Speaker: Raúl Tintaya

Center for Mathematical Modeling, U. de Chile

Date: Tuesday, June 9, 2026 at 2:00 p.m. Santiago time

Abstract:

This talk presents fast optimization algorithms from the viewpoint of continuous dynamical systems.
We begin with the classical correspondence between gradient flow and gradient descent, and then discuss how nonsmooth gradient flows naturally lead to proximal-type methods.
The main focus is on inertial dynamical systems, where second-order terms introduce memory and momentum into the optimization process.
Through this perspective, we explain how continuous-time models such as the heavy-ball system and Nesterov-type dynamics provide insight into acceleration, damping, stability, and convergence of fast first-order methods.
We also discuss how these ideas can be extended beyond standard minimization problems, including recent directions for nonconvex minimax optimization.

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

Speaker: Danko Aldunate

Center for Mathematical Modeling, U. de Chile

Date: Tuesday, May 26, 2026 at 2:00 p.m. Santiago time

Abstract:

We study the spectral properties of the Dirac operator L_0 obtained by linearizing the one-dimensional Soler model around standing waves with power nonlinearity f(s) = s|s|^{p-1}, p > 0. We give a sharp characterization of the spectral gap. If p ≥ 1, the gap contains no eigenvalues other than the symmetry-induced energies -2ω and 0. If 0 < p < 1, additional eigenvalues bifurcate from the thresholds of the essential spectrum and enter the gap. We further prove that the thresholds are never eigenvalues for any p > 0 and that there are no resonances for p > 1.

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

Speaker: Juan José Maulén

Center for Mathematical Modeling, U. de Chile

Date: Tuesday, May 19, 2026 at 2:00 p.m. Santiago time

Abstract:

Optimization algorithms are essentially discrete iterative procedures. However, many of them can be derived from continuous dynamical systems through suitable discretization schemes. In this talk, we explore this perspective in the context of primal–dual optimization methods for constrained and saddle-point problems. We introduce the idea of proximal operators, explain how different discretizations lead to different algorithms, and compare the resulting methods in numerical instances.

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

Speaker: André Dosea

Universidade Federal de Sergipe

Date: Tuesday, May 05, 2026 at 2:00 p.m. Santiago time

Abstract:

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

Speaker: Julien Boulanger

Center for Mathematical Modeling, U. de Chile

Date: Tuesday, April 28, 2026 at 2:00 p.m. Santiago time

Abstract:

In 1893, Hurwitz showed that a compact Riemann surface of genus g ≥ 2 has at most 84(g-1) automorphisms. This bound is optimal for an infinite family of genera but there is also an infinite family of genera for which the bound is not optimal. The Hurwitz automorphism problem consists in finding the optimal bound for every genus, and apart from partial results in specific cases it is far from being solved. In this talk we will explain the first sentence of this abstract and give a geometric intuition for the result. On the way, I will discuss a similar problem for translation surfaces.

Translation surfaces can be seen a Riemann surfaces with an additional structure, and an automorphism of a translation surface must preserve this additional structure: in particular, there are even less automorphisms and a compact translation surface of genus g ≥ 2 has at most 4(g-1) automorphisms. This last bound was obtained by J.C. Schlage-Puchta and G. Weitze-Schmidhüsen in 2013, and they also show that the bound is optimal if and only if g-1 is either even or a multiple of 3. In a joint work with R.Gutierrez-Romo and E.Lanneau, we study the other cases and provide the optimal bound for example when g = pq+1 with p,q ≥ 5 prime numbers.

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

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