Speaker:  Kitty Varga
Budapest University of Technology and Economics
Date: Monday, June 30, 2025 at 2:30 p.m. Santiago time

Abstract:  

Inverse and reverse optimization problems aim to adjust the objectivefunction of an underlying optimization problem while minimizing the extent of modification. In inverse optimization, the goal is to modify the objective function so that a given feasible solution becomes optimal. In reverse optimization, the goal is to modify the objective function so that the optimum value attains a specified number.

In this talk, we mainly focus on inverse maximum-capacity optimization problems under the bottleneck Hamming distance, the weighted infinity norm and weighted span objectives. Our main contributions include simple, purely combinatorial algorithms that efficiently solve these general problems, assuming that an efficient algorithm is available for the underlying optimization problem.

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

Speaker:  Juan Pablo Contreras Fernández
Universidad Diego Portales
Date: Monday, June 16, 2025 at 2:30 p.m. Santiago time

Abstract:  

In this talk, we present a survey of techniques and results on error bounds and convergence rates for both deterministic and stochastic fixed-point iterations, with a focus on methods such as the Krasnoselskii-Mann and Halpern iterations. Our primary emphasis is on general normed spaces, where we employ tools from optimal transport to derive tight error bounds. For spaces with additional structure, such as Hilbert spaces, we also discuss existing techniques and the sharp results established in the literature. Finally, we highlight applications of these findings in reinforcement learning and optimization, and outline open questions and potential directions for future research.

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

Speaker:  Haritha Cheriyath
Center for Mathematical Modeling, U. de Chile
Date: Monday, June 02, 2025 at 2:30 p.m. Santiago time

Abstract:  

A dynamical system is usually made up of a state space and a rule (a map acting on the space) that tells us how the system evolves over time. One of the central questions in studying these systems is figuring out when two of them are essentially the same, or conjugate, as we usually say. There are several known features, called invariants, that stay the same under conjugacy, but so far, no single invariant can completely characterize when two systems are conjugate.

Because of that, it is natural to look at a slightly weaker idea of equivalence, called strong orbit equivalence. All conjugate systems turn out to be strongly orbit equivalent, and what is nice is that, in this setting, a complete invariant does exist.

In this talk, we will take a look at some familiar invariants from the world of conjugacy and see how they behave in the context of strong orbit equivalence.

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

Speaker:  Svenja Griesbach
Center for Mathematical Modeling, U. de Chile
Date: Monday, May 19, 2025 at 2:30 p.m. Santiago time

Abstract:  

In the impartial selection problem, a subset of agents up to a fixed size k among a group of n is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is \alpha-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of \alpha of the votes received by the subset of size k with the highest number of votes.
We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly 1/\lceil 2n/k\rceil. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of 1/k for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to k agents are to be selected, with a loss in the approximation ratio of 1/2.

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

Speaker:  Christopher Cabezas
Center for Mathematical Modeling, U. de Chile
Date: Monday, April 21, 2025 at 2:30 p.m. Santiago time

Abstract:  

An important question in dynamical systems is the classification, i.e., to be able to distinguish two isomorphic dynamical systems. In this work, we focus on the family of multidimensional substitutive subshifts. Constant-shape substitutions are a multidimensional generalization of constant-length substitutions, where any letter is assigned a pattern with the same shape. We prove that in this class of substitutive subshifts, under the hypothesis of having the same structure, it is decidable whether there exists a factor map between two aperiodic minimal substitutive subshifts. The strategy followed in this work consists in giving a complete description of the factor maps between these substitutive subshifts. We will also discuss related results, such as a condition to ensure that the substitution defines a subshift, and some consequences on coalescence, automorphism group and number of symbolic factors. This is a joint work with Julien Leroy.

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

Speaker:  Mirabel Mendoza
Center for Mathematical Modeling, U. de Chile
Date: Monday, March 31, 2025 at 2:30 p.m. Santiago time

Abstract:  

We consider the Shortest Odd Path (SOP) problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum weight. For the case when the weight function is conservative, i.e., when every cycle has non-negative total weight, the complexity of the SOP problem had been open for 20 years, and was recently shown to be NP-hard. I’ll present a polynomial-time algorithm for the special case when the weight function is conservative and the set of negative-weight edges forms a single tree. The algorithm exploits the strong connection between SOP and the problem of finding two internally vertex-disjoint paths between two terminals in an undirected edge-weighted graph. This is a joint work with Alpár Jüttner, Csaba Király, Gyula Pap, Ildikó Schlotter, and Yutaro Yamaguchi.

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

Speaker:  María Fernanda Espinal
Center for Mathematical Modeling, U. de Chile
Date: Monday, March 17, 2025 at 2:30 p.m. Santiago time

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. He suggested to use a geometric flow, which is now known as the Yamabe flow. The k-Yamabe flow is a fully non-linear extension to the Yamabe flow that appears naturally in problems related to topological classification in higher dimensions. In this talk we describe the construction, classification and asymptotic behavior of radially symmetric gradient k-Yamabe solitons that are locally conformally flat [ES24], these are special solutions to this flow that play a central role in the theory. Our study extends the results obtained by P. Daskalopouolos and N. Sesum in [DS13] in the case n > 2k.

Joint work with Mariel Sáez.

References
[DS13] Panagiota Daskalopoulos and Natasa Sesum. The classification of locally conformally flat yamabe solitons. Advances in Mathematics, 240:346–369, 2013.
[ES24] Mar´ıa Fernanda Espinal and Mariel S´aez. On the existence and classification of k-yamabe gradient solitons. arXiv preprint arXiv:2410.06942, 2024.

Venue: Jacques L Lions Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker:  Sani Biswas
Center for Mathematical Modeling, U. de Chile
Date: Monday, December 16, 2024 at 2:30 p.m. Santiago time

Abstract:  

We present a general Milstein-type scheme for McKean-Vlasov stochastic differential equations (SDEs) driven by Brownian motion and Poisson random measure and the associated system of interacting particles where drift, diffusion and jump coefficients may grow super-linearly in the state variable and linearly in the measure component. The strong rate of -convergence of the proposed scheme is shown to be arbitrarily close to one under appropriate regularity assumptions on the coefficients. For the derivation of the Milstein scheme and to show its strong rate of convergence, we provide an It\^o formula for the interacting particle system connected with the McKean-Vlasov SDE driven by Brownian motion and Poisson random measure. Moreover, we use the notion of Lions derivative to examine our results. The two-fold challenges arising due to the presence of the empirical measure and super-linearity of the jump coefficient are resolved by identifying and exploiting an appropriate coercivity-type condition).

Venue: Jacques L Lions Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor

Speaker:  Laura Jiménez
Center for Mathematical Modeling, U. de Chile
Date: Monday, December 02, 2024 at 2:30 p.m. Santiago time

Abstract:  

I will delve into three key topics of my research in quantitative ecology and how the outcomes contribute to understanding and preventing biodiversity loss. In each case, I will describe the ecological context, the data at hand, and the primary modeling tools used to address the problems of interest. First, I will talk about optimal survey design, which involves techniques to efficiently estimate population density by balancing sample size, spatial distribution, and survey effort. Next, I will explain how statistical calibration techniques are applied for error correction and data fusion from diverse sources to improve biomass or abundance estimates, which are then used to design management and conservation strategies for coral reef fish. Lastly, I will demonstrate the use of ecological niche models to describe where a species lives and predict its likely distribution under climate change and anthropogenic disturbances.

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

Speaker: David Torregrosa Belén
Center for Mathematical Modeling, U. de Chile
Date: Monday, November 18, 2024 at 2:30 p.m. Santiago time

Abstract:  

Many situations in convex optimization can be modeled as the problem of finding a zero of a monotone operator, which can be regarded as a generalization of the gradient of a differentiable convex function. In order to numerically address this monotone inclusion problem it is vital to be able to exploit the inherent structure of the monotone operator defining it. The algorithms in the family of the splitting methods are able to do this by iteratively solving simpler subtasks which are defined by separately using some parts of the original problem. In this talk, we will introduce some of the most relevant monotone inclusion problems and present their applications to optimization. We will describe the different difficulties arising in their treatment, which urge to consider specific splitting schemes suitable for each monotone operator.

Venue: Jacques L Lions Seminar Room, CMM, Beauchef 851, North Tower, 7th Floor