Mathematical Modeling and Analysis

Åke Brännström

Main area of research: Mathematical Ecology 

Åke Brännström Professor

Email

+46 90 786 78 62

Christian Ewald

Main area of research: Mathematical Finance and Economics

Topic areas for bachelor theses:

• mathematical modeling and pricing of financial derivatives
• modeling of natural resources and their extraction
• financial risk management and insurance

Example of possible thesis projects:

• applying Monte-Carlo simulation to price exotic derivatives contracts
• use dynamic programming to determine optimal extraction rates of natural resources such as minerals, forestry or fisheries
• mathematical modeling of principal agent problems, incentives, both static and dynamics

Christian Ewald Professor

Email

+46 90 786 73 14

Eric Libby

Main area of research: Mathematical biology and modeling

Topic areas for bachelor theses:

• Differential equations-based models of biological populations
• Computational simulations of evolution
• Spatial models of organismal growth
• Network models of interactions

Example of possible thesis projects:

• Modeling competition and cooperation in microbial populations
• Simulating the growth and development of an organism following different programs in different environments
• Applying physics-based or economics-based concepts to microbial populations

Eric Libby Associate professor

Email

+46 90 786 91 70

Niklas Lundström

Many fundamental laws of physics and chemistry can be formulated as ordinary or partial differential equations. In the social sciences, mechanics, optimization, control theory, economics and life sciences, differential equations and systems of differential equations are often used to model the behavior of complicated systems.

Example of possible thesis projects:

• Management strategies for hydropower plants
• Harvesting strategies and stability of fish population
• Analysis of vibration in rotor systems
• Hidden chaos in a Jeffcott rotor with clearance
• The p-Laplace equation and the stochastic game tug-of-war
• Growth of viscosity subsolutions of nonlinear PDEs in unbounded cylinders
• Existence and uniqueness of solutions to systems of PDEs related to optimization

You may choose to work mainly with the application or with the mathematical theory, or both. If interested, contact:

Niklas Lundström Associate professor

Email

+46 90 786 63 86

Antti Perälä

The study of various spaces of analytic functions is a topic active ongoing research. The most common spaces are different variants of Hardy, Bergman, BMOA and Bloch spaces. The basic theory of all of these provides good topics for thesis projects that can be adapted to the student's interests and ambitions. There are also many natural concrete operators acting on these spaces, such as Toeplitz, Hankel, Volterra and composition operators.

Possible topics:

• Basic theory of Hardy and/or Bergman spaces
• Bergman kernel and Bergman projection
• Bloch space and conformal mappings
• Theory of one or several concrete operators on these spaces
• Carleson measures

It is also possible to make project of more functional analytic nature. These projects do not necessarily need to be linked to complex analysis or operator theory.

Possible topics:

• Spectral theory and Fredholm operators
• Topological vector spaces
• Zorn's lemma in analysis

Other topics can also be discussed. Many of these topics are quite advanced for a BSc project; instead it possible to choose one these topics and study the basic theory needed for dealing with these.

Suggested literature (note that all of these books go way beyond the scope of a BSc/Msc project):

• Zhu, Operator theory in function spaces
• Zhu, Spaces of holomorphic functions in the unit ball
• Böttcher and Silbermann, Analysis of Toeplitz operators
• Pavlovic, Function classes in the unit disk
• Rudin, Functional analysis
• Horvath, Topological vector spaces and distributions

Antti Perälä Associate professor

Email

+46 90 786 53 75