry that seeks for existence of metrics with constant scalar curvature within a conformal class. The problem was posed by H. Yamabe in 1960 as a possible extension of the famous uniformization theorem, which states that every simply connected Riemann surface is conformally equivalent to the open unit disk, the complex plane or the Riemann sphere. After the conjecture was already confirmed by the work of R. Schoen, an alternative approach was proposed by R.Hamilton in 1989....
“Classification of Semigraphical Translators: The yeti doesn’t exist!”
Abstract: In this talk I will discuss the non-existence of certain solutions to the equation that determines translating solutions to Mean Curvature Flow. This result completes the classification to semigraphical translators.
Numerical solution of optimal control problems under uncertainty.
Abstract: The topic of this talk is a class of optimal control problems subject to uncertainty. We highlight some of the difficulties in the infinite-dimensional setting, which is of interest in physics- based models where a control belonging to a Banach space acts on a system described by a partial differential equation (PDE) with random inputs or parameters. We compare numerical approaches based on sample average approximation (SAA) and stochastic approximation (SA). The latter approach can be shown to perform competitively for applications...
The Burial of Coupling Constraints in Linear Bilevel Optimization.
Abstract: It has been common sense in (linear) bilevel optimization that problems with coupling constraints are more difficult to tackle than those without such constraints. While the modeling capabilities in terms of the feasible sets are indeed richer because coupling constraints allow to model disconnected feasible sets, complexity theory did not see any difference between problems with our without coupling constraints. In this talk, we show that there is no difference at all when one considers optimal solutions instead of just...
Acciones Evanescentes Aunque Recurrentes.
RESUMEN En los años 60, Edelstein dio ejemplos de isometrías afines sin punto fijo de espacios de Hilbert para las cuales una sucesión de iterados converge a la identidad. Este fenómeno no puede producirse en dimensión finita, incluso para métricas no hilbertianas. En esta charla veremos que ejemplos del tipo de Edelstein aparecen naturalmente asociadas a dinámicas clásicas sobre ciertos espacios. La charla girará en torno a la reciente prepublicación https://arxiv.org/pdf/2501.12120; se presentarán varios problemas abiertos y eventuales...
A stochastic differential Colonel Blotto game in a Stackelberg contract theory setting.
Abstract: The Colonel Blotto game is a resource allocation game where players decide where to focus their forces between different battlefields. We extend the standard Blotto game to a dynamic stochastic setting, in a time-continuous, two-player, zero-sum game. Using the dynamic programming principle, we explicitly characterize some Nash equilibrium strategies as well as the value of the game through a Hamilton-Jacobi-Bellman equation admitting a smooth solution. We formulate the game generally enough to allow for various rewards, as well as...
Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains.
Abstract: We consider the subcritical nonlinear Schrödinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical and theoretical point of view in the case of bounded domains. In this paper, we introduce a PINNs method to treat the case of unbounded domains and show rigorous bounds on the associated approximation error in terms of the energy and Strichartz norms, provided reasonable integration schemes are available....
Multiple normalized solutions to a system of nonlinear Schrödinger equations.
Abstract: We present recent results concerning normalized solutions to a system of coupled nonlinear Schr¨odinger equations. The problem appears in different areas of mathematical physics, e.g. in the analysis of Bose-Einstein condensation or in nonlinear optics. By means of spectral results, the Cwikel-Lieb-Rozenblum theorem, the Morse index and new Liouville-type results we show the existence of multiple normalized solutions for sufficiently large coupling. The talk is based on joint work with Andrzej Szulkin.
“Hamilton-Jacobi-Bellman Solution Approximation with Machine Learningfor the Synthesis of Optimal Feedbacks”
Abstract: The design of optimal feedbacks for control problems is a challenging task. The classical method for tackling this problem is based on dynamic programming. This involves finding the value function of the control problem by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, this equation suffers from the “curse of dimensionality”, i.e., the computational cost of solving it grows exponentially with the dimension of the underlying control problem. For this reason, several methods based on machine learning have...
Nonexistence and uniqueness of breathers for modified Zakharov-Kuznetsov models.
Abstract: In this talk we will consider the (focusing) modi ed Zakharov-Kuznetsov (mZK) in dimension N ≥ 1: ut + (∆u + 2u3)x1 = 0,for a given real-valued function u = u(t, x), where t ∈ R and x ∈ RN . This equation is a specialcase of the completely integrable modi ed Korteweg-de Vries (mKdV) equation ut + (uxx +2u3)x = 0. During this talk we will present results related to existence and nonexistence of quasimonochromatic breathers solution for the mZK equation, depending on the dimnesion N . Additionally we will show how the...
