Commutative Algebra and Algebraic Geometry
Current topic: Investigation of algebraic singularities and their application to robotics
(Eero Hyry and Samuli Piipponen).
Discrete geometry
Current topic: Discrete Ricci curvatures on graphs
- How to derive global properties from local data?
- Related to graph theory, analysis, combinatorics, linear algebra, stochastics
- Theoretical results, applications, software
- International research group: Durham-Hefei-Tampere
(Riikka Kangaslampi)
Number theory
- We investigate mainly arithmetic functions (i.e., sequences of numbers) and matrices of integers
- Sequences and matrices appear almost everywhere in science and technology
- Our purpose is to explain the behaviour of these objects with theaid of algebraic, linear algebraic, number theoretic and discretemathematics tools
- We also apply computer-aided experimental methods jointly withJori Mäntysalo and others
- As an example let us mention that we could disprove latticetheoretically the famous Bourque-Ligh conjecture which claimsthat LCM matrices on GCD closed sets are always nonsingular.
(Pentti Haukkanen, Mika Mattila)
Topological data analysis
Current topic: develop algebraic theory of topological data analysis
(Eero Hyry, Markus Klemetti, Ville Puuska)