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# Seminarios

## Futuros Eventos

2017-04-21

16hrs.

**Coloquio de Matemática UC**

Christian Sadel. PUC

Sobre los Operadores Aleatorios

Sala 2

Abstract:

Random operators such as the Anderson model have been introduced and widely studied by physicists to model the quantum mechanics in disordered systems, such as doped semi-conductors and imperfect crystals. We will give some overview of the theory on random operators and state some more recent results and also discuss some open conjectures

2017-04-07

16hrs.

**Coloquio de Matemática UC**

Nikola Kamburov. PUC

Tba

Sala 2

Abstract:

TBA

2017-04-04

16:00hrs.

**Seminario de Análisis y Geometría**

Erwan Hingant. Universidad del Bio-Bio

Tba

Sala 2, Facultad de Matemáticas UC

2017-03-31

14:30hrs.

**Seminario de Geometría Algebraica**

José Ignacio Yáñez. PUC

Introducción al Minimal Model Program

Sala 2

Abstract:

Este semestre estudiaremos el Minimal Model Program (o teoría de Mori) para superficies algebraicas con borde. El objetivo principal es entender la demostración del teorema de boundedness dada por Alexeev a comienzos de los 90s. Este teorema implica que la compactificación del espacio de moduli de superficies algebraicas de tipo general, dada por Kollár y Shepherd-Barron y generalización de la compactificación de Deligne-Mumford para curvas, define una variedad proyectiva. En particular, las singularidades de las correspondientes superficies están acotadas a través de los números de Chern (de hecho K^2 basta), formando una lista finita. ¿Cuál es esa lista para K^2 dado?

La idea es desarrollar todos los prerequicitos para poder entender los detalles de la demostración.

En esta charla se definirán superficies con bordes, las singularidades involucradas junto a sus discrepancias, el teorema del cono, y todo aspecto básico relacionado con MMP.

2017-03-29

13:00hrs.

**Seminario de Ingeniería Matemática y Computacional**
Pablo Barcelo. U Chile

Querying Graph Databases

Sala Seminario San Agustín, Campus San Joaquín

Abstract:

Graph databases have gained renewed interest in the last years, due to their applications in areas such as the Semantic Web and Social Networks Analysis. We study the problem of querying graph databases, and, in particular, the expressiveness and complexity of evaluation for several general-purpose navigational query languages, such as the regular path queries and its extensions with conjunctions and inverses. We distinguish between two semantics for these languages. The ?rst one, based on simple paths, easily leads to intractability in data complexity, while the second one, based on arbitrary paths, allows tractable evaluation for an expressive family of languages.

We also study two recent extensions of these languages that have been motivated by modern applications of graph databases. The ?rst one allows to treat paths as ?rst-class citizens, while the second one permits to express queries that combine the topology of the graph with its underlying data.
2017-03-29

14:30hrs.

**Seminario Agco**

Kevin Schewior. U Chile / Max Planck Institute For Informatics

Chasing Convex Bodies

U Chile, Campus Beauchef, República 779 B, Sala 3er Piso

2017-03-28

16:00hrs.

**Seminario de Análisis y Geometría**
Sophia Jahns . Tübingen University, Germany

Trapped Light In Stationary Spacetimes

Sala 2, Facultad de Matemáticas UC

Abstract:

Light can circle a massive object (like a black hole or a neutron star) at a "fixed distance", or, more generally, circle the object without falling in or escaping to infinity. This phenomenon is called trapping of light and well understood in static, asymptotically flat (AF) spacetimes. If we drop the requirement of staticity, similar behavior of light is known, but there is no definiton of trapping available. We present some known results about trapping of light in static AF spacetimes. Using the Kerr spacetime as a model, we then show how trapping can be better understood in the framework of phase space and work towards a definition for photon regions in stationary AF spacetimes.

## Eventos Pasados

2017-03-24

14:30hrs.

**Seminario de Geometría Algebraica**
Fabien Trihan. U Sophia, Japón

Abelian varieties over function fields and related conjecture

Abstract:

We will talk about abelian varieties over function fields of positive characteristic and conjectures related to those such as the Birch-Swinnerton-Dyer, the equivariant Tamagawa number conjecture or the Iwasawa Main conjectures

sala 2

2017-03-24

16.30hrs.

**Coloquio de Matemática UC**

Jan Felipe Van Diejen. Universidad de Talca

Bispectralidad y sistemas de partículas cuánticas integrables

Abstract:

En 1985 Duistermaat y Grünbaum introdujeron el concepto del llamado "problema bispectral". En breve, un problema espectral se llama bispectral si la función propia satisface además una ecuación diferencial lineal en el parámetro espectral. En esta charla explicaremos como la noción de bispectralidad nos provee de una herramienta poderosa en el estudio de las funciones propias de sistemas de partículas cuánticas integrables.

Sala 2

2017-03-23

17:00hrs.

**Seminario de Teoría Espectral**
Rafael Tiedra de Aldecoa. Facultad de Matem'aticas, PUC

Spectral analysis of quantum walks with an anisotropic coin

Abstract:

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.

This is a joint work with Serge Richard (Nagoya University) and Akito Suzuki (Shinshu University).

Sala 1

2017-03-22

14:30hrs.

**Seminario Agco**
Krzysztof Fleszar. U Chile

Maximum Disjoint Paths: New Algorithms based on Tree-Likeness

Abstract:

Maximum Edge Disjoint Paths is a classical NP-hard problem of finding a

maximum-size subset from a given set of k terminal pairs that can be

routed via edge-disjoint paths.

One of the big open problems in approximation algorithms is to close the

gap between the best known approximation upper bound of $\sqrt{n}$

(Chekuri et al. (2006)) and the best known lower bound of $2^{\sqrt{\log

n}}$ (Chuzhoy et al. (2016)). In their seminal paper, Raghavan and

Thompson (Combinatorica, 1987) introduce the technique of randomized

rounding for LPs; their technique gives an O(1)-approximation when edges

may be used by $O(\log n / \log\log n)$ paths.

In this talk, I introduce the problem and present two of our algorithms

(ESA 2016) that strengthen the fundamental results above. They provide

new bounds formulated in terms of the feedback vertex set number r of a

graph, which measures its vertex deletion distance to a forest.

- An $O(\sqrt{r} \log{kr})}$-approximation algorithm. Up to a

logarithmic factor, it strengthens the best known ratio $\sqrt{n}$ due

to Chekuri et al., as $r \le n$.

- An $O(1)$-approximation algorithm with congestion bounded by

$O(\log{kr} / \log\log{kr})$, strengthening the bound obtained by the

classic approach of Raghavan and Thompson.

At the end, an open problem will be stated.

República 779 B, Sala 3er Piso (Beauchef)

2017-03-21

16:00hrs.

**Seminario de Análisis y Geometría**

Mauricio Bogoya. Universidad Nacional de Colombia, Bogota

A NON-LOCAL DIFFUSION COUPLED SYSTEM EQUATIONS IN A BOUNDED DOMAIN

Sala 2, Facultad de Matemáticas UC

2017-03-16

17:00hrs.

**Seminario de Teoría Espectral**
Hermann Schulz-Baldes. Universidad de Erlangen, Alemania

Finite volume calculation of topological invariants

Abstract:

Odd index pairings of K1-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a lattice, it is shown how to calculate the resulting index as the signature of a suitably constructed finite-dimensional matrix, more precisely the finite volume restriction of the so-called Bott operator. The index is also equal to the eta-invariant of the Bott operator. In presence of real symmetries, secondary $Z_2$-invariants can be obtained as the sign of the Pfaffian of the Bott operator. These results reconcile two complementary approaches to invariants in topological insulators. Joint work with Terry Loring.

Sala 1

2017-03-15

14:30hrs.

**Seminario Agco**

Saeed Hadikanlo. Univ. de Paris 9

Learning in NonAtomic Anonymous Games: Application to First Order Mean Field Games

Abstract:

We introduce a model of anonymous games where the actions are chosen from possibly player dependent sets. We propose several learning procedures similar to the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the classical monotonicity condition. Typical examples are First Order Mean Field Games.

República 779 B, Sala 3er Piso.

2017-03-14

16:00hrs.

**Seminario de Análisis y Geometría**

Marcos de la Oliva. Universidad Autónoma de Madrid

Relaxation of a model for nematic elastomers

Abstract:

The direct method of the calculus of variations to find minimizers is based on compactness and lower semicontinuity of the energy functional. In the absence of lower semicontinuity, one option is to find the relaxation, i.e., the largest lower semicontinuous functional below a given one. In nonlinear elasticity, computing the relaxation is difficult beacuse of the non-standard growth conditions. In this talk we show that the relaxation for a model in nonlinear elasticity is given by the quasiconvexification of the integrand. We also propose a model for nematic elastomers (a kind of liquid crystals) in which the energy has a part in the reference configuration and a part in the deformed configuration. We show again that the relaxation is given by the quasiconvexification.

Sala 2, Facultad de Matemáticas UC

2017-03-13

17:00hrs.

**Seminario de Sistemas Dinámicos**
Tanya Firsova. Kansas State University

Deformation spaces of rational functions

Abstract:

A celebrated Theorem of W.Thurston gives a topological condition when a postcritically finite branched cover can be realized by a rational map. A.Epstein, building on the work of Thurston, studied the spaces of maps constrained by certain postcritically finite relations. He defined deformation spaces for such maps that live in certain Teichmuller spaces. Epstein proved transversality results in holomorphic dynamics using deformation spaces.

We will discuss how these deformation spaces relate to the ones studied by Mary Rees. We will also discuss topological properties of the Epstein's deformation spaces and give a sufficient condition that guarantees that a given deformation space is not contractible. This is a joint work with J. Kahn and N. Selinger.

Sala 1, Fac. Mates, PUC

2017-03-13

16:00hrs.

**Seminario de Sistemas Dinámicos**
Mao Shinoda. Keio University

The existence of a dense subset of uncountably maximized continuous functions

Abstract:

The main purpose of the ergodic optimization is to single out invariant measures which maximize the space average of a performance function on a dynamical system.

We mainly consider a dynamical system defined by a continuous self-map on a compact metric space.

There is a major conjecture that for ``many" performance functions there exist unique maximizing measures and the unique measures are supported by a single periodic orbit.

Jenkinson shows that for a generic continuous function there exists unique maximizing measure.

We prove, on the other hand, there exits a dense subset of continuous functions which have uncountably many ergodic maximizing measures.

The main idea of our proof is the application of the Bishop Phelps theorem to the context of maximizing measures.

Sala 1, Fac. Mates, PUC

2017-03-10

15:00hrs.

**Seminario de Geometría Algebraica**

Dulip Piyaratne. Kavli Ipmu, University Of Tokyo

Stability conditions on derived categories of varieties

Abstract:

The aim of this talk is to discuss Bridgeland stability conditions on smooth projective varieties. The notion of stability appears in many guises and it is fundamental to geometric invariant theory. There is a systematic way of studying stability conditions due to Bridgeland and his approach is essentially an abstraction of the usual slope stability for sheaves. This categorical stability notion was introduced in order to understand the work of Douglas on Pi-stability in superconformal field theories. However, construction of Bridgeland stability conditions on higher dimensional varieties is a challenging problem, and from string-theoretic point of view, stability conditions on smooth projective threefolds are the most interesting ones. In this talk, I will recall some important notions associated to derived categories of varieties and stability conditions, with special emphasis on curves and surfaces.

Sala 2

2017-03-10

16:00hrs.

**Seminario de Geometría Algebraica**

Dulip Piyaratne. Kavli Ipmu, University Of Tokyo

Stability conditions on derived categories of varieties II

Abstract:

In this talk I will discuss stability conditions on projective threefolds. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for some 3-folds including Fano 3-folds of Picard rank one. However, Schmidt and Martinez gave some counter-examples for Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality in order to get a family of Bridgeland stability conditions, and why it holds for general Fano 3-folds.

Sala 2

2017-03-06

12:00hrs.

**Seminario de Estadística**
Garritt Page. Brigham Young University

Estimation and Prediction in the Presence of Spatial Confounding for Spatial Linear Models

Abstract:

In studies that produce data with spatial structure it is common that covariates of interest vary spatially in addition to the error. Because of this, the error and covariate are often correlated. When this occurs it is difficult to distinguish the covariate effect from residual spatial variation. In an iid normal error setting, it is well known that this type of correlation produces biased coefficient estimates but predictions remain unbiased. In a spatial setting recent studies have shown that coefficient estimates remain biased, but spatial prediction has not been addressed. The purpose of this paper is to provide a more detailed study of coefficient estimation from spatial models when covariate and error are correlated and then begin a formal study regarding spatial prediction. This is carried out by investigating properties of the generalized least squares estimator and the best linear unbiased predictor when a spatial random effect and a covariate are jointly modeled. Under this setup we demonstrate that the mean squared prediction error is possibly *reduced* when covariate and error are correlated.

Sala 2, Facultad de Matemáticas

2017-01-16

17:00hrs.

**Seminario de Sistemas Dinámicos**

Luna Lomonaco. Usp

The Mandelbrot set and its satellite copies

Abstract:

For a polynomial on the Riemann sphere, infinity is a (super) attracting fixed point, and the filled Julia set is the set of points with bounded orbit. Consider the quadratic family $P_c(z)=z^2+c$. The Mandelbrot set M is the set of parameters c such that the filled Julia set of $P_c$ is connected. Douady and Hubbard, using renormalization, proved the existence of homeomorphic copies of M inside of M, which can be primitive (if, roughly speaking, they have a cusp) or satellite (if they don't). They conjectured that the primitive copies of M are quasiconformal homeomorphic to M, and that the satellite ones are quasiconformal homeomorphic to M outside any small neighbourhood of the root. These results are now theorems due to Lyubich. The satellite copies are not quasiconformal homeomorphic to M, but are they mutually quasiconformally homeomorphic? In a joint work with C. Petersen we prove that this question, which has been open for about 20 years, has in general a negative answer.

Sala 1, Fac. Mates, PUC

2017-01-16

16:00hrs.

**Seminario de Sistemas Dinámicos**

Jiangang Yang. Uff

Continuity of Lyapunov exponents in the C0 topology

Abstract:

This is a joint with Marcelo Viana.

We prove that the Bochi-Mañé theorem is false, in general, for linear cocycles over non-invertible maps: there are $C_0$-open subsets of linear cocycles that are not uniformly hyperbolic and yet have Lyapunov exponents bounded from zero.

Sala 1, Fac. Mates, PUC

2017-01-13

16hrs.

**Coloquio de Matemática UC**
Javier Arsuaga. Department Of Mathematics & Department Of Molecular And Cellular Biology, UC Davis

Using random knot theory to understand the three dimensional organization of genomes

Abstract:

Uncovering the basic principles that govern the three dimensional (3D) organization of genomes poses one of the main challenges in mathematical biology of the postgenomic era. Certain viruses and some organisms, such as trypanosomes, accommodate knotted or linked genomes. Others, such as bacteria, are known to have unknotted genomes. It remains to be determined if the genomes of higher organisms, such as humans, admit topologically complex forms.

In this talk I will present some mathematical results and computational methods that have been developed when addressing these biological questions. Biological implications of these results will also be discussed.

Sala 2

2017-01-13

14:40 Hrshrs.

**Seminarios Extraordinarios**
Tyrone Crisp . Max- Planck Institute For Mathematics, Bonn

Representation theory of reductive groups via operator algebras and their modules

Abstract:

Abstract: Operator algebra theory combines algebra and functional analysis to study collections of linear operators. Applications to the study of infinite-dimensional group representations have been a major driving force in the development of operator algebra theory from the 1940s up to the present. In this talk I shall present a novel approach to the representation theory of real reductive groups (for example, GL(n,R)) using operator-algebraic techniques. (This is partly based on joint work with P. Clare, N. Higson and R. Yuncken.)

Sala 2 Facultad de Matemáticas

2017-01-12

16:00 hrs hrs.

**Seminarios Extraordinarios**

Benjamin Matschke. Max Planck Institute For Mathematics, Bonn

Discrete versus continuous - topics in discrete geometry, topology and number theory.

Abstract:

In many fields of mathematics there is an interplay between

the discrete and the continuous world, sometimes through analogies

between statements, and sometimes methods from one side need to be

used to solve problems on the other side, and vice versa.

This talk is essentially on some interesting examples of that:

Geometric incidence theorems, colored Tverberg theorems*, successive

spectral sequences, and S-unit equations**.

* Joint with Pavle Blagojevi?, Günter Ziegler, and Roman Karasev.

** Joint with Rafael von Känel.

Sala 2

2017-01-11

15:00hrs.

**Seminario de Análisis y Geometría**

Marie-Françoise Bidaut-Véron. Université François Rabelais, Tours, France

A priori estimates and ground states of solutions of an Emden-Fowler equation with gradient

Sala 2, Facultad de Matemáticas UC

2017-01-11

11:00hrs.

**Seminario de Estadística**
Ying Sun. King Abdullah University Of Science And Technology (Kaust), Saudi Arabia

Total Variation Depth for Functional Data

Abstract:

There has been extensive work on data depth-based methods for robust

multivariate data analysis. Recent developments have moved to

infinite-dimensional objects such as functional data. In this work, we

propose a new notion of depth, the total variation depth, for functional

data. As a measure of depth, its properties are studied theoretically, and

the associated outlier detection performance is investigated through

simulations. Compared to magnitude outliers, shape outliers are often

masked among the rest of samples and harder to identify. We show that the

proposed total variation depth has many desirable features and is well

suited for outlier detection. In particular, we propose to decompose the

total variation depth into two components that are associated with shape

and magnitude outlyingness, respectively. This decomposition allows us to

develop an effective procedure for outlier detection and useful

visualization tools, while naturally accounting for the correlation in

functional data. Finally, the proposed methodology is demonstrated using

real datasets of curves, images, and video frames. The talk is based on

joint work with Huang Huang.

Sala 2, Facultad de Matemáticas

2017-01-11

16:00hrs.

**Seminario de Análisis y Geometría**

Laurent Véron. Université François Rabelais, Tours, France

Initial trace of positive solutions of some nonlinear diffusion equations

Sala 2, Facultad de Matemáticas UC

2017-01-11

12:00hrs.

**Seminario de Estadística**
Marc G. Genton. King Abdullah University Of Science And Technology (Kaust), Saudi Arabia

Computational Challenges with Big Environmental Data

Abstract:

Two types of computational challenges arising from big environmental data

are discussed. The first type occurs with multivariate or spatial

extremes. Indeed, inference for max-stable processes observed at a large

collection of locations is among the most challenging problems in

computational statistics, and current approaches typically rely on less

expensive composite likelihoods constructed from small subsets of data. We

explore the limits of modern state-of-the-art computational facilities to

perform full likelihood inference and to efficiently evaluate high-order

composite likelihoods. With extensive simulations, we assess the loss of

information of composite likelihood estimators with respect to a full

likelihood approach for some widely-used multivariate or spatial extreme

models. The second type of challenges occurs with the emulation of climate

model outputs. We consider fitting a statistical model to over 1 billion

global 3D spatio-temporal temperature data using a distributed computing

approach. The statistical model exploits the gridded geometry of the data

and parallelization across processors. It is therefore computationally

convenient and allows to fit a non-trivial model to a data set with a

covariance matrix comprising of 10^{18} entries. We provide 3D

visualization of the results. The talk is based on joint work with Stefano

Castruccio and Raphael Huser.

Sala 2, Facultad de Matemáticas

2017-01-09

15:00 Hrs.hrs.

**Seminarios Extraordinarios**
Mircea Petrache. Max- Planck Institute For Mathematics, Bonn

Sharp asymptotics and equidistribution for large particle systems with long-range interactions

Abstract:

We consider the asymptotic behaviour of systems of a very large number of particles subject to long-range pairwise repulsive interactions. Such questions appear in several branches of mathematics, such as the study of Fekete points in constructive approximation, Ginzburg-Landau vortex models for superconductors, or in the study of random matrices. Jointly with Sylvia Serfaty we obtained the characterization of the behavior of the system at the microscopic scale: When the temperature tends to zero, our gas "crystallizes" to a minimizer of W, conjectured to be the "Abrikosov" triangular lattice in 2 dimensions.

Steps towards such strong structural results are equidistribution results obtained in joint works with Simona Rota-Nodari and the development of tools for studying minimisation problems on lattices, with Laurent Betermin.

I will also mention the link to the asymptotics for multimarginal optimal transport problems appearing in computational chemistry, as well as other future directions of investigation.

Sala 1 de la Facultad de Matemáticas de la P. Universidad Católica de Chile

2017-01-09

16:30 Hrs.hrs.

**Seminario Local de Sistemas Dinámicos**
Ian Morris, Surrey.

Matrix thermodinamic formalism

Abstract:

Equilibrium states of real-valued potentials over subshifts of finite type have been investigated since the 1970s and their basic ergodic properties have long been well understood: they are exponentially mixing, Bernoulli and have positive entropy. Much more recently a theory has emerged of equilibrium states associated to matrix-valued potentials. In this talk I will describe how the ergodic properties of a matrix equilibrium state depend on the semigroup generated by the underlying matrices. At the end I will discuss some consequences for self-affine fractals in the plane.

Sala 1 de la Facultad de Matemáticas de la Universidad Católica

2017-01-06

16:00hrs.

**Coloquio de Matemática UC**

Valery Alexeev. University Of Georgia

Volumes of open surfaces

Abstract:

The volume of a smooth projective variety measures asymptotically the number of pluricanonical sections. For a surface, it is a positive integer. Similarly, the volume of an open smooth surface measures the number of pluri LOG canonical sections. Easy examples show that it could be a rational number. If nonzero, how small could it be? I will discuss some general results in this area and the new records obtained jointly with Wenfei Liu.

Sala 2

2017-01-05

17:00hrs.

**Seminario de Teoría Espectral**
Jake Fillman. Virginia Tech

Ballistic propagation for limit-periodic Jacobi operators

Abstract:

W

e will talk about the propagation of wave packets in a one-dimensional medium with limit-periodic background potential. If the amplitudes of the low-frequency modes of the potential decay sufficiently rapidly, then wavepackets travel ballistically in the sense that the group velocity is injective on the domain of the position operator. Since the underlying Hamiltonian has purely absolutely continuous spectrum, this answers a special case of a general question of J. Lebowitz regarding the relationship between ac spectrum and ballistic wavepacket spreading. Sala 1

2017-01-03

16:00 hrs.hrs.

**Seminarios Extraordinarios**

Giancarlo Lucchini. Centre de Mathématiques Laurent Schwartz

Congruencias, aproximación y grupos algebraicos

Abstract:

Cuando uno estudia las soluciones racionales de ecuaciones polinomiales, una pregunta que uno puede hacerse es si éstas son densas en el conjunto de las soluciones reales. De forma análoga. Uno puede hacerse la misma pregunta para otras completaciones de Q, es decir para lo que uno llama los números p-ádicos. Sin embargo, esta segunda pregunta puede ser traducida en términos de simples congruencias módulo n para un cierto entero n. El objetivo de esta charla es estudiar ambas preguntas simultáneamente para un conjunto particular de ecuaciones: aquellas cuyo conjunto de soluciones posee una estructura de grupo. En términos más técnicos, estudiaremos la propiedad de "aproximación débil" para los "grupos algebraicos". Mirando un ejemplo muy particular (la ecuación x^2 + y^2 = 1), veremos cómo la estructura de grupo puede ser usada para probar (o refutar) esta propiedad en el caso de los grupos algebraicos lineales, como fue hecho por Sansuc en 1981.

Sala 2 de la Facultad de Matemáticas