Speaker:  Theophile Thiery

Zurich University ETH

Date: Tuesday, April 21, 2026 at 2:00 p.m. Santiago time

Abstract:

During my two-month visit to CMM, I began exploring a new direction in Online Matching.
Online Matching is a typical model for decision-making under uncertainty: resources must be allocated to requests arriving sequentially in real time, without full knowledge of future demand, to maximize welfare or utility.
This question arises in many settings, including ridesharing platforms, the allocation of goods and services, and (perhaps unfortunately) online advertising.
Since its introduction in the 1990s by Karp, Vazirani, and Vazirani, this problem has become a benchmark in the field of online problems.
This talk aims to introduce the problem, convey the main ideas and techniques used in its analysis, and then present the specific question I am currently investigating.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851

Speaker:  Jhoan Sebastián Báez Acevedo

Center for Mathematical Modeling, U. de Chile

Date: Tuesday, April 7, 2026 at 2:00 p.m. Santiago time

Abstract:

Compartmental models have become a fundamental tool for understanding the spread of infectious diseases and evaluating the potential impact of public health interventions. By dividing populations into epidemiological classes and describing transitions between them, these models provide a flexible mathematical framework for studying disease dynamics across a wide range of contexts.

In this talk, I will present an overview of compartmental modeling for infectious diseases, including model formulation, qualitative analysis, intervention strategies, and interpretation of outcomes. Particular attention will be given to how these models can be adapted to capture different transmission mechanisms and inform decision-making under realistic epidemiological settings.

The discussion will be illustrated through two case studies developed during the last year: acute respiratory infections (ARI), with emphasis on RSV dynamics, and dengue as a vector-borne disease. These examples highlight both the strengths and limitations of compartmental approaches, and motivate a broader discussion on the role of mathematical modeling in public health and digital health research.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851

Speaker: Georgios Kontogeorgiou
Center for Mathematical Modeling, U. de Chile
Date: Tuesday, March 17, 2026 at 2:00 p.m. Santiago time

Abstract: A graph is called quasi-transitive if it has finitely many orbits under automorphism. I will present some recent advances on quasi-transitive graphs, especially in the planar and minor-free cases. I will also talk about some related recent work with Agelos Georgakopoulos and Bobby Miraftab.

Venue: Sala John Von Neumann, 7th floor, Beauchef 851

Speaker: Marisa Cantarino

Centro de Modelamiento Matemático
Date: Tuesday, December 9, 2025 at 4:00 p.m. Santiago time

Abstract: 

We introduce, with examples, what a smooth dynamical system is and some associated objects, such as invariant measures, foliations, and Lyapunov exponents. We use these objects to illustrate the interplay between topological, measurable, and differential properties for smooth dynamical systems, having as motivation how they appear in classification problems or in understanding the behavior of a “typical” system.

Venue: /!\ This talk will be the last talk of the year, so the time and place are modified for the occasion : it will be at 4pm at the bar restaurant ‘Pipiolo’ (Orrego Luco 034, Providencia). Everyone is welcome !

Speaker: Ginaldo Sá

Centro de Modelamiento Matemático
Date: Tuesday, November 25, 2025 at 2:00 p.m. Santiago time

Abstract:

Abstract: Elliptic and parabolic partial differential equations modeling diffusive processes arise naturally across several areas of science. Understanding their regularity theories is essential for describing the qualitative behavior of solutions and for developing robust analytical tools. When the underlying models involve discontinuities, regime changes, or a priori unknown regions, one encounters free boundary problems, which introduce additional challenges and have driven significant advances in the modern theory of PDEs.
In this talk, we will discuss the analytical foundations underlying regularity in diffusive equations, present the current landscape of free boundary theory, and highlight recent developments that have deepened our understanding of these phenomena.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker: Juan Marshall-Maldonado
Centro de Modelamiento Matemático
Date: Tuesday, November 18, 2025 at 2:00 p.m. Santiago time

Abstract:

In this work, we present an overview of fundamental results in the theory of uniform distribution modulo 1 and the closely related field of discrepancy theory. After introducing the main concepts, tools, and classical theorems, we explore how these ideas can be applied to problems arising in dynamical systems and fractal analysis. In particular, we discuss their role in understanding the spectral properties of substitution dynamical systems and in the study of Bernoulli convolutions.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker: Ignacio Vergara
Departamento de Matemática y ciencias de la computación (USACH)
Date: Tuesday, October 21, 2025 at 2:00 p.m. Santiago time

Abstract:

The Haagerup property is an analytic property of groups that generalises amenability. It originated from the study of C*-algebras, and it has found applications in several areas of mathematics, including harmonic analysis, geometric group theory, topology, and ergodic theory. This talk will consist in an introduction to this property and its connections to group actions on Banach spaces.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker: Nicolás Zalduendo
Centro de Modelamiento Matematico
Date: Tuesday, October 7, 2025 at 2:00 p.m. Santiago time

Abstract:

Branching processes are mathematical models for populations that evolve by random reproduction: each individual lives for some time and then gives birth to new individuals, whose lives and offspring evolve independently. When such systems are enriched with spatial or structural information—allowing individuals to move, interact, or carry traits—they form infinite-dimensional stochastic processes that capture a wide range of phenomena, from cell division to particle systems.

In this talk, I will discuss recent results on the central limit theorem (CLT) for a large class of such structured branching processes. Roughly speaking, the CLT describes how the random fluctuations around the average exponential growth of the population become Gaussian in the long run. I will first revisit the classical finite-dimensional case to build intuition, and then explain how the same ideas extend to spatially dependent and non-local models. The main novelty is that, by combining probabilistic and analytic techniques—most notably Stein’s method—we can not only prove convergence but also quantify the speed at which it happens.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker: Vasilis Livanos
Centro de Modelamiento Matematico
Date: Tuesday, September 30, 2025 at 2:00 p.m. Santiago time

Abstract: 

Secretary problems constitute a classical setting of online
decision-making, where discrete elements arrive in uniformly random
order, reveal their weight, and must be accepted or rejected
irrevocably, with the aim of maximizing a given function over the
selected set. In the most general form of the problem, we are given a
combinatorial feasibility constraint (e.g. a matroid) and the selected
set has to be feasible with respect to that constraint. In such
problems, the objective is to design algorithms which guarantee a
multiplicative factor approximation with respect to the optimal feasible
set if we knew the weights of the elements in advance. By far the most
important open problem in this area is the Matroid Secretary conjecture,
which states that there exists a constant-factor approximation algorithm
for every given matroid, and has been open for almost two decades now.

In this talk, I will introduce secretary problems, describe some
standard ideas and approaches for them, as well as present what is
probably my favourite algorithm of all time: Korula and Pal’s
1/(2e)-approximate algorithm for the graphic matroid setting (i.e.
selecting an acyclic set of edges in an undirected graph where the
weights of the edges is revealed online in uniformly random order).
Later on, if time permits, I will present some recent progress on
algorithms for the general Matroid Secretary conjecture. This talk will
be partly based on joint work with Kristóf Bérczi, José Soto and Victor
Verdugo that appeared in IPCO 2025.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker: Felix Hommelsheim
Centro de Modelamiento Matematico
Date: Monday, September 1, 2025 at 2:30 p.m. Santiago time

Abstract:  

We study the 2-edge-connected spanning subgraph (2-ECSS) problem: Given a graph $G$, compute a connected subgraph $H$ of $G$ with the minimum number of edges such that $H$ is spanning, i.e., $V(H) = V(G)$, and $H$ is 2-edge-connected, i.e., $H$ remains connected upon the deletion of any single edge, if such an $H$ exists. The $2$-ECSS problem is known to be NP-hard. In this work, we provide a polynomial-time $(\frac 5 4 + \varepsilon)$-approximation for the problem for an arbitrarily small $\varepsilon>0$, improving the previous best approximation ratio of $\frac{13}{10}+\varepsilon$.

Our improvement is based on two main innovations: First, we reduce solving the problem on general graphs to solving it on structured graphs with high vertex connectivity. This high vertex connectivity ensures the existence of a 4-matching across any bipartition of the vertex set with at least 10 vertices in each part. Second, we exploit this property in a later gluing step, where isolated 2-edge connected components need to be merged without adding too many edges. Using the 4-matching property, we can repeatedly glue a huge component (containing at least 10 vertices) to other components. This step is reminiscent of the Pac-Man game, where a Pac-Man (a huge component) consumes all the dots (other components) as it moves through a maze. These two innovations lead to a significantly simpler algorithm and analysis for the gluing step compared to the previous best approximation algorithm, which required a long and tedious case analysis.

Venue: John Von Neumann Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor