# MAM Seminars Spring term 2018

Higher seminars in the subject Mathematics/Applied Mathematics, Spring term 2018.

School of Education, Culture and Communication (UKK), Mälardalen University.

**Program for Mathematics and Applied Mathematics seminar. **

**Spring term 2018**

*Wednesdays afternoon is the normal time for MAM seminars with deviations when necessary. The program is always provisional. The information about each specific talk at MAM seminar becomes final the day before.*

*Suggestions for talks at MAM seminar are very welcome to *

*Prof. Sergei Silvestrov sergei.silvestrov@mdh.se.*

**March 21, 2018, Wednesday, 15.15-16.30**

Location: U3-083 (Hilbert room), Västerås, UKK, Mälardalen University

__Speaker__: Andriy Andreev, Associate Professor, Department of Statistics, Stockholm University, Sweden

__Title: __Conditional Value of Risk Estimation using Diffusion Theory

__Abstract:__

Conditional Value-at-Risk (CVaR) has received a good deal of attention as an appealing tool for risk management. Major advantage of CVaR is that in addition to being intuitive, we can often calculate it analytically. In this talk, we present closed formulas, which give us exact CVaR for several given marginal distributions. Student’s t-distribution will be discussed in more detail as a partial case of general solution.

**May 14, 2018, Monday, 15.15 - 16.00**

Location: U2-129, Västerås, Mälardalen University

__Speaker__: Antonio Possolo, NIST Fellow and the Chief Statistician for the National Institute of Standards and Technology (NIST)

(https://www.nist.gov/people/antonio-possolo)

__Title:__ Trustworthy Measurement for Reproducible Research

__Abstract:__

In a 2014 editorial published in Nature, Marcia McNutt (President, National Academy of Sciences) notes: "Reproducing an experiment is one important approach that scientists use to gain confidence in their conclusions. Recently, the scientific community was shaken by reports that a troubling proportion of peer-reviewed preclinical studies are not reproducible." Once recognized best practices in measurement science will become widely adopted throughout the sciences, they will help boost confidence in scientific conclusions, and mitigate the so-called "reproducibility crisis". Those best practices can be subsumed in the concept of trustworthy measurement, which tracks the truth sufficiently closely, with assuredly high confidence. This presentation explains the meaning of these characteristics that define trustworthy measurement, including a discussion of measurement uncertainty, calibration, traceability, comparability, and consilience. Several concrete examples serve as illustrations, including historical retrospectives on the measurement of the Planck constant and of the speed of light.

__About Speaker: __

Antonio Possolo is a NIST Fellow and the Chief Statistician for the National Institute of Standards and Technology (NIST). NIST is the national metrology institute of the U.S., responsible for ensuring the inter-comparability of measurements made in all areas of science, engineering, and commerce, nationally and internationally, and for the production of measurement standards. NIST employs about 3000 scientists, engineers, technicians, and support and administrative personnel. NIST scientists have won the Nobel prize in physics on four different occasions, most recently in 2012. Antonio holds a Ph.D. in Statistics from Yale University. Besides his current role in government, he has previous experience in industry (General Electric, Boeing), and in academia (Princeton University, University of Washington in Seattle, University of Lisboa). He is committed to the development and application of probabilistic and statistical methods that contribute to advances in science and technology, and in particular to measurement science. Antonio is a member of the Commission on Isotopic Abundances and Atomic Weights, of the International Union of Pure and Applied Chemistry. He is also a member of Working Group 1 of the Joint Committees for Guides in Metrology, at the International Bureau of Weights and Measures (Paris, France), responsible for the Guide to the Expression of Uncertainty in Measurement. He chairs the Working Group on Statistics and Uncertainty of the Inter-American System of Metrology.

**May 16, 2018, Wednesday, 16.10 (Note time!) - 17.00**

Location: U2-158, Västerås, Mälardalen University

__Speaker__: Mohammad Hossein Mehrabi, Department of Applied Mathematics, Iran University of Science and Technology

__Title:__ The rearrangement of a function and some properties of it

__Abstract:__

About the solution of an inverse semilinear elliptic equation, we involved in a concept which is called "rearrangement of a function". So, the title of my speech can be "The rearrangement of a function and some properties of it". We say two real-valued functions is the rearrangement of each other, if measure of every superlevel set of them is equal to each other.

**May 29, 2018, Wednesday, 15.30-16.30**

**PhD defense of Alex Behakanira Tumwesigye **

Location: Kappa, Västerås, Mälardalen University

The public defense of Alex Behakanira Tumwesigye's doctoral thesis in Mathematics/Applied Mathematics will take place at Mälardalen University, room Kappa (Västerås Campus) at 13.00 on May 29, 2018.

The title of the thesis is “Dynamical systems and commutants in non-commutative algebras”.

**Summary**

The thesis treats commutativity which is a fundamental topic in mathematics, physics, engineering and many other fields. Two processes are said to be commutative if the result of the processes does not depend on the order in which the processes are applied. Commutativity of addition can be observed when paying for items at the counter by cash. No matter the order in which bills are handed over, they always give the same total, whereas washing and then drying clothes, and drying and then washing produce markedly different results.

Another example of the importance of commutativity comes from signal processing. Signals pass through filters (often called operators on a Hilbert space by mathematicians) and commutativity of two operators corresponds to having the same result even when filters are interchanged.

Many important relations in mathematics, physics and engineering are represented by operators satisfying a number of commutation relations. This means that the operators do not actually commute but there is an explicit relation for the difference of the two possible products of the operators.

The first part of this thesis treats commutativity of monomials of pairs of operators satisfying certain commutation relations. We consider products of powers of the operators, called monomials, and derive commutativity conditions of the said monomials. It is shown that this is related to the existence of periodic points of certain one-dimensional dynamical systems.

In the second part of the thesis, Maximal commutative subalgebras of crossed products of algebras of piecewise constant functions with the integers. By the crossed product of an algebra with the integers we mean a generalization of Laurent polynomials with coefficients from the algebra. We describe commutants (set of elements that commute with a given set) and the center (set of elements that commute with the whole algebra) in a number of cases.

Finally, we turn attention to Ore extensions. By an Ore extension of a ring, We mean a generalization of polynomials with coefficients from the ring. I describe the commutant of the coefficient algebra for the Ore extension of the algebra of functions on a set.

**May 30, 2018, Wednesday**

**EMMI-AAA 2018 International workshop**

**Engineering Mathematics and Mathematics in Industry – Algebra, Analysis and Applications**

Location: Zeta 10.00-12.00, Lambda after 13.00-18.00, Västerås, Mälardalen University