Thesis topics
Yaroslav Bazaykin / Yaroslav Bazaikin · Department of Mathematics, UJEP
Possible directions to discuss. The scope and prerequisites are adapted to your background; a thesis may focus on theory, computation or mathematical exposition.
Curvature and the evolution of plane curvesBachelor’s / master’s
Study curve-shortening flow through explicit examples and simple numerical experiments. Start with circles and closed plane curves; a master’s extension may address stability or comparison of discretisations. Background: calculus and ordinary differential equations.
Topology of digital images: components, holes and persistenceBachelor’s / master’s
Construct small cubical complexes and compute topological descriptors. Examine how noise and image resolution change the result; extend to persistent homology or image reduction. Background: linear algebra; basic programming for the computational version.
Diffusion on networks and slow release from poresBachelor’s / master’s
Derive compartment models and compare networks with similar steady transport but different transient behaviour. Study conservation, eigenvalues and characteristic time scales. A master’s extension compares a reduced model with a diffusion PDE. Background: linear algebra and ODEs.
Sintering and surface-diffusion modelsMaster’s; introductory bachelor’s option
Explore how curvature-driven surface evolution changes a pore or a pair of particles. Compare geometric and phase-field descriptions, tracking volume, surface area and numerical error. Background: differential equations and numerical methods. An introductory version focuses on model derivation and simple examples.
Discrete geometry and affine invariants of polygonal curvesBachelor’s / master’s
Investigate which properties of a polygonal curve survive affine transformations. Begin with explicit planar examples and visualisations; more advanced work can study reconstruction or higher-dimensional curves. Background: linear algebra and geometry.
Interested? Email me with your programme and preferred direction. Teaching and supervision can be conducted in English.