Thesis supervisor: Miklós Pálfia
Location of studies (in Hungarian): CUB Abbreviation of location of studies: BCE
Description of the research topic:
"The theory of gradient flows is an active research area of dynamical systems that is fundamental to solving differential equations and optimization problems. In the 1950s this theory was developed in Banach spaces by the Crandall-Liggett theory. This theory constructs nonlinear operator semigroups by using the resolvent operator, and this semigroup provides the solution to the associated initial value problem. Here the theory of monotone (non-linear) operators plays a key role in obtaining contraction properties of these flows. These tools are also suitable for examining and solving PDEs. The heat flow is such a semigroup which links this to the field to probability theory. The law of large numbers has recent generalizations that use the discrete form of gradient flows, which is nothing but an application of the gradient method to solve a convex least squares optimization problem. This way, the law of large numbers can be generalized to non-Euclidean spaces, thus opening the way towards a nonlinear probability theory. The goal is to generalize the classical theorems of probability theory and other important nonlinear convex optimization methods to solve problems. Applications include medical imaging, radar technology, DNA sequencing, control theory in robotics to name a few.
The ideal candidate has basic knowledge in probability theory, analysis and optimization theory, as well as good English language skills. Previous research experience and knowledge of functional analysis is an advantage."
Number of students who can be accepted: 1
Deadline for application: 2024-12-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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