Seminarios

Futuros Eventos

2019-04-25
14:00hrs.
Seminario de Geometría Algebraica
Fernando Figueroa. PUC Chile
Calculos: " Singularidades Acotables "
sala 1
2019-04-25
15:30hrs.
Seminario de Postgrado en Matemáticas
Roberto Maturana. PUC Chile
Tba
Sala 2
2019-04-24
15:45 hrs.
Seminario Fismat
Svetlana Jitomirskaya. University of California, Irvine
Tba
Sala 5
2019-04-23
14:00hrs.
Seminario de Geometría Algebraica
Diana Torres. PUC Chile
Mmp Necesita Singularidades
sala 1
2019-04-22
16:30--17:30hrs.
Seminario de Sistemas Dinámicos
Mónica Moreno Rocha. Cimat
On The Dynamics of Elliptic Functions of The Form P+B
USACH, Sala de seminarios del 4to piso del Departamento de Matemáticas y Ciencia de la computación ( Las Sophoras nº 173, Santiago, Estación Central).
Abstract:
The dynamical system obtained by iteration of the Weierstrass P function over real square lattices can be characterized by the behavior of its single free critical orbit. In contrast, as soon as P is “perturbed” by the addition of a complex parameter b, the elliptic function P+b exhibits at least two free critical orbits, which complicates the study of its dynamics and connectedness locus. This talk I will present some of the results and open questions regarding the rich structures found in dynamical and parameter plane of P+b when b is restricted to a complex line and P is defined over real square lattices. This is a joint work with Jane M. Hawkins, UNC-Chapel Hill.
2019-04-22
15:30-16:20hrs.
Seminario de Sistemas Dinámicos
Cristobal Rivas. Usach
Sobre el Grupo de Higman
USACH, Sala de seminarios del 4to piso del Departamento de Matemáticas y Ciencia de la computación ( Las Sophoras nº 173, Santiago, Estación Central).
Abstract:
Les contaré sobre el grupo de Higman. Porqué no tiene cocientes finitos y porqué no admite representaciones lineales.
Si aún hay tiempo, diré algunas palabras sobre sus representaciones en grupos de difeomorfismos y homeomorfismos.

Eventos Pasados

2019-04-17
17:00hrs.
Seminario de Modelamiento Matemático
Reinaldo B. Arellano-Valle. PUC Chile
Scale and Shape Mixtures of Multivariate Skew-Normal Distributions
Abstract:
We introduce a broad and flexible class of multivariate distributions obtained by both scale and shape mixtures of multivariate skew-normal distributions. We present the probabilistic properties of this family of distributions in detail and lay down the theoretical foundations for subsequent inference with this model. In particular, we study linear transformations, marginal distributions, stochastic representations and hierarchical representations.

We also describe an EM-type algorithm for maximum likelihood estimation of the parameters of the model and demonstrate its implementation on a wind dataset. Our family of multivariate distributions unifies and extends many existing models of the literature that can be seen as submodels of our proposal.
 
Joint work with: Clécio S. Ferreira1, Department of Statistics, Federal University of Juiz de Fora, Juiz de Fora, Brazil. Marc G. Genton2, CEMSE Division, King Abdullah University of Science and Technology, Thuwal,
Saudi Arabia.
 
References
[1] Arellano-Valle, R. B., Ferreira, C. S., and Genton, M. G. (2018) Scale and shape mixtures of multivariate skew-normal distributions, Journal of Multivariate Analysis, 166, 98-110.
 

Sala 1,
2019-04-17
15:45 hrs.
Seminario Fismat
Walter de Siqueira Pedra. University of São Paulo
Thermodynamical Stability and Dynamics of Lattice Fermions with Mean-Field Interactions
Abstract:
For lattice fermions we study the thermodynamic limit of the time evolution of observables when the corresponding finite-volume Hamiltonians contain mean-field terms (like, e.g., the BCS model). It is well-known that, in general, this limit does not exist in the sense of the norm of observables, but may exist in the strong operator topology associated to a well-chosen representation of the algebra of observables. We proved that this is always the case for any cyclic representation associated to an invariant minimizer of the free energy density, if the Hamiltonians are invariant under translations. Our proof uses previous results on the structure of states minimizing the free energy density of mean-field models along with Lieb-Robinson bounds for the corresponding families of finite-volume time evolutions. This is a joint work with Jean-Bernard Bru, Sébastien Breteaux and Rafael Miada.
Sala 5
2019-04-16
16:00hrs.
Seminario de Análisis y Geometría
Duván Henao. Pontificia Universidad Católica de Chile
Aplicando la geometría diferencial para comprender la estructura de los cristales líquidos
Abstract:
Veremos como el teorema de Liouville y los teoremas de Schoen-Uhlenbeck nos permiten demostrar que a bajas temperaturas los defectos de los minimizadores del funcional de Landau-de Gennes son necesariamente biaxiales. (En particular, a bajas temperaturas es falso que sus frustraciones topológicas las resuelvan derritiéndose, como se asume comúnmente.)
sala 2, Facultad de Matemáticas, PUC
2019-04-16
14:00hrs.
Seminario de Geometría Algebraica
Nicolás Vilches. PUC Chile
Singularidades ADE / Du Val / Canónicas
sala 1
2019-04-16
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Robert Auffarth. Universidad de Chile
Trisecantes de la variedad de Kummer de una variedad Jacobiana
Abstract:
La variedad de Kummer de una variedad abeliana es el cociente de la variedad abeliana por el automorfismo que envía un elemento a su inverso. Dada una polarización principal en la variedad abeliana, la variedad de Kummer tiene una inmersión canónica a algún espacio proyectivo. Gracias al trabajo de Fay, Gunning, Welters, Debarre y Krichever, entre otros, se sabe que la variedad de Kummer de una variedad Jacobiana posee una pecularidad: existe una familia 4-dimensional de rectas que intersectan la variedad de Kummer en por lo menos tres puntos, y esta propiedad caracteriza a las Jacobianas dentro de las demás variedades abelianas (principalmente polarizadas indescomponibles). En esta charla daremos un survey de estas ideas, y relacionaremos las rectas trisecantes de una Jacobiana con la aplicación de Gauss de su divisor theta.
Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-04-16
15:30-16:30hrs.
Seminario Local de Sistemas Dinámicos
Sebastián Pavez. PUC
Teorema de Kucherenko-Wolf
Sala 1, Facultad de Matemáticas PUC
2019-04-15
15:30--16:20hrs.
Seminario de Sistemas Dinámicos
Ryo Moore. PUC
Nonconventional Coboundaries
Sala 1, PUC, Facultad de Matemáticas
2019-04-15
16:30--17:30hrs.
Seminario de Sistemas Dinámicos
Thomas Jordan. University of Bristol
Multifractal analysis for self-affine systems
Abstract:
 joint work with Balazs Barany, Antti Kaenmaki and Michal Rams. If you consider a uniformly expanding Markov map on the interval and a continuous function. You can consider level sets of point for which the Birkhoff average is some fixed point. A typical problem I need multifractal analysis is to look at the dimension of these level sets. We will show how this can be done using the topological pressure and then how results can be obtained in the setting of certain self-affine sets in two dimensions using the sub-additive pressure and approximation by dominated subsystems.
Sala 1, PUC, Facultad de Matemáticas
2019-04-12
16:00hrs.
Coloquio de Matemática UC
Thomas Fuhrer. PUC Chile
PROBLEMAS BI-LAPLACIANOS -- FORMULACIONES VARIACIONALES, TRAZAS Y APROXIMACIONES
Abstract:
En esta charla voy a revisar el problema bi-Laplaciano que describe la deformación de placas y es una EDP del orden cuatro.
Para definir métodos numéricos para aproximar soluciones de esta ecuación tenemos que definir y analizar formulaciones variacionales del problema.
Eso incluye:
(i)   Definición de espacios de Sobolev apropiados.
(ii)  Analisis de espacios duales y operadores de trazas.
(iii) Aproximaciones de soluciones en subespacios.
Especificamente voy a hablar sobre el caso donde la frontera es solamente Lipshitz y no convexa, lo que permite funciones singulares como soluciones del problema.
auditorio Ninoslav Bralic
2019-04-12
14:00hrs.
Seminario de Teoría de Números
Marcos Morales. Pontificia Universidad Católica de Chile
Puntos de Fekete y diámetro transfinito
Abstract:
En este seminario se dará la definición de lo que son los puntos de Fekete y se explicará lo que es el diámetro transfinito, se usarán herramientas como la desigualdad de Hadamard y la matriz de Vandermonde para calcular los puntos de Fekete y el diametro transfinito del circulo unitario.
Sala 2
2019-04-11
15.30hrs.
Seminario de Postgrado en Matemáticas
Gabriel Ramírez. PUC Chile
Cotas para un análogo del máximo común divisor de funciones holomorfas.
Abstract:
El trabajo presentado en esta charla se realizó en conjunto con Natalia García-Fritz. En una primera parte, mostraremos las bases de la teoría de distribución de valores de funciones holomorfas y su relación con aproximaciones diofánticas, además de dar un breve repaso de teoría de probabilidades. Tras eso, explicaremos el problema que nos interesa tratar y presentaremos algunos resultados obtenidos.
Sala 2
2019-04-11
14:00hrs.
Seminario de Geometría Algebraica
Diana Torres. PUC Chile
CALCULOS: " La superficie detrás de una suma de Dedekind "
sala 1
2019-04-09
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Irene Spelta. Università Di Pavia
On special subvarieties of Ag contained in the Torelli locus
Abstract:

We will speak about the Coleman-Oort conjecture on totally geodesic subvarieties of Ag, the moduli space of abelian varieties of dimension g. In order to understand the subject, we will summarize properties of Jacobians of curves, abelian varieties and the Torelli morphism.

The examples of totally geodesic subvarieties known so far are obtained as families of Jacobians of Galois coverings of curves f:C→ C'. All of them satisfy a sufficient condition, which we will denote by (∗). We will briefly explain why condition (∗) works and we will explicitly construct and study a particular example.

We will show that condition (∗) gives us a bound on the genus g' of C'. Computer calculations allow us then to say that, up to a certain genus bounded genus g of C, there are only 6 families: all of them describe Galois coverings of elliptic curves. We will quickly illustrate them.

Finally, we study the Prym maps of these families (which we will define accordingly): we will demonstrate that these families are fibered, via their Prym map, in totally geodesic curves.


Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-04-09
14:00hrs.
Seminario de Geometría Algebraica
Fernando Figueroa. PUC Chile
Log MMP para superficies
sala 1
2019-04-09
15:30 - 16:30hrs.
Seminario Local de Sistemas Dinámicos
Sebastián Pavez. PUC
Optimización Ergódica: Introducción y ejemplo del Pescado
Abstract:
El objeto de estudio de la optimizaci\'on erg\'odica es describir las \'orbitas de cierto sistema din\'amico que maximizan cierta funci\'on \textit{performance} dada. En el contexto de esta charla, consideraremos el caso de $(X,T)$ un sistema din\'amico, con $X$ un espacio m\'etrico compacto, $f \in \mathcal{C}(X)$, y queremos estudiar qu\'e ocurre con las \'orbitas que maximizan el problema:
 
$$\displaystyle \beta(f)= \sup_{x \in X} \lim_{n \rightarrow \infty}  \frac{1}{n} (f(x)+f(T(x))+...+f(T^{n-1}(x)))$$
 
donde este l\'imite exista. El problema (1) se puede trabajar equivalente como un problema de Teor\'ia Erg\'odica
 $$\beta(f)= \sup_{\mu \in \mathcal{M}_{T}} \int f d\mu$$
donde $\mathcal{M}_{T}$ denota las medidas de probabilidad $T$-invariantes. Luego de enunciar algunos resultados en el contexto del problema (2), vamos a hablar en espec\'ifico del ejemplo del Pescado de Bousch. A lo largo de esta charla, vamos tanto a repasar como motivar los conceptos y resultados que son conocidos en Teor\'ia Erg\'odica que se usar\'an para los prop\'ositos de lo que vamos a introducir.

Sala 1, Facultad de Matemáticas PUC
2019-04-08
16:30--17:30hrs.
Seminario de Sistemas Dinámicos
Gabriela Alexandra Estevez Jacinto. Universidade de São Paulo
Renormalization of multicritical circle maps
Abstract:
We study $C^3$ orientation preserving circle homeomorphisms with irrational rotation number and non-flat critical points. By Yoccoz, two of these maps with same irrational rotation are topologically conjugate. In this talk, we define the Renormalization operator of this kind of maps and assuming some properties of this operator we prove that the conjugacy is a $C^{1+\alpha}$ diffeomorphism. This result is valid for a total Lebesgue measure set of irrational rotation numbers. This is a joint work with Pablo Guarino (Universidade Federal Fluminense, Brazil).
Sala 1, PUC, Facultad de Matemáticas
2019-04-08
15:30--16:20hrs.
Seminario de Sistemas Dinámicos
Italo Cipriano. PUC
Typical determinant of random matrices
Abstract:
Let $M_n$ be an $n\times n$ matrix with random entries in $\{+1,-1\}.$   In this talk I will discuss properties of the determinant of these matrices when $n$ tends to infinity. In particular, what is the probability that the determinant is zero? What is the typical value of the determinant? The talk is based on a result in [Tao and Vu, On random +-1 matrices, singularity and determinant. Random Structures and Algorithms, 2005 ].
Sala 1, PUC, Facultad de Matemáticas
2019-04-05
14:00hrs.
Seminario de Teoría de Números
Vicente Monreal. Pontificia Universidad Católica de Chile
Criterio de irreductibilidad de Cohn
Abstract:
Se presentará el criterio de Cohn, como resultado del estudio de polinomios en $\mathbb{Z}[x]$, que ejemplifica la profunda relación entre números primos y polinomios irreducibles.
Sala 2http://www.mat.uc.cl/~natalia.garcia/stn.html
2019-04-05
16:00hrs.
Club de Matemática
Ricardo Menares. PUC
Matemática y mensajes
Abstract:
Cuando un emisor envía un mensaje a través de un sistema remoto, ocasionalmente ocurre que, debido a la presencia de ruidos, el receptor recibe la transmisión con algún error. Para que el sistema de transmisión resulte práctico, su diseño debe incorporar una solución a este problema.
 
En esta charla presentaremos los códigos correctores de errores, que son objetos matemáticos que permiten codificar mensajes de manera a la vez redundante y eficiente. Veremos los fundamentos matemáticos de algunas construcciones de tales códigos, que involucran conceptos de aritmética y geometría.

Auditorio Ninoslav Bralic,http://www.clubdematematica.cl/
2019-04-05
12:00hrs.
Seminario de Estadística
Ilias Diakonikolas. University of Southern California
Algorithmic Questions in High-Dimensional Robust Statistics
Abstract:
Fitting a model to a collection of observations is one of the quintessential questions in statistics. The standard assumption is that the data was generated by a model of a given type (e.g., a mixture model). This simplifying assumption is at best only approximately valid, as real datasets are typically exposed to some source of contamination. Hence, any estimator designed for a particular model must also be robust in the presence of corrupted data. This is the prototypical goal in robust statistics, a field that took shape in the 1960s with the pioneering works of Tukey and Huber. Until recently, even for the basic problem of robustly estimating the mean of a high-dimensional dataset, all known robust estimators were hard to compute. Moreover, the quality of the common heuristics degrades badly as the dimension increases.

In this talk, we will survey the recent progress in algorithmic high-dimensional robust statistics. We will describe the first computationally efficient algorithms for robust mean and covariance estimation and the main insights behind them. We will also present practical applications of these estimators to exploratory data analysis and adversarial machine learning. Finally, we will discuss new directions and opportunities for future work.

The talk will be based on a number of joint works with (various subsets of) G. Kamath, D. Kane, J. Li, A. Moitra, and A. Stewart.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chilehttp://midas.mat.uc.cl
2019-04-04
14:00hrs.
Seminario de Geometría Algebraica
Diana Torres . PUC Chile
CALCULOS: " Sumas de Dedekind y fraciones continuas "
sala 1
2019-04-03
15:45 hrs.
Seminario Fismat
Jorge Antezana. National University of la Plata
Quasicrystals and Fourier analysis
Abstract:
Quasicrystals are non-periodic structures discovered by Shechtman in 1984 (see [Sh]). Nowadays, one of the best mathematical descriptions quasicrystals are the so called "model sets". These sets were introduced by Meyer in [M], many years before the discovery of Shechtman. In that moment, one of the aims of Meyer was to study approximation of algebraic characters by continuous ones in locally compact abelian groups (see also [L]).

Recently, important applications of quasicrystals to Fourier Analysis have been found (see [MM], [GL], [LO], [AACM] ). In this talk we will discuss some of these applications, making focus in those related with problems of sampling and interpolation in Paley Wiener spaces.

[AACM]  E. Agora, J. Antezana, C. Cabrelli, Existence of quasicrystals and universal stable sampling and interpolation in LCA groups, to appear in Trans. Amer. Math. Soc.

[GL] S. Grepstad, N. Lev,  Multi-tiling and Riesz bases. Adv. Math. 252 (2014), 1-6.

[L] J. C. Lagarias, Mathematical quasicrystals and the problem of diffraction. Directions in mathematical quasicrystals,  CRM Monogr. Ser., 13, Amer. Math. Soc., Providence (2000) 61-93.

[LO] N. Lev, A. Olevskii, Quasicrystals and Poisson's summation formula, Invent. math. 200 (2015), 585-606.

[MM] B. Matei, Y. Meyer, Simple quasicrystals are sets of stable sampling, Complex Var. Elliptic Equ. 55 (2010), 947-964.

[M] Y. Meyer, Algebraic Numbers and Harmonic Analysis, (1970) North Holland.

[Sh] D. Shechtman, I. Blech, D. Gratias, J.W. Cahn,  Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53 (1984) 1951-1953.
Sala 5
2019-04-03
17:00hrs.
Seminario de Modelamiento Matemático
Elsa Cazelles . CMM (Center for Mathematical Modelling)
Statistical properties of regularized barycenters in the Wasserstein space and application to the registration of flow cytometry data.
Abstract:
In this talk, we discuss the study of data that can be described by random probability measures (discrete or absolutely continuous) with support on Rd. The aim is to provide a first order statistical analysis on this space endowed with the Wasserstein distance, which boils down tothe study of the Frechet mean (or barycenter). In particular, we focus on the case of discrete data (or observations) sampled from absolutely continuous probability measures (a.c.) with respect to the Lebesgue measure. We thus introduce an estimator of the barycenter of random measures, penalized by a convex function, making it possible to enforce its a.c.
Another estimator is regularized by adding entropy when computing the Wasserstein distance (which has first been introduced for computational reasons). We are particularly interested in controlling the variance of these estimators.
Thanks to these results, the principle of Goldenshluger and Lepski allows us to obtain an automatic calibration of the regularization parameters. We then apply this work to the registration of multivariate densities, especially for flow cytometry data.
Sala 1, Edificio Rolando Chuaqui, Campus San Joaquín, Avda. Vicuña Mackenna 4860, Macul, Chile.
2019-04-02
16:00-17:00hrs.
Seminario de Sistemas Dinámicos
Roberto Markarian . Universidad de la República
Billares Caóticos. Resultados y métodos
Abstract:
La teoría matemática de billares estudia modelos simples de dinámicas en que hay choques de partículas y con las fronteras de un recipiente. Luego de indicar algunas motivaciones se expondrán propiedades ergódicas y estadísticas sobre las que se han hecho avances sustantivos en los últimos decenios, siguiendo muchos de los lineamientos abiertos, en particular, por la escuela de Ya. G. Sinai
PUC, Sala 1
2019-04-02
14:00hrs.
Seminario de Geometría Algebraica
Pedro Montero. Utfsm
MMP en superficies nosingulares
sala 1
2019-04-02
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Mikhail Borovoi. Tel Aviv University, Temporarily Usach
Real models of spherical homogeneous spaces
Abstract:
Let $G$ be a connected reductive algebraic group over the field of complex numbers $\mathbb{C}$. Let $Y=G/H$ be a spherical homogeneous space of $G$ (a homogeneous space of special kind). Let $G_0$ be a real model (real form) of $G$, that is, a model of $G$ over the field of real numbers  $\mathbb{R}$. In the talk I will discuss the following question: does there exist a $G_0$-equivariant real model $Y_0$ of $Y$? This is interesting even in the case when $G = G' \times G'$, where $G'$ is a connected semisimple group over $\mathbb{C}$, and $H=G'$ embedded diagonally into $G' \times G'$.
This is a joint work with Giuliano Gagliardi, Tel Aviv - Hannover. No preliminary knowledge of spherical varieties will be assumed.

Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-04-02
16:00hrshrs.
Seminario de Análisis y Geometría
Ariane Trescases. Cnrs Imt Toulouse
Quaternions in collective motion
Abstract:
We present a model for multi-agent dynamics based on rigid alignment. Each agent is described by its position and body attitude: it travels at a constant speed while trying to coordinate its solid orientation with the solid orientation of the neighboring agents. The body orientations are represented by unitary quaternions. We first introduce an individual based model in the spirit of the Vicsek model, enhanced with the body orientation dynamics. We then derive the corresponding kinetic model. From there we compute the hydrodynamical limit, leading to a self-organized hydrodynamical system based on quaternions.
Sala 2, Facultad de Matemáticas
2019-04-02
16:00hrs.
Seminario de Probabilidad
Roberto Markarián. Universidad de la República
Billares Caóticos. Resultados y métodos
Abstract:

La teoría matemática de billares estudia modelos simples de dinámicas en que hay choques de partículas y con las fronteras de un recipiente. Luego de indicar algunas motivaciones se expondrán propiedades ergódicas y estadísticas sobre las que se han hecho avances sustantivos en los últimos decenios, siguiendo muchos de los lineamientos abiertos, en particular, por la escuela de Ya. G. Sinai.


sala 1 facultad de matemáticas
2019-04-01
15:30-16:20hrs.
Seminario de Sistemas Dinámicos
Sebastián Donoso. Cmm, Universidad de Chile
On subsets with no arithmetic progressions
Abstract:
For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a subset of \{1,\ldots,N\} that contains no arithmetic progression of length 3. Finding upper and lower bounds for $\nu(N)$ has been a challenging problem for decades. In this talk I will survey this problem and present a proof of a theorem by Behrend in the 40's, that gave a surprising lower bound to $\nu(N)$.
CMM
2019-04-01
16:30-17:30hrs.
Seminario de Sistemas Dinámicos
Angel Pardo. Cmm, Universidad de Chile
Counting problem on infinite periodic billiards and translation surfaces
Abstract:
The Gauss circle problem consists in counting the number of integer points of bounded length in the plane. This problem is equivalent to counting the number of closed geodesics of bounded length on a flat two dimensional torus or, periodic trajectories, in a square billiard table.

Many counting problems in dynamical systems have been inspired by this problem. For 30 years, the experts try to understand the asymptotic behavior of closed geodesics in translation surfaces and periodic trajectories on rational billiards. (Polygonal billiards yield translation surfaces naturally through an unfolding procedure.) H. Masur proved that this number has quadratic growth rate.

In these talk, we will study the counting problem on infinite periodic rational billiards and translation surfaces. The first example and motivation is the wind-tree model, a Z^2-periodic billiard model. In the classical setting, we place identical rectangular obstacles in the plane at each integer point; we play billiard on the complement.

I will first present some quite precise results that are only valid for the wind-tree model (and some natural generalizations) and then, a general result which is valid for a.e. infinite periodic translation surfaces that uses completely different techniques: a dynamical analogous, for the algebraic hull of a cocycle, to strong and super-strong approximation on algebraic groups.
CMM
2019-03-29
16:00hrs.
Coloquio de Matemática UC
Cristobal Rojas. Unab
Complejidad computacional en el análisis de sistemas dinámicos
Abstract:
La importancia que actualmente tienen los computadores en el análisis, exploración y predicción de sistemas dinámicos es incuestionable. Comprender los límites de esta metodología es por tanto una tarea de gran interés, más aún si tenemos en cuenta las aplicaciones a la física y la ingeniería. En esta charla discutiremos cómo es posible usar las herramientas de la teoría de la calculabilidad y complejidad computacional para entender dichos límites, y su interacción con las propiedades dinámicas, analíticas o geométricas del sistema. En particular, revisaremos algunos ejemplos que ilustran el panorama general: si bien fenómenos de alta dificultad computacional pueden emerger en sistemas muy simples, en general se espera que el comportamiento exhibido por sistemas genéricos sea computacionalmente tratable. Todas las nociones necesarias serán introducidas en la charla.
auditorio Ninoslav Bralic
2019-03-29
14:00hrs.
Seminario de Teoría de Números
Javier Reyes. Pontificia Universidad Católica de Chile
Teorema de Monsky
Abstract:
Se introducirá el concepto de norma 2-ádica junto con técnicas de coloración para probar que no se puede dividir un cuadrado en una cantidad impar de triángulos de la misma área.
Sala 2http://www.mat.uc.cl/~natalia.garcia/stn.html
2019-03-27
17:00hrs.
Seminario de Modelamiento Matemático
Claire Delplancke. Center of Mathematical Modeling in Santiago, Universidad de Chile
Bayesian modeling for inverse problems? The example of a scalable algorithm for passive seismic tomography in mining.
Sala 1, Edificio Rolando Chuaqui, Campus San Joaquín, Avda. Vicuña Mackenna 4860, Macul, Chile.
2019-03-27
14.00hrs.
Seminario de Análisis Complejo
Iason Efraimidis. Universidad Católica de Chile
Sobre estiramientos de mapeos armónicos univalentes
Abstract:

Presentaremos el reciente trabajo de Aydogan, Bshouty, Lyzaik y Sakar [Complex Anal. Oper. Theory (2018)] donde se demuestra que es falsa la conjetura de que cada mapeo armónico univalente es el estiramiento en alguna dirección de una función analítica univalente. Comentaremos sobre el análogo de esta conjetura para mapeos convexos.


FMAT Sala 2
2019-03-26
16:00hrs.
Seminario de Análisis y Geometría
Satoshi Tanaka. Okayama University of Science, Japan
Uniqueness of positive radial solutions of superlinear elliptic equations in annuli
Abstract:
This is a joint work with Naoki Shioji (Yokohama National University) and
Kohtaro Watanabe (National Defense Academy).

The Dirichlet problem
\begin{equation*}
 \left\{
  \begin{array}{cl}
   \Delta u + f(u) =0 &  \mbox{in} \ x \in A, \\[1ex]
    u=0 & \mbox{on} \ \partial A
  \end{array}
 \right.
\end{equation*}
is considered, where $A:=\{x\in {\bf R}^N : a< |x| <b$,\  $N \in {\bf N}$, $N \ge 2$, $0<a<b<\infty$,
$f \in C^1[0,\infty)$, $f(u)>0$ and $uf'(u) \ge f(u)$ for $u>0$.
Positive radial solutions are studied.
Hence the boundary value problem
$$u'' + \frac{N-1}{r} u' + f(u) = 0, \quad r \in (a,b); \qquad   u(a) = u(b) = 0$$
is considered.
Uniqueness results of positive solutions are shown.
Sala 2
2019-03-26
14:00hrs.
Seminario de Geometría Algebraica
Pedro Montero. Utfsm
Introducción al Minimal Model Program y acotamiento
Abstract:
Uno de los objetivos de la geometría algebraica es la clasificación de variedades proyectivas. En dimension 1, existe una clara distinción entre los tipos de curvas de género 0, 1 y mayor o igual a 2, tanto de un punto de vista topológico (revestimiento universal), de la curvatura y, más algebraicamente, de acuerdo a la negatividad, trivialidad o positividad de su clase canónica. En esta charla, discutiremos sobre cómo el Minimal Model Program (MMP) permite conjeturalmente asociar a toda variedad algebraica un "modelo minimal" y reducir el problema de clasificación a estudiar tres grandes familias: variedades de Fano (canónico negativo), Calabi-Yau (canónico trivial) y canónicamente polarizadas (canónico positivo). En este marco, la existencia de una cantidad finita de familias (acotamiento) es crucial para poder esperar obtener clasificaciones explícitas, y unos de los primeros grandes pasos en esta dirección son los resultados de acotamiento de variedades de Fano y canónicamente polarizadas obtenidos por Alexeev en el caso de superficies (medianamente singulares). Dichos resultados han sido generalizados recientemente a dimensiones superiores por Birkar en el caso de variedades de Fano (gracias a lo cual ha obtenido la medalla Fields) y por Hacon-McKernan-Xu en el caso canónicamente polarizado. El objetivo de este seminario será entender el lenguaje y técnicas del MMP en el caso de superficies singulares así como el rol de la "teoría de complementos", introducida por Shokurov y utilizada por Birkar para extender los resultados de Alexeev.
 
El plan preliminar de las charlas podría ser entonces el siguiente (también, modificar a gusto):
1. Introducción al Minimal Model Program y acotamiento (Pedro)
2. MMP para superficies suaves (Pedro)
3. Log MMP para superficies.
4. Singularidades ADE
5. Propiedades de pares logarítmicos
6. Clasificación de pares log canónicos en dimensión 2
7. Adjunción y Lema de Conectividad

sala 1
2019-03-26
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
David Leep. University of Kentucky
Liouville's problem on quaternary quadratic forms
Abstract:
In 1856, motivated by Lagrange's theorem that every positive integer is a sum of four integral squares, Liouville tried to find all quadratic forms $x^2 + ay^2 +bz^2 +abw^2$, with $a$, $b$ positive integers, that integrally represent all positive integers.  Of the seven possible candidates that he found, Liouville could resolve the problem for only six of them.  Liouville was unable to decide if $x^2 + 2y^2 +5z^2 +10w^2$ integrally represents all positive integers.  Although L. E. Dickson eventually proved this using advanced techniques, the question has remained whether there is an elementary method that Liouville missed.  This talk will present the background to this problem, including results by Lagrange that foreshadowed more advanced results from the late 19th century.  Time permitting, I will also give some details about an elementary proof that shows $x^2 + 2y^2 +5z^2 +10w^2$ integrally represents all positive integers. 

Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-03-25
16:30 - 17:30hrs.
Seminario de Sistemas Dinámicos
Michele Triestino. U. Bourgogne
Cantor dynamics and simple left-orderable groups
Abstract:
I will present a construction of simple groups of homeomorphisms of the real line.

Given a homeomorphism of a Cantor set $\sigma: X \to X$, consider the suspension $Y=X \times [0,1] / (x,1) \sim (\sigma(x),0)$, and look at the group $H_0(Y)$ of homeomorphisms of $Y$, isotopic to the identity. If $\sigma$ is minimal, then $H_0(Y)$ is simple [Aliste-Prieto - Petite], and I will describe countable subgroups $T(Y)$ which are also simple. These are reminiscent of the classical Thompson groups, and feature several nice properties. For instance, when \sigma is a minimal subshift, $T(Y)$ is finitely generated.

Joint work with Nicolás Matte Bon.
USACH, Sala de seminarios del 4to piso del Departamento de Matemáticas y Ciencia de la computación ( Las Sophoras nº 173, Santiago, Estación Central)
2019-03-22
14:00hrs.
Seminario de Teoría de Números
Natalia García. Pontificia Universidad Católica de Chile
Alturas en Teoría de Números
Abstract:
En esta charla vamos a definir algunas funciones de altura, las cuales son esencialmente una manera de medir complejidad aritmética, y constituyen una herramienta fundamental. Veremos también algunas de sus propiedades aplicadas a diversos temas en teoría de números.
Sala 2http://www.mat.uc.cl/~natalia.garcia/stn.html
2019-03-22
16:00hrs.
Club de Matemática
Jan Kiwi. PUC
¿ Cómo ubicarse? Matemáticas y GPS
Abstract:
Uno de los inventos relativamente recientes que nos ha cambiado la vida es el GPS (Global Positioning System). En esta charla veremos algunos aspectos matemáticos involucrados en el funcionamiento de este sistema de posicionamiento.
Ninoslav Bralichttp://www.clubdematematica.cl/
2019-03-22
12:00 hrs.
Seminario de Estadística
Debajyoti Sinha. Florida State University
Semiparametric Bayesian latent variable regression for skewed multivariate data
Abstract:
For many real-life studies with skewed multivariate responses, the level of skewness and association structure assumptions are essential for evaluating the covariate eff ects on the response and its predictive distribution. We present a novel semiparametric multivariate model and associated Bayesian analysis for multivariate skewed responses. Similar to multivariate Gaussian, this multivariate model is closed under marginalization, allows a wide class of multivariate associations, and has meaningful physical interpretations of skewness levels and covariate eff ects on the marginal density. Other desirable properties of our model include the Markov Chain Monte Carlo computation through available statistical software, and the assurance of consistent Bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions. We illustrate the practical advantages of our methods over existing alternatives via simulation studies, the analysis of a clinical study on periodontal disease and extensions to Bayesian regression trees.

This is a joint work with Drs. A.Bhingare, S.Lipsitz, D.Bandopadyay and A.Linero.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chilehttp://midas.mat.uc.cl
2019-03-20
14:00hrs.
Seminario de Ingeniería Matemática y Computacional
Ignacio Labarca. Alumno Magíster, Instituto de Ingeniería Matemática y Computacional
Convolution Quadrature methods for Time-Domain Scattering from unbounded penetrable interfaces
Abstract:
We present a class of boundary integral equal on methods for the numerical solution of acoustic and electromagnetic time-domain scatering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The proposed methodology relies on Convolution Quadrature (CQ) methods in conjunction with the recently introduced Windowed Green Function (WGF) method. As in standard time-domain scatering from bounded obstacles, a CQ method of the user’s choice is utilized to transform the problem into a finite number of (complex) frequency-domain
problems posed on the domains involving penetrable unbounded interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method—which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Helmholtz boundary integral equation solver capable of handling complex wavenumbers with large imaginary part. A high-order Nystrom method based on Alpert quadrature rules is utilized here. A variety of numerical examples including wave propagation in open waveguides as well as scatering from multiply layered media, demonstrate the capabilities of the proposed approach.

Auditorio San Agustín Campus San Joaquin
2019-03-19
16:00hrs.
Seminario de Análisis y Geometría
Azahara de la Torre Pedraza. University of Freiburg
On higher dimensional singularities for the fractional Yamabe problem
Abstract:
We consider the problem of constructing solutions to the fractional Yamabe problem that are singular at a given smooth sub-manifold, for which we establish the classical gluing method of Mazzeo and Pacard for the scalar curvature in the fractional setting. This proof is based on the analysis of the model linearized operator, which amounts to the study of a fractional order ODE,
and thus our main contribution here is the development of new methods coming from conformal geometry and scattering theory for the study of non-local ODEs. Note, however, that no traditional phase-plane analysis is available here. Instead, first, we provide a rigorous construction of radial fast-decaying solutions by a blow-up argument and a bifurcation method. Second, we use conformal geometry to rewrite this non-local ODE, giving a hint of what a non-local phase-plane analysis should be. Third, for the linear theory, we use complex analysis and some non-Euclidean harmonic analysis to  examine a fractional Schrödinger equation with a Hardy type critical potential. We construct its Green's function, deduce Fredholm properties, and analyze its asymptotics at the singular points in the spirit of  Frobenius method. Surprisingly enough, a fractional linear ODE may still have a two-dimensional kernel as in the second order case.
Sala 2
2019-03-19
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
José Ignacio Burgos Gil. Instituto de Ciencias Matemáticas, Madrid
Height pairing between arithmetic cycles
Abstract:
The linking number between two circles is the number of windings of one circle around the other. This is a topological invariant and is a first example of a secondary characteristic class. Analogues of the linking number can be defined in many situations. For instance the height pairing between algebraic cycles is a generalization of the cross ratio between four points in the projective line and can be seen as a "linking number" that has a very nice Hodge theoretical interpretation. 
Higher Chow groups have been introduced by Bloch as a concrete way to represent motivic cohomology. In this talk I will explain how to define a height pairing between higher cycles. This is joint work with S. Goswami and G. Pearlstein.

Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-03-18
16:30-17:30hrs.
Seminario de Sistemas Dinámicos
Yiwei Zhang. Center for Mathematical Sciences, Huazhong University of Science and Technology, China
Understanding physical mixing processes via transfer operator approach
Abstract:
Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications.In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint.

In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introductionon the relationships between the spectral properties of the associated transfer operator and the estimations of the optimal mixing rate of the mixing process. Moreover, I will address how the optimal mixing rate varies according to the stretch and fold map has "cutting and shuffling'' behaviour (i.e., composing with a permutation). 

If time permits, I will also talk about how to interpret this problem to the eigenvalue estimations for the Random bi-stochastic matrices (free probability theory) and the locations of poles of the dynamical zeta function.
Sala 1, PUC, Facultad de Matemáticas, Av. Vicuña Mackenna 4860, Macul, La Florida
2019-03-15
16:00hrs.
Coloquio de Matemática UC
Aníbal Medina. University of Notre Dame
Conmutatividad en topología, homotopía y análisis de datos
Abstract:
En esta charla hablaremos sobre el uso de la conmutatividad en la clasificación de espacios topológicos. Recordaremos la construcción del invariante "cohomología" con su estructura de álgebra conmutativa y cómo ésta se levanta, módulo homotopias coherentes, a un modelo de cocadenas. Dicha manifestación homotópica de la conmutatividad nos entrega aún más información topológica que, gracias al desarrollo de nuevos algoritmos, puede ser efectivamente incorporada en los actuales protocolos para el análisis topológico de datos.
auditorio Ninoslav Bralic
2019-03-15
14:00hrs.
Seminario de Teoría de Números
Ricardo Menares. Pontificia Universidad Católica de Chile
La constante de Hermite
Abstract:
Un empaquetamiento de discos en el plano es una familia de discos del mismo radio y cuyos interiores no se intersectan. No es posible cubrir el plano con un empaquetamiento de discos, por lo que la pregunta natural es encontrar uno que recubra la mayor área posible. La respuesta involucra un cierto reticulado del plano.
 
En esta charla consideraremos empaquetamientos de bolas en un espacio euclidiano de dimensión arbitraria n. Nos restringiremos a empaquetamientos provenientes de reticulados. La n-ésima constante de Hermite mide la eficiencia, en términos de volumen recubierto, que puede alcanzar un empaquetamiento de bolas en tal espacio. 
 
La constante de Hermite es conocida solo para valores pequeños de n. También se dispone de información sobre su valor asintótico. Explicaremos algunos de estos resultados, así como las preguntas abiertas. No asumiremos conocimientos especializados de Teoría de Números.

Sala 2http://www.mat.uc.cl/~natalia.garcia/stn.html
2019-03-14
16:30 -- 17:30hrs.
Seminario de Sistemas Dinámicos
Neil Dobbs. University of Geneva
TBA
Sala 5
2019-03-13
15:45 hrs.
Seminario Fismat
Monika Anna Winklmeier. Universidad de los Andes
Estimates for eigenvalues in gaps of the essential spectrum
Abstract:
In this talk I will show how bounds for eigenvalues in gaps of the essential spectrum of a linear operator can be obtained. The main example will be a one-dimensional Dirac type operator.
Sala 5
2019-03-12
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Sebastián Herrero. Instituto de Matemáticas, Pucv
Equidistribución p-ádica de puntos enteros en hipersuperficies cuadráticas
Abstract:
En la primera parte de esta charla repasaremos resultados de Pommerenke, Linnik, Duke y Schulze-Pillot, entre otros, sobre la equidistribución de puntos enteros en hipersuperficies cuadráticas en espacios euclideanos. 
En la segunda parte presentaremos resultados análogos en el mundo p-ádico, cuya demostración hace uso de la teoría de formas modulares y cotas para sus coeficientes de Fourier.
Los resultados que serán presentados forman parte de un proyecto en colaboración con R. Menares y J. Rivera-Letelier.

Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-03-12
16:30 -- 18:00hrs.
Seminario de Sistemas Dinámicos
Hamal Hubbard. Cornell University
Construccion de aplicaciones pseudo-Anosov
Sala 1
2019-03-12
16:00hrs.
Seminario de Análisis y Geometría
Andrés Larraín-Hubach. University of Dayton, Ohio
Conexiones auto-duales sobre espacios Taub-NUT
Abstract:
Las ecuaciones de Yang-Mills son un sistema de ecuaciones en derivadas parciales, definidas sobre variedades suaves en cuatro dimensiones, con un profundo significado geométrico. Las propiedades de las soluciones de estas ecuaciones, sobre variedades compactas, han sido  analizadas desde los años sesenta y han arrojado resultados importantes tanto en matemáticas como en física. Las soluciones sobre  variedades no compactas no han sido estudiadas tan ampliamente y aún hay muchas preguntas importantes sin respuesta. En esta charla, basada en resultados obtenidos en colaboración con Sergey Cherkis y Mark Stern, explicaré diversas propiedades de ciertas  soluciones a las ecuaciones de Yang-Mills, definidas sobre unas variedades abiertas especiales llamadas Espacios Taub-NUT. En particular, explicaré dos argumentos distintos para probar un teorema de índice necesario en la construcción.
 

Sala 2
2019-03-11
16:30 -- 18:00hrs.
Seminario de Sistemas Dinámicos
Hamal Hubbard. Cornell University
Construccion de aplicaciones pseudo-Anosov
Sala 1
2019-03-08
16:00hrs.
Coloquio de Matemática UC
Heisuke Hironaka. Japan Association for Mathematical Sciences / Harvard University
Embedded Resolution of Singularities in Algebraic Geometry
Abstract:
Algebraic geometry underwent phenomenal transform from *geometric* to *algebraic* in the manner of concepts and proof techniques. Resolution of singularity is typical example among many other classical and/or new problems.

Personally, I had been strongly influenced and much indebted by foundational contributions of my teachers: Oscar Zariski, Masayoshi Nagata, Alexander Grothendieck and many others.

Here I want to present my own additions and implementations strictly focusing my attention on problems about embedded resolution of singularities. Technically new concepts and techniques in my own contributions will be explained by the following technical terms:

1) "Idealistic exponent" and its application to "MOIE"
2) Singularity set "S" and algebraic translation "P"
3) "Q" smoothing of arithmetic singularity
4) "Escalator-elevator"  imagery transformation of "Q" smooth
Auditorio Ninoslav Bralic
2019-03-08
15:00hrs.
Coloquio de Matemática UC
Mark Spivakovsky. Institut de Mathématiques de Toulouse, Université Paul Sabatier
Introduction to the problem of resolution of singularities in algebraic geometry
Abstract:
The subject of this talk is the problem of resolution of singularities in algebraic geometry, but it is intended for a general mathematical audience. The problem of resolution of singularities asks whether, given an algebraic variety X over a field k, there exists a non-singular algebraic variety X' and a proper map X' -> X which is one-to-one over the non-singular locus of X. If we cover X' by affine charts, the problem becomes one of parametrizing pieces of X by small pieces of the Euclidean space k^n.

All the basic notions such as algebraic variety, singularity, birational map, etc., will be defiend from scratch. We will describe an algorithm for resolving the singularities of plane curves. We will explain how to generalize this algorithm to higher dimensions, thereby giving a brief sketch of the proof of Hironaka's celebrated theorem on resolution of singularities of varieties over fields of characteristic zero.

Time permitting, we will briefly discuss the difficulties that arise in trying to generalize Hironaka's result to fields of positive characteristic.
Auditorio Ninoslav Bralic
2019-03-06
15:45 hrs.
Seminario Fismat
Christian Jaekel. University of São Paulo
On reflection positivity, modular localisation and Connes cocycles
Abstract:
The unitary irreducible representations of the Lorentz group carry an intrinsic notion of localisation on de Sitter space, known as modular localisation. An extension of Araki’s perturbation theory of modular automorphisms can be used to define interacting representations of the Lorentz group, as well as the corresponding Haag-Kastler nets. The analyticity properties of the correlation functions allow us to extend these theories to “nets" of (non-abelian) von Neumann algebras on the sphere. Reflection positivity can be used to recover the interacting quantum (field) theories on the de Sitter space from the sphere. Explicit examples are scalar bosons with polynomial or exponential interactions in 1+1 space-time dimensions, but our aim is to classify all interacting quantum theories compatible with the space-time symmetries. The Minkowski space limit is the limit of space-time curvature to zero, which is well-behaved on the level of local von Neumann algebras.
Sala 5
2019-03-05
16:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Stefan Gille. University of Alberta
Residue maps for hermitian forms of central simple algebras
Abstract:
Residue maps for quadratic forms over fields of characteristic not 2 are well known and a useful tool to study these objects. One can construct these maps also using derived Witt groups, and this approach can be generalized to hermitian Witt groups of central simple algebras with involutions. In case of involutions of the first can there is also a direct definition possible, and one can prove an analog of Springer's exact sequence. The latter holds for certain more general involutions as well.

Sala de seminarios (4to piso, lado norte de) Dpto de Matemática y Ciencia de la Computación USACH
2019-01-25
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Diego Izquierdo. Mpim Bonn
Dimensión de los cuerpos, K-teoría y aritmética de los espacios homogéneos
Abstract:
En 1986, Kato y Kuzumaki hicieron varias conjecturas con las que esperaban dar una caracterización diofántica de la dimensión cohomológica de los cuerpos en términos de K-teoría de Milnor y de puntos racionales sobre hipersuperficies proyectivas de pequeño grado. Hoy en día, sabemos que estas conjecturas son falsas en general. En esta charla, veremos que si uno sustituye las hipersuperficies proyectivas de pequeño grado por los espacios homogéneos, la conjectura de Kato y Kuzumaki se vuelve cierta. Se trata de un trabajo en colaboración con Giancarlo Lucchini Arteche.
Sala 2
2019-01-14
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Piecewice chaotic maps
Abstract:
We will consider the class of Cr unidimensional piecewise maps with a transitive attractor. These maps can have simultaneously discontinuities, criticalities and singularities. We will show that topological chaos is equivalent to metric chaos. We recall that this result is known in several classes strictly contained in the general class that we are presenting.
Sala 2
2019-01-11
12:00 hrs.
Seminario de Estadística
David Dahl. Department of Statistics, Brigham Young University
Summarizing Distributions of Latent Structure
Abstract:
In a typical Bayesian analysis, consider effort is placed on "fitting the model" (e.g., obtaining samples from the posterior distribution) but this is only half of the inference problem.  Meaningful inference usually requires summarizing the posterior distribution of the parameters of interest.  Posterior summaries can be especially important in communicating the results and conclusions from a Bayesian analysis to a diverse audience.  If the parameters of interest live in R^n, common posterior summaries are means, medians, and modes.  Summarizing posterior distributions of parameters with complicated structure is a more difficult problem.  For example, the "average" network in the posterior distribution on a network is not easily defined. This paper reviews methods for summarizing distributions of latent structure and then proposes a novel search algorithm for posterior summaries.  We apply our method to distributions on variable selection indicators, partitions, feature allocations, and networks.  We illustrate our approach in a variety of models for both simulated and real datasets.

Seminario organizado por el Centro para el Descubrimiento de Estructuras en Datos Complejos - MiDaS.
Sala 5, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chilehttp://midas.mat.uc.cl
2019-01-10
12:00 hrs.
Seminario de Estadística
Dae-Jin Lee. Bcam - Basque Center for Applied Mathematics
Hierarchical modelling of patient-reported outcomes data based on the beta-binomial distribution
Abstract:
The beta-binomial distribution does not belong to the exponential family and, hence classical regression techniques cannot be used when dealing with outcomes following the mentioned distribution. In this talk, we propose and develop regression models based on the beta-binomial distribution for the analysis of U, J or inverse J-shaped discrete and bounded outcomes. In fact, although this work is focused on the analysis of patient-reported outcomes (PROs), which usually follow the mentioned distributional shapes, proposed models can also be extended to several fields. First of all, we make a review and comparison of existing beta-binomial regression approaches in independent data context, concluding that the marginal approach is the most adequate. However, PRO studies are usually carried out in a longitudinal framework, where patients' responses are measured over time. This leads to a multilevel or correlated data structure and consequently, we extend the marginal beta-binomial regression approach to the inclusion of random effects to accommodate the hierarchical structure of the data. We develop the estimation and inference procedure for the model proposal. Furthermore, we compare the performance of our proposal with similar approaches in the literature, showing that it gets better results in terms of reducing the bias of the estimates. We apply the model to a longitudinal Chronic Obstructive Pulmonary Disease study carried out at Galdakao Hospital in Biscay, Spain, reaching clinically and statistically relevant results about the evolution of the patients over time. PROs are usually obtained using rating scale questionnaires consisting of questions or items, grouped into one or more subscales, often called dimensions or domains. Therefore, we also propose a multivariate regression model based on the beta-binomial distribution for the joint analysis of all the longitudinal dimensions provided by different questionnaires. Finally, it is worth mentioning that we have implemented all the proposed regression models in the PROreg R- package which is available at CRAN.
Sala 1, Facultad de Matemáticas, Edificio Rolando Chuaqui, Campus San Joaquin, Pontificia Universidad Católica de Chile
2019-01-10
16:30hrs.
Seminario de Sistemas Dinámicos
Alberto Pinto. Faculty of Sciences, University of Porto
Pseudo-Anosov diffeomorphisms
Abstract:
We will introduce pseudo Cr smooth structures on surfaces that will have the following property; the Pseudo-Anosov diffeomorphisms are uniformly Cr hyperbolic. We will conjecture that the Bochi-Mane theorem will extend to such pesudo C1 smooth structures recovering the duality of the result for all surfaces.
Sala 2
2019-01-04
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Yuri Bilu. Université de Bordeaux
Singular units do not exist
Abstract:
In the first part, I will revise the classical theory of complex multiplication of elliptic curves (or C-lattices); in particular, I will define the notion of a singular modulus, the j-invariant of an elliptic curve (or a C-lattice) with complex multiplication.  According to the old result of Weber, a singular modulus is an algebraic integer. In the second part, I will briefly describe the recent work of Habegger, Kühne and myself proving that a singular modulus cannot be algebraic unit.
Sala 2
2019-01-03
16:00hrs.
Seminario de Análisis y Geometría
Armin Schikorra . University of Pittsburgh
Self-repulsive curvature energies for curves and surfaces: regularity theory and relation to harmonic maps
Abstract:
I will talk about a class of curvature energies for curves, the O'Hara energies, that are nonlocal in nature. In particular, I will present an approach for regularity theory of minimizers and critical points for these curves which is based on a relation to (fractional) harmonic maps. Then I will present some results towards attempts of generalizing this idea to surfaces.
Sala 2