Watse Sybesma, Háskóli Íslands

Carlos Argaez Garcia, október 27, 2020

Math Phys seminar

Fyrirlesari: Watse Sybesma, Háskóli Íslands

Titill: Myndun svarthola og risamassinn í miðju sólkerfisins.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 30.október kl.12:00

Ágrip:

Nóbelsverðlaunin í eðlisfræði í ár snúast um svarthol, bæði út frá kenningum og rannsóknum. Breski eðlisfræðingurinn Roger Penrose setti fram kenningu sem tengir saman myndun svarthola og almennu afstæðiskenninguna og þýski stjarneðlisfræðingurinn 
Reinhard Genzel og bandaríski stjörnufræðingurinn Andrea Ghez hafa sýnt fram á að ósýnilegur og afar eðlisþungur hlutur stýrir hreyfingu stjarna í miðju sólkerfis okkar og risasvarthol er eina mögulega skýringin. Í fyrirlestrinum verður farið yfir þessar rannsóknir og þær kynntar. Athugið að fyrirlesturinn fer fram á ensku.

Adam Timar, University of Iceland

Carlos Argaez Garcia, október 23, 2020

Math colloquium

Fyrirlesari: Adam Timar, Háskóli Íslands

Titill: Uniform Spanning Forests of infinite graphs.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 30.október kl.10:00

Ágrip:

Consider a spanning tree of a given finite graph, chosen uniformly at random. The so-defined Uniform Spanning Tree (UST) has long been an object of interest, since it is intimately connected to harmonic functions on the graph and random walks.
Given an infinite graph G, such as a cubic lattice, one can take its exhaustion by finite graphs G_n and consider a suitably defined limit of the UST of G_n. The limiting measure is called the Uniform Spanning Forest of G. The resulting random object has had crucial importance in statistical physics on 2 dimensional lattices, but also turned out to be interesting when G is a Cayley graphs of a group. Among other uses, it allows for a simple probabilistic interpretation of an intricate geometric parameter.
The talk will be addressed to a general math audience. We will give a brief overview of the above topics, and present some recent results that are joint work with Gábor Pete.

Kristján Jónasson, University of Iceland.

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Kristján Jónasson, University of Iceland.

Titill: Maximum likelihood estimation of multivariate normal parameters when values are missing.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 18.September kl.10:00

Ágrip:

I have been working on a program to estimate the covariance matrix of a multivariate normal distribution in the presence of missing values via maximum likelihood. Many programs offer to do this by computing pairwise covariances (giving a potentially non-positive-definite matrix). There is a package in R (mvnmle) to do the ML-computation, but it is inefficient on several counts. Matlab’s statistical toolbox has a function mvnmle, and its financial toolbox has ecmnmle which are both quite fast, but they lack flexibility, for example to incorporate REML to eliminate bias, to use regularization (when many values are missing), or to reduce the number of parameters by incorporating some variance structure.

This work is in progress and still unpublished but preliminary results are promising. In the talk I shall tell you a little about the program and the underlying algorithms.

Bobby Cheng, University of Sussex, UK

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Bobby Cheng, University of Sussex, UK

Titill: Quantum Resonances in Relativistic Systems.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 9.október kl.10:00

Ágrip:

Significant amounts of research have been completed on mathematical quantum resonances in the non-relativistic setting. However success in generalizing these results to the relativistic setting have been limited. In this talk I will describe the work undertaken to study resonances of the Dirac operator, perturbed by an electric potential with certain ‘nice’ properties, and establish two key trace formulae.

Peter Giesl, University of Sussex, UK

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Peter Giesl, University of Sussex, UK

Titill: Existence and construction of a contraction metric as solution of a matrix-valued PDE.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 2.október kl.10:00

Ágrip:

A contraction metric is a Riemannian metric, with respect to which the distance between adjacent solutions of an ordinary differential equation (ODE) decreases.

A contraction metric can be used to prove existence and uniqueness of an equilibrium of an autonomous ODE and determine a subset of its basin of attraction without requiring information about its location. Moreover, a contraction metric is robust to small perturbations of the system. 

We will prove a converse theorem, showing the existence of a contraction metric for an equilibrium by characterising it as a matrix-valued solution of a certain linear partial differential equation (PDE). This leads to a construction method by numerically solving the matrix-valued PDE using mesh-free collocation. We use and present a recent extension of mesh-free collocation of scalar-valued functions, solving linear PDEs, to matrix-valued ones. Finally, we briefly discuss a method to verify that the computed metric satisfies the conditions of a contraction metric.

This is partly work with Holger Wendland, Bayreuth as well as Sigurdur Hafstein and Iman Mehrabinezhad, Iceland.

Joachim Toft , Department of mathematics, Faculty of Technology, Linnæus University, Växjö, Sweden

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Joachim Toft , Department of mathematics, Faculty of Technology, Linnæus University, Växjö, Sweden

Titill: Analytic pseudo-differential calculus via the Bargmann transform.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 25.September kl.10:00

Ágrip:

The Bargmann transform is a transform which maps Fourier-invariant function spaces and their duals to certain spaces of formal power series expansions, which sometimes are convenient classes of analytic functions.

In the 70th, Berezin used the Bargmann transform to translate problems in operator theory into a pseudo-differential calculi, where the involved symbols are analytic functions, and the corresponding operators map suitable classes of entire functions into other classes of entire functions.

Recently, some investigations on certain Fourier invariant subspaces of the Schwartz space and their dual (distribution) spaces have been performed by the author. These spaces are called Pilipovi ́c spaces, and are defined by imposing suitable boundaries on the Hermite coefficients of the involved functions or distributions. The family of Pilipovi ́c spaces contains all Fourier invariant Gelfand- Shilov spaces as well as other spaces which are strictly smaller than any Fourier invariant non-trivial Gelfand-Shilov space. In the same way, the family of Pilipovi ́c distribution spaces contains spaces which are strictly larger than any Fourier invariant Gelfand-Shilov distribution space.

In the talk we show that the Bargmann images of Pilipovi ́c spaces and their distribution spaces are convenient classes of analytic functions or power series expansions which are suitable when investigating analytic pseudo-differential operators (i. e. Berezin or Wick operators).

We deduce continuity properties for such pseudo-differential operators when the symbols and target functions possess certain (weighted) Lebesgue estimates. We also show that the counter image with respect to the Bargmann transform of these results generalise some continuity results for (real) pseudo-differential operators with symbols in modulation spaces, when acting on other modulation space.

The talk is based on collaborations with Nenad Teofanov and Patrik Wahlberg, and parts of the content of the talk is available at:

N. Teofanov, J. Toft Pseudo-differential calculus in a Bargmann setting, Ann. Acad. Sci. Fenn. Math. 45 (2020), 227–257.

Yadollah Zare, Galatasaray University

Carlos Argaez Garcia, júní 9, 2020

Math colloquium

Fyrirlesari: Yadollah Zare, Galatasaray University

Titill: Center conditions: pull-back of differential equations.

Ágrip:

The space of polynomial differential equations of a fixed degree with a center singularity has many irreducible components. We prove that pull-back differential equations form an irreducible component of such a space. This method is inspired by Ilyashenko and Movasati’s method. The main concepts are the Picard-Lefschetz theory of a polynomial in two variables with complex coefficients, the Dynkin diagram of the polynomial and the iterated integral.

Staðsetning: V-158, VR-II
Tími: Föstudag 12.Júní kl.10:00

Notice that is recommended to keep two meters apart from other attendants.

María Óskarsdóttir, Háskólinn í Reykjavík

Carlos Argaez Garcia, mars 5, 2020

Math colloquium

Fyrirlesari: María Óskarsdóttir, Háskólinn í Reykjavík

Titill: Ranking nodes relative to influence with the Personalized PageRank algorithm applied to fraud detection and credit risk measurement

Staðsetning: VRII-258
Tími: Fimmtudagur 12.mars kl. 10:50

Ágrip:

Various phenomena in both the physical and the digital world can be represented with networks, that is, entities that are connected in some way, for example communication, computer, financial and social networks. A central theme in the analysis of networks is finding the most important nodes in a network. The PageRank algorithm was developed to rank webpages in search engines, to find the most important webpages on the internet, but has been applied in numerous others applications. The ranking can be personalized so that nodes which are important relative (or close) to a predefined set of nodes are ranked higher. This approach has been used to identify certain behavior in networks where there is a strong social effect, for example fraud and churn. In this presentation we show how the personalized PageRank algorithm can be extended for two specific types of networks. First, we look at a bipartite network which consists of claims and the involved parties, i.e. policyholders and brokers, with the goal of finding fraudulent insurance claims. Then we consider multiplex networks, in which each node can be connected to another node by more than one type of edge, such as two different networks connecting the same individuals. They arise naturally in lending, as two borrowers can be connected by geographical location, economic activity, and many other relationships. We present a methodology to leverage multiplex networks by a novel multiplex Personalized PageRank algorithm, which we subsequently apply to credit risk assessment.

Sangmin Lee, Seoul National University

Carlos Argaez Garcia, febrúar 19, 2020

  Math colloquium

Fyrirlesari: Sangmin Lee, Seoul National University

Titill: Complete 1st post-Minkowskian potential from scattering amplitudes.

Staðsetning: VHV-007 (Veröld)
Tími: Mánudagur 24.Janúar kl.10:00

Ágrip:

Building upon recent progress in applying amplitude techniques to perturbative general relativity, we propose a closed-form formula for the conservative Hamiltonian of a spinning binary system at the 1st post-Minkowskian order. It is applicable for general spinning bodies with arbitrary spin multipole moments. It is linear in gravitational constant by definition, but exact to all orders in momentum and spin expansions. At each spin order, our formula implies that the spin-dependence and momentum dependence factorize completely. We compare our formula to a similar one derived in 2017 from a spinning test-body near a Kerr black hole and find perfect agreement.

Ragnar Sigurðsson, University of Iceland

Carlos Argaez Garcia, febrúar 1, 2020

Math colloquium

Fyrirlesari: Ragnar Sigurðsson, University of Iceland

Titill: Norms on complexifications of real vector spaces.

Staðsetning: VRII-258
Tími: Fimmtudagur 6.febrúar kl. 10:50

Ágrip:

The subject of this lecture is of general interest and it only requires knowledge of elementary linear algebra.

The complexification V_C of a real vector space
V is the smallest complex vector space which contains V
as a real subspace. If V is a normed space, then it is
of interest to know how norms may extend from V to V_C.

I will look at a real normed space V and give formulas
for the smallest and largest extension of a general norm
on V to a norm on V_C. These formulas are not explicit
so it is of interest to find explicit formulas in particular
examples. This is possible for extentions of norms induced
by inner products. The Lie norm is the largest
extension of the Euclidean norm on R^n to a complex norm
on C^n.

In complex analysis we deal a lot with plurisubharmonic
functions and an important source for examples are
functions of the form log||f||, where f is a holomorphic
map from a complex manifold into C^n and ||.|| is a norm
on C^n. In his thesis, Auðunn Skúta Snæbjarnarson, studied
the Lie norm on C^n and calculated interesting formulas for
the so called Monge-Ampere measure of log||f||, which is
indeed not an easy task.