Väitös (matematiikka): MSc Rahim Kargar


26.6.2024 klo 12.00 - 16.00
MSc Rahim Kargar esittää väitöskirjansa ”Metrics and Quasiconformal Maps” julkisesti tarkastettavaksi Turun yliopistossa keskiviikkona 26.06.2024 klo 12.00 (Turun yliopisto, Agora, XX-luentosali, Turku).

Yleisön on mahdollista osallistua väitökseen myös etäyhteyden kautta: https://utu.zoom.us/j/61578190536 (kopioi linkki selaimeen).

Vastaväittäjänä toimii professori Swadesh Kumar Sahoo (Indian Institute of Technology Indore, Intia) ja kustoksena professori Matti Vuorinen (Turun yliopisto). Tilaisuus on englanninkielinen. Väitöksen alana on matematiikka.

Väitöskirja yliopiston julkaisuarkistossa: https://urn.fi/URN:ISBN:978-951-29-9765-7


Tiivistelmä väitöstutkimuksesta:

In my dissertation, I studied the geometric function theory, which is a subfield of classical analysis. The subject of research is conformal and quasi-conformal mappings, as well as harmonic mappings and their properties. One key topic is to study the distortion of the distances of pairs of points under the mappings with the help of special functions.

The importance of the research field is based on connections and applications, e.g. physics, technology, and other fields of mathematics, e.g. dynamical systems, potential theory, and number theory.

In my research, I examine various methods of determining the distances between pairs of points within subdomains of Euclidean space with the help of metrics and the transformation of the distances measured in this way under the mappings. The most suitable metrics include hyperbolic, quasihyperbolic, and visual angle metrics.

The most important observations are the following:
• comparison of the hyperbolic metric with intrinsic metrics within a convex polygonal domain;
• an efficient algorithm for calculating special functions that occur;
• new formulas for the visual angle metric of the unit disk and with the help of these, a new version of Schwarzs lemma was stated;
• considerations related to Harnacks inequality;
• presentation of topics suitable for further research.

My research brings new ideas to the theory of this research area and illustrates the accuracy of the achieved results with examples.