Abstract: 
Consider the heat equation on a closed domain with C 2 boundary, subject to a random Wentzell boundary condition modeling stickiness and elastic killing, with coefficients undergoing Markovian switching. We derive the quenched and annealed evolution equations of these systems, inboth forward and backward directions. We show that as the switching rate tends to infinity, thesystem converges in the quenched L1 -sense to a heat equation with deterministic Wentzell condition,whose parameters are determined by the stationary law of the driving continuous-time Markov chain.

We further quantify the quenched uniform-in-time L1-error between the fast-switching process andits homogenized limit, establishing a rigorous error bound. In particular, for the time-dilatation t/ε,this error is o(ε−1/6 ), while the error between their time marginals is o(ε−1/2 ), as ε → 0. Finally, we apply our results to a model of neuronal receptor dynamics, where strong and weak ligand bindingcorrespond to distinct boundary regimes governing neurotransmitter clearance.

Speaker: Alexis Anagnostakis (CMM, U. de Chile)

Durante esta charla se presentará metodología avanzada para el mapeo de combustibles superficiales de la clasificación KITRAL. Para ello, se construyó un Data Cube integrando series temporales estacionales del programa Copernicus, combinando índices ópticos de Sentinel-2 y retrodispersión de radar de Sentinel-1, fusionados con variables topográficas y de estructura vegetal.

El expositor será Camilo Matus-Olivares, Doctor en Ciencias Agroalimentarias y Medioambiente de la Universidad de La Frontera (Chile).

El evento  también se transmitirá en vivo por el canal de YouTube de CopernicusLAC Chile en este enlace: https://bit.ly/seminario28agosto

Abstract: Given a $k$-uniform hypergraph $H$, the Ramsey number $R(H)$ is the smallest $N$ such that every $2$-colouring of the edges of $K_N^{(k)}$ contains a monochromatic copy of $H$. For graphs, Burr gave two constructions bounding $R(T)$ from below for a tree $T$, and his formula is now known to be exact for trees of small maximum degree. In the hypergraph setting, almost nothing is known beyond loose paths and cycles.

We study $R(T^{(k)})$, where $T^{(k)}$ is the $k$-expansion of a tree $T$, obtained by adding $k-2$ new vertices to each edge. We show that for bounded-degree trees the Ramsey number is at most $(1+\eta)\frac{1}{2}(2k-1)n$, and we prove a general lower bound $R(H) \geq |V(H)| + \tau(H) – 1$ for connected $k$-graphs $H$, where $\tau$ is the vertex cover number. These bounds are asymptotically tight for loose paths. In this talk, we will see how Burr's constructions generalise to the hypergraph setting, what the resulting lower bound looks like for expansions, and discuss the conjectures this work suggests.

Speaker: Vicente Sandoval (DIM, U. Chile)

Abstract: In this talk, we will consider the massless Boltzmann equation on FLRW spacetime with spatial topology $\mathbb{T}^3$ in the linear and decelerated expanding regimes, where the scale factor is $t^q$ with $q\in (0,1]$. In these backgrounds, the massless Boltzmann equation admits a non-stationary Maxwell-Jüttner equilibrium that maximises the entropy of the system. In this work, this equilibrium is shown to be non-linearly stable for the massless Boltzmann equation in the case of hard ball interaction. We will also discuss the non-linear stability of the vacuum solution when $q\in (1/3,1]$. This is joint work with Robert M. Strain (University of Pennsylvania) and Martin Taylor (Imperial College London).

For those unable to attend in person, the talk will also be available via Zoom at the following link: https://uchile.zoom.us/j/97781230158?pwd=MDIJ5OSVvuObCde6BEes5HcHwxeSa8.1

Speaker: Renato Velozo Ruiz (Universidad de Chile)

Durante el seminario se presentará Harpía Watch Forest, un sistema automatizado que es usado para el monitoreo de la cobertura forestal en Panamá, mediante imágenes satelitales y técnicas de teledetección. Se abordará la metodología empleada para la detección de cambios en la cobertura vegetal utilizando imágenes Sentinel-2, índices espectrales como el NDVI y algoritmos de análisis temporal. Además, se mostrarán los principales resultados obtenidos, las capacidades del sistema para apoyar la vigilancia ambiental y su contribución a la toma de decisiones para la conservación y el manejo sostenible de los recursos forestales.

Los expositores serán Yubrany González y Elvis García, profesionales del Departamento de Teledetección de la Dirección de Información Ambiental del Ministerio de Ambiente de Panamá.

El evento se realizará en el Centro de Modelamiento Matemático (CMM) albergado en la Universidad de Chile y se transmitirá en vivo por el canal de YouTube de CopernicusLAC Chile a través del siguiente enlace: https://bit.ly/seminario21agosto

Abstract:  In Lorentzian geometry, the light-ray transform is the operator that integrates functions over lightlike geodesics. It appears naturally in the study of wave equations, geometric scattering rigidity, and inverse problems. In this talk, I will discuss some work in progress with L. Busch and L. Oksanen, about the stability of this operator. First, I will present an instability result: the modulus of continuity cannot be smaller than certain polynomial. This can be upgraded to a logarithmic bound in the Gevrey category. Secondly, on stationary geometries, I will show how to obtain a stability result for moments of order k, using moments of the light-ray transform from 0 to k.

Speaker: Sebastián Muñoz Thon, Université Paris-Saclay

Abstract: 
We study a discrete dynamical system of pairwise trades among m agents exchanging n+1 divisible goods, each holding a strongly concave  utility. Two agents trade a single good for money whenever gradient-based price thresholds — ratios of partial utility derivatives — admit a mutually improving exchange within a prescribed bid-ask spread. Using convex analysis, we characterize the fixed points of this dynamics: an allocation is invariant, at every spread level, exactly when it satisfies the normal-cone (first-order) conditions of a Walrasian equilibrium. The key technical result is a quantitative descent lemma showing each trade raises the two agents' utilities by an amount bounded below by the square of the spread, which precludes stagnation and forces termination after finitely many trades at any fixed spread. Letting the spread shrink to zero yields a sequence of such approximate equilibria that, by a strict-concavity argument, converges to a unique limit rather than merely a cluster point. Numerical experiments illustrate convergence for economies with up to 100 goods and 10 agents.

Speaker: Alejandro Jofré (with J. Deride y  R. T. Rockafellar)

GUE Fluctuations Near the Origin in One-Sided Ballistic Deposition

Abstract: We will introduce a variation of the ballistic deposition model in which vertically falling blocks can only stick to the top or the upper right corner of growing columns. For this model, we will establish that the fluctuations of the height function at points near the origin are given by the GUE ensemble and its corresponding Tracy–Widom limiting distribution. The talk is based on joint work with Pablo Groisman, Santiago Saglietti and Sebastian Zaninovich.

Speaker: Alejandro Ramírez (NYU Shanghai)

Integrable stochastic processes in half-space 

Abstract: Integrable probabilistic systems have historically generated much interest not only for their elegant mathematical properties, but also for their capacity to rigorously describe real- world universal phenomena. Most notably, they have proven central to our understanding of the Kardar-Parisi-Zhang universality class. Recent years have seen a surge in interest the rich mathematical and physical properties of integrable systems with open boundaries. In this talk I will outline a systematic construction of the integrable open-boundary six-vertex model, as well as its relation to other interacting particle systems.

Speaker:  Will Mead ( Universität Bonn)

Join the Zoom: https://reuna.zoom.us/j/84521834914?pwd=OTZ6Y0NWM3pYTGtTbEt3c0luTG96UT09

Abstract:
Optimisation lies at the foundation of applied mathematics, providing the quantitative framework for selecting an optimal decision from a set of candidate solutions. For decades, the field has primarily relied on convex models, yielding clean theoretical convergence guarantees and reliable numerical algorithms. However, modern machine learning applications frequently give rise to loss functions that are intrinsically nonconvex. In these settings, traditional convex paradigms fall short, requiring novel algorithmic strategies tailored to nonconvex problems.

In this talk, we explore optimisation methods designed for nonconvex problems that explicitly exploit the underlying structure of the models. In particular, we will cover splitting methods, a family of algorithms that decompose complex models into simpler, computationally tractable subproblems. We will also discuss the central theoretical and practical difficulties inherent in solving nonconvex problems. These include the necessity of settling for stationary points or local minimisers rather than global optima, as well as pathological convergence issues, such as conservative stepsizes that may stall the iterative process. Finally, we will present recent developments aimed at overcoming these bottlenecks, illustrating how structure-exploiting algorithms bridge the gap between rigorous mathematical theory and practical numerical performance.

Speaker: Felipe Atenas (CMM, U. de Chile)

Abstract: Motivated by applications in statistical physics, we study the induced dynamical systems (M(X),T) and (H(X),T), consisting respectively of Borel probability measures and non- empty closed subsets of a dynamical system (X,T). In this talk, we first survey the inheritance of various well-studied dynamical properties, including equicontinuity, distality, pointwise almost periodicity, transitivity, weak mixing, nullness, tameness, and zero entropy. We then turn to mean equicontinuity, diam-mean equicontinuity, and weak-mean equicontinuity, and discuss new inheritance results with respect to these notions. These results complete the picture and reveal another interesting asymmetry between the hyperspace and measure-theoretic constructions. The talk focuses on continuous surjective maps T: X → X, while the new results can also be extended to actions of locally compact σ-compact amenable groups.

Speaker: Till Hauser (Pontificia Universidad Católica).

Abstract: Resumen:  Differential equations driven by signals too irregular to be semimartingales arise in many models; fractional Brownian motion with Hurst parameter $H<1/2$ is the classical such driver. For these equations the solution is not a continuous function of the driving path. Rough path theory restores continuity, but only after the driver is enriched with its iterated integrals. A discrete model therefore converges to such an equation only if its enhanced driver converges. Invariance principles at the enhanced level are available, but their limit is Brownian. Enhanced fractional Brownian motion is reached only by construction, either starting from it or imposing a fractional kernel on a random walk. The fractional Donsker theorem, available for over a decade, stops at the level of paths. What is missing is the combination: a fractional limit, reached from a discrete model, at the enhanced level. We supply it. For a centred, strictly stationary, not necessarily Gaussian sequence in $\R^d$ whose normalised partial sums converge finite-dimensionally to fractional Brownian motion with $H\in(1/3,1/2)$, control of covariances and cumulants forces the canonical level-two lift to converge weakly to enhanced fractional Brownian motion in the $\a$-Hölder rough path topology. Continuity of the solution map then transfers the convergence back to the equations we started from.

Join the seminar via Zoom: 
https://reuna.zoom.us/j/84521834914?pwd=OTZ6Y0NWM3pYTGtTbEt3c0luTG96UT09
ID de reunión: 845 2183 4914
Código de acceso: 997973

Speaker: Tomás Laengle (Universidad Humboldt de Berlín).