Category: Math Colloquium

Kristján Jónasson, University of Iceland.

Carlos Argaez Garcia, September 11, 2020

Math colloquium

Speakers: Kristján Jónasson, University of Iceland.

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

Room:  Via Zoom. Link to be sent.
Time: Friday 18th September, 10:00am

Abstract:

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This work is in progress and still unpublished but preliminary results are promising.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

Speakers: Bobby Cheng, University of Sussex, UK

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

Room:  Via Zoom. Link to be sent.
Time: Friday 9th October, 10:00am

Abstract:

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

Speakers: Peter Giesl, University of Sussex, UK

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

Room:  Via Zoom. Link to be sent.
Time: Friday 2nd October, 10:00am

 

Abstract:

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

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

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

Room:  Via Zoom. Link to be sent.
Time: Friday 25th September, 10:00am

Abstract:

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, June 9, 2020

Math colloquium

Speakers: Yadollah Zare, Galatasaray University

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

Abstract:

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.

Room:  V-158, VR-II
Time: Friday 12th June, 10:00am

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

María Óskarsdóttir, Háskólinn í Reykjavík

Carlos Argaez Garcia, March 5, 2020

Speaker: María Óskarsdóttir, University of Reykjavík

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

Room: VRII-258
Time: Thursday 12th March, 10:50hrs

Abstract:

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, February 19, 2020

 

Math colloquium

Speakers: Sangmin Lee, Seoul National University

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

Room: VHV-007 (Veröld)
Time: Monday 24th January  10:00hrs

Abstract:

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, February 1, 2020

Math colloquium

Speaker: Ragnar Sigurðsson, University of Iceland

Title: Norms on complexifications of real vector spaces.

Room: VRII-258
Time: Thursday February 6th, 10:50 hrs.

Abstract:

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.

Lukas Schneiderbauer

Carlos Argaez Garcia, November 22, 2019

Staðsetning: HB5 (Háskólabíó)
Tími: Föstudag 29.Nóvember kl.11:40

Math colloquium

Speakers: Lukas Schneiderbauer, University of Iceland

Title: Non-Commutative Geometry: An introduction.

Room: HB5 (Háskólabíó)
Time: Friday 29th November, 11:40hrs

Abstract:

This is my attempt to introduce non-commutative geometry to mathematicians. After putting forward the main ideas and main theorem(s), I will concentrate on the construction of simple examples in the context of fuzzy spaces (special cases of non-commutative geometries). In case time still allows it, I shall tell you about my past research in this area.

Anna Helga Jónsdóttir och Benedikt Steinar Magnússon

Valentina Giangreco, November 19, 2019

Math colloquium

Speakers: Anna Helga Jónsdóttir and Benedikt Steinar Magnússon, University of Iceland

Title 1: Student evaluations of teaching at the University of Iceland – analysis of data from 2013 – 2017.

Abstract 1:

Student evaluations of teaching (ísl. kennslukönnun) is administrated at the end of each and every course at the University of Iceland with the purpose of improving teaching and learning. In the talk, analysis of data from student evaluations from 2013 to 2017 at the UI will be presented. Mixed effect models were used to investigate possible relationships between the grades students give courses and several variables, such as the age and gender of the student and the teacher, number of students taking the course and the average final grade in the course.

Title 2: Online course notes in Edbook and the role of the textbook

Abstract 2:

In the last years I, with the help of many good people, have been developing a platform for online course notes called Edbook (http://edbook.hi.is). It consists of using Sphinx, which was developed for and in Python, along with specialized extension suited for teaching material in Mathematics. We have been using these notes in a few courses, mostly big calculus courses. The students have overall been very happy with them but in the spring of 2019 I had students in Mathematical Analysis II (STÆ205G) answer a more detailed survey about their usage of the teaching material they used. I will introduce the Edbook platform and the results of the survey which raises some questions about the role of the textbook today.

Room: HB5 (Háskólabíó)
Time: Friday 22th November, 11:40hrs