Correo Electrónico
DNINFOA – SIA
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UN encuentro 70 años
Departamento de matemáticas
Un espacio académico que reúne a estudiantes, docentes, egresados e investigadores alrededor de conferencias de alto nivel en matemáticas y ciencias de la computación.
Conferencistas
Investigadores de Colombia, Reino Unido, Estados Unidos, Finlandia y Argentina compartirán sus perspectivas y avances en diferentes áreas de las matemáticas y las ciencias de la computación
Mauro Artigiani
Unal Bogotá
Translation Surfaces: from Dynamics to Geometry, and back
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The dynamics of an ideal billiard ball in a polygon leads naturally to the study of translation surfaces. These objects sit at the intersection of geometry, dynamics and low dimensional topology, and can be viewed from several different, yet deeply intertwined, perspectives. In this talk, we will explore some classical examples and results that illustrate these connections, from billiard trajectories and geodesic flows to moduli spaces and renormalization. We will conclude with some recent work with A. Pardo on counting cylinders on translation surfaces.
Philip Candelas
Oxford
Black holes and the arithmetic of Calabi-Yau varieties: connections between number theory and physics (part 2)
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The main goal of these talks is to explore questions of common interest for number theorists, geometers and physicists.
We will focus on the mathematics of Calabi-Yau varieties and their periods. These varieties have been the object of intense interest in mathematics and arise
in string theory. There are many such connections, and in these talks we will emphasise black hole solutions of superstring theory and flux vacua.
The main quantities of interest in the arithmetic context are the numbers of points of the variety, considered as a variety over a finite field. A mathematician is interested in the computation of these numbers and their dependence on the moduli of the variety. The number of points determine the zeta function, about which much is known in virtue of the Weil conjectures. The surprise for a physicist is that the number of points over a finite field are also given by expressions that involve the periods of the variety. These periods, which in our applications are integrals of a special differential form over a homology basis, determine many aspects of the physical theory.
We will try to give a self contained introduction to these topics aimed at a mixed audience of mathematicians.
Natalia Cardona-Tobón
UNAL Bogotá
A random game in a graph
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We study a variant of a classical two-player game where Alice and Bob alternately make n moves, each choosing between two options. In the standard version, the outcome depends on both players’ exact sequences of moves, and a sharp threshold p_c separates the regimes where each player has, with high probability, a winning strategy. In our modification, the outcome still depends on Alice’s sequence, but for Bob only the number of times he plays move 1 matters. We show that this version also exhibits a sharp threshold p’_c determining which player with large probability has a winning strategy when n tends to infinity. Joint work with Anja Sturm (University of Göttingen) and Jan M. Swart (The Czech Academy of Sciences).
Xenia de la Ossa
Oxford
Black holes and the arithmetic of Calabi-Yau varieties: connections between number theory and physics (part 1)
Ver más
The main goal of these talks is to explore questions of common interest for number theorists, geometers and physicists.
We will focus on the mathematics of Calabi-Yau varieties and their periods. These varieties have been the object of intense interest in mathematics and arise
in string theory. There are many such connections, and in these talks we will emphasise black hole solutions of superstring theory and flux vacua.
The main quantities of interest in the arithmetic context are the numbers of points of the variety, considered as a variety over a finite field. A mathematician is interested in the computation of these numbers and their dependence on the moduli of the variety. The number of points determine the zeta function, about which much is known in virtue of the Weil conjectures. The surprise for a physicist is that the number of points over a finite field are also given by expressions that involve the periods of the variety. These periods, which in our applications are integrals of a special differential form over a homology basis, determine many aspects of the physical theory.
We will try to give a self contained introduction to these topics aimed at a mixed audience of mathematicians.
Juan Galvis
UNAL Bogotá
Numerical Approximation of Flow Problems in Heterogeneous Multiscale Media
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This talk presents a mathematical and computational overview of multiscale approximation methods for elliptic flow problems in heterogeneous media.
In the first part, we discuss the complete numerical workflow, from mathematical modeling and finite-dimensional approximation to digital representation, computational complexity, and the emerging role of data analysis and artificial intelligence. We then introduce classical multiscale finite element methods and illustrate why standard multiscale basis functions can perform well for moderate coefficient contrasts but may fail to capture disconnected high-conductivity structures.
In the second part, time permitting, we introduce the Generalized Multiscale Finite Element Method (GMsFEM) as a systematic approach to addressing this limitation through carefully designed local spectral problems. The resulting eigenfunctions identify relevant subgrid features and provide systematically enriched coarse spaces. We discuss their use both for reduced-order approximation and for the construction of robust two-level domain decomposition preconditioners.
Ehud Hrushovski
Oxford
Approximate subgroups and the search for the model theoretic Galois group.
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I will try to tell two large, different, but occasionally intersecting stories. One is the search for `the’ symmetry group of a first-order theory, generalising the absolute Galois group of $\Qq$ when the theory is that of the complex field. The other is of approximate subgroups:
subsets $X$ of a group $G$, such that while products $xy$ for $x,y \in X$ need not all remain in $X$, they do remain within a finite union of translates of $X$. They appear in manifold junctures in mathematics, and model theory helps discover their general structure.
Daniel López-Castaño
Johns Hopkins
Wasserstein approximation of measures via orthogonal frames
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How well can we estimate the latent orthogonal factors of a probability distribution from random samples? This question sits at the intersection of optimal transport theory and factor analysis. In this talk, we show how to recover the orthogonal frame that best approximates a distribution in Wasserstein distance, via empirical risk minimization and an online stochastic subgradient method on the Stiefel manifold. A central difficulty is that the empirical objective is non-smooth, so standard M-estimation arguments do not apply. We circumvent this with a Clarke subdifferential analysis combined with a geometric covering argument on the sphere. The result is near-parametric convergence rates with polynomial, rather than exponential, dependence on the dimension, escaping the curse of dimensionality inherent in Wasserstein approximation. We close with numerical examples and real-world data applications.
Miguel Moreno
U-Tampere
Logic meets LLMs: Attention has a logic
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Modern AI systems, and transformers in particular, have revolutionized natural language processing, yet their computational principles remain surprisingly elusive. Logic has long provided elegant characterizations of classical models of computation. Can it also explain the architecture behind large language models?
In this talk, I will present recent work establishing a logical characterization of encoder–decoder transformers with cross-attention. We show that these transformers are expressively equivalent to a temporal logic and to a class of distributed automata, revealing cross-attention as a natural form of distributed message passing. Along the way, I will illustrate how ideas from modal logic, distributed computing, and automata theory come together to shed light on one of today’s most influential AI architectures.
Carolina Neira
UNAL Bogotá
Pseudodifferential Operators on the Noncommutative Torus
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Pseudodifferential calculus is a very useful tool in analysis and geometry. On smooth manifolds, this calculus is performed via symbols which are locally defined concepts. On manifolds equipped with certain symmetry (through the action of a Lie group), it is possible to develop a notion of the global symbol of a pseudodifferential operator. In this talk, we consider such a notion and use it to define a pseudodifferential calculus on the noncommutative torus, which is a mild noncommutative perturbation of the ordinary torus, and a prototypical object in noncommutative geometry. This is done by using an analogue of the Fourier series representation of a function in the (commutative) torus. Moreover, we will compare such a definition with the one where the definition of pseudodifferential operators is given as an analogue to the standard pseudodifferential operators on closed manifolds.
Oscar Riaño
UNAL Bogotá
A Brief Introduction to Dispersion, Nonlinearity, and Solitons
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Dispersive partial differential equations arise in a variety of physical models and describe the interplay between dispersion and nonlinearity. In this talk, we will introduce some of the fundamental ideas behind these equations and explore phenomena such as the formation of solitary waves (traveling waves). Finally, we will discuss some of the mathematical questions that arise in studying their evolution and that motivate current research.
Manuel Rivera
Purdue ( UNAL – Bogotá 2026-2027)
Symmetry and structure in loop spaces
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The loop space of a topological space is the space of continuous maps from the circle into that space. I will discuss combinatorial, algebraic, and geometric structures arising when studying loop spaces in the context of manifold topology and mathematical physics.
Combinatorics: I will describe a family of polytopes, one in each dimension, discovered by appropriately symmetrizing the “smallest possible” cellular model for the loop space of a simplicial complex. Remarkably, each polytope is self-dual (its face lattice is isomorphic to its opposite) suggesting a deeper symmetry.
Algebra: The cellular chain complex of this model is naturally isomorphic to the Hochschild complex of the Koszul dual of a coalgebra associated to the underlying simplicial complex, revealing a connection with homological algebra.
Geometry: When the underlying space is a smooth manifold, one can study operations arising from transverse intersections, concatenation, and splitting of families of loops, that can be viewed as manifestations of Poincaré duality. Understanding the general structure and significance of these operations is the central theme of “string topology.” The combinatorial and algebraic constructions above provide tractable models for these structures.
Gisela Tartaglia
U-La Plata
Actions of algebraic quantum groups
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In this talk, we will present algebraic quantum groups, their notion of duality, and the concept of action on an algebra. Likewise, we will propose a definition of a compact quantum subgroup and, motivated by the construction for discrete groups, show through two particular cases how to obtain – from an algebra $A$ with an action of a compact subgroup $U\subset G$ – an algebra $B$ with an action of $G$, such that $A # U$ is Morita equivalent to $B # G$. (Joint work with Eugenia Ellis and Ana González)
Daniel Vargas
UNAL Bogotá
Algebraicity (Congruences) Modulo p.
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In this talk, we will show how to use algebraicity (congruences) modulo p to prove the transcendence and algebraic independence of certain power series known as G-functions, which were introduced by Siegel in 1929 and play a central role in arithmetic geometry. Furthermore, we will explore how to apply these congruences to study the p-integrality of series known as mirror maps. For this purpose, we will introduce the notion of a strong Frobenius structure, a fundamental concept in the theory of p-adic differential equations, which serves as the cornerstone for understanding the connections between congruences, transcendence, algebraic independence, and p-integrality.
Mario Velásquez
UNAL Bogotá
A Chern Character for (Twisted) Equivariant K-Theory for Compact Lie Group Actions
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In this talk, we will give a construction of the Chern character for actions of compact Lie groups on compact spaces. This Chern character is constructed in two steps. First, we show that rational (twisted) equivariant K-theory can be decomposed as a subgroup of the direct sum of the restrictions to the fixed points of maximal topologically cyclic subgroups in each isotropy group. Following this, we will show how we can use the classical Chern character construction to define the equivariant Chern character. Finally, time permitting, we will present some applications, in particular the proof of a conjecture formulated by Adem, Cantarero, and Gómez.
Anderson Vera
UNAL Bogotá
Comparison of Johnson-type filtrations for homology cobordisms
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Let M denote the mapping class group of Σ, a compact connected oriented surface with one boundary component. The action of M on the nilpotent quotients of the fundamental group π_1(Σ) of the surface allows to define the so-called Johnson filtration and the Johnson homomorphisms. J. Levine introduced a new filtration of M and a version of the Johnson homomorphisms for this new filtration. These constructions extend in a natural way to the monoid of homology cobordisms of the surface. In this talk, we show how to compare these filtrations up to some surgery operations.
Cursillos Extendidos
Sesiones especiales de profundización académica como parte de la celebración UN Encuentro 70.
Lugar: 404-200 (Edificio Yu Takeuchi)
Chair: Nicolás Nájar Salinas
Geometría en ciencias de datos
Este curso busca introducir la intuición geométrica que sustenta métodos recientes en ciencias de datos y machine learning. En lugar de considerar los métodos como “black-boxes”, exploraremos los principios geométricos que los sustentan, entenderemos por qué funcionan y adquiriremos el vocabulario necesario para leer y analizar literatura actual. Los temas incluirán optimización en variedades diferenciables, teoría del transporte óptimo y sus aplicaciones, como la teoría del flujo gradiente en el espacio de Wasserstein y otras.
Daniel López Castaño
Johns Hopkins University
Daniel López (Matemático, UNAL 2018) es un matemático aplicado. Su trabajo se enfoca en aplicaciones de geometría a la ciencia de datos y al machine learning, particularmente en teoría de transporte óptimo, optimización riemanniana y aprendizaje de variedades.
19 de agosto
5:30 p.m. – 6:30 p.m.
20 de agosto
6:45 p.m. – 7:45 p.m.
21 de agosto
2:30 p.m. – 3:30 p.m.
De transformers a lógica: Probando resultados de expresividad
Uno de los objetivos centrales de la complejidad descriptiva es caracterizar los modelos computacionales mediante formalismos lógicos. Trabajos recientes han demostrado que esta perspectiva se extiende más allá de los algoritmos clásicos hacia las arquitecturas modernas de redes neuronales.
Este tutorial de tres partes está dedicado a la demostración de una caracterización lógica de los transformers codificador-decodificador (encoder–decoder) con atención cruzada (cross-attention).
Miguel Moreno
Universidad de Tampere
Miguel Moreno (Matemático, UNAL 2010) es investigador posdoctoral en la Universidad de Tampere (Finlandia). Su investigación combina lógica matemática, teoría de autómatas, complejidad descriptiva y machine learning para estudiar el poder expresivo de las arquitecturas neuronales modernas. Su trabajo reciente se centra en caracterizaciones lógicas de los modelos transformer, estableciendo conexiones con la lógica temporal y los autómatas distribuidos. Anteriormente, trabajó en teoría de modelos y en teoría descriptiva generalizada de conjuntos.
19 de agosto
6:45 p.m. – 7:45 p.m.
20 de agosto
5:30 p.m. – 6:30 p.m.
21 de agosto
3:45 p.m. – 4:45 p.m.
Comité Organizador
Alexander Cruz
UNAL-Bogotá
Nicolás Nájar Salinas
UNAL-Bogotá
Andrés Villaveces
UNAL-Bogotá
Ciencias UNAL
Para más información sobre la este evento, no dudes en ponerte en contacto con nosotros.
Contacto
Correo electrónico
avillavecesn@gmail.com
jacruzmo@unal.edu.co
Teléfono
(+57 601) 316 5000 Ext. 13152
Redes
Departamento de matemáticas