Лекции профессора Штефана Шмита по алгебраическому анализу данных

Уважаемые коллеги, приглашаем Вас на доклады гостя отделения прикладной математики и информатики проф. Штефана Шмидта (Политехнический Университет Дрездена, Институт Алгебры), которые состоятся в здании на Покровском бульваре д.11 (см. аннотации внизу) среда 26 мая, 13:00, аудитория Д-316 Лекции организованы при финансовой поддержке компании "Яндекс"  

Уважаемые коллеги,

 

приглашаем Вас на доклады гостя отделения прикладной математики и информатики проф. Штефана Шмидта (Политехнический Университет Дрездена, Институт Алгебры), которые состоятся в здании на Покровском бульваре д.11 (см. аннотации внизу)

 

среда 26 мая, 13:00, аудитория Д-316

 

Лекции организованы при финансовой поддержке компании "Яндекс" 

 

Speaker: Stefan E. Schmidt

 

Titlte: On Algebraic Data Analysis

 

 

четверг 27 мая, 15:00, аудитория Д-316

 

Speakers: Stefan E. Schmidt and Franziska Leonhardi

 

Title: Musicà MathàArtsàMusicà

 

 

С уважением,

Заведующий Отделением

прикладной математики и информатики

 

С.О. Кузнецов

 

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Wednesdsay, May 26, 13:00

 

Speaker: Stefan E. Schmidt

 

Titlte: On Algebraic Data Analysis

 

 

 

Abstract: In our lecture we will discuss interdependencies between qualitative and quantitative methods

in data approximation. Our modeling crucially involves idempotent isotone selfmaps on posets (partially ordered sets) on the qualitative side and isotone evaluations of posets on the quantitative side. We will discuss how the general dimension theory for lattices developped by Fred Wehrung can be weakenend adequately. This will lead us to approximations of the concept of probability via the concepts of belief and plausibility (as introduced by Dempster and Shafer and vastly extended by Grabisch). On the qualitative side this approximation is reflected in the concepts of kernel and closure operators on lattices. Finally, we will discuss applications to data clustering via rough set theory and formal concept analysis.

 

Thursday May 26, 15:00

 

Speaker: Stefan E. Schmidt and Franziska Leonhardi

 

Title: Musicà MathàArtsàMusicà

 

Abstract: Among those pioneering mathematicians who shed some light on the world of music theory, we want to mention Pythagoras and Leonhard Euler, and more contemporary, Rudolf Wille and Guerino Mazzola. Their common objective was the description of phenomena of music via mathematical means, that is, they came up with a mathematical modeling of music theory. While Pythagoras and Euler developed a theory of proportions and harmony, Wille and Mazzola sketched out a set-theoretic approach which is closely related to category theory.  A systematic description of tone, chroma, and interval is given in Wille’s and Neumeier’s “extensional standard language” for music theory; also concepts like sound (pattern) and harmony (pattern) are strictly defined in a formal mathematical fashion, which contrasts the more ambiguous use in classical music theory.

 

The fundamental modeling idea is a psychoacoustic one, which is not primarily based on physics. For example, a fifth plus a fourth is an octave, while in physics the proportion of the fifth multiplied by the proportion of the fourth is the proportion of an octave, that is, (3:2)x(4:3)=1:2.

 

Our presentation will differ from a usual lecture style since we aim to combine a traditional mathematical modeling approach with semiotics using graph theory and category theory. This will lead us to the fundamental notion of a tone structure where a covariant functor transforms syntactical intervals into semantic ones. Our considerations will be put into the framework of a general theory of measurement.

 

In a second part, we will connect the previous with arts. In particular, we will discuss how one may be able to see music. Can mathematics help to give people some good visual experience of music? What can we say about relationships between mathematics, arts and music involving sign language? We will present how collaboration with the artist Franziska Leonhardi in a project www.paulus2011.de  has raised questions about the visualization of music using fine arts and mathematics. Can the oratorio of Mendelssohn Bartholdy be experienced by deaf people?

 

The mathematical language involving semiotics will be confronted with semiotics used in arts of different cultures around the world.  Our presentation itself should be considered as a contribution which aims to experience mathematics within a greater cultural context.

 

Everyone is cordially invited to the interdisciplinary lecture jointly given by the mathematician and musician Prof. Dr. Stefan E. Schmidt, Dresden University of Technology, and by Franziska Leonhardi, artist for painting/graphic/other visual media www.franziska-leonhardi.de.