Algebra and Discrete Mathematics
Welcome to the home page of the research area of
Algebra and Discrete Mathematics at Aalto University. Our members conduct research in areas that include algebraic geometry, algebraic statistics, combinatorics, coding theory, cryptography, Lie theory, matrix theory, number theory, and representation theory.
Members
Faculty
Algebra and algebraic geometry
Coding theory and cryptography
Combinatorics
Lie theory and representation theory
Number theory
News
- Camilla Hollanti and Ragnar Freij-Hollanti, together with their international team, have won an international mathematical challenge launched by GMV in collaboration with Trampoline Network.
- Rahinatou Yuh Njah Nchiwo won the 3 Minute Thesis competition at the Finnish Quantum Days in September 2024.
- Oscar Kivinen started as an Assistant Professor in September 2023.
Prospective students
Research
We provide
bachelor's,
master's and
doctoral theses topics related to the above areas. The links contain lists of current topics and past theses. Contact the faculty and check their personal webpages for more info.
You are also welcome to take part in any of our
lecture courses related to algebra and discrete mathematics.
Recent publications
Here is the
research output for the Algebra and Discrete Mathematics area. On this site you can also find the research output of individuals and links to full texts of articles when available. For preprints check the
math arxiv and individual homepages.
Scientific events
Seminars
Upcoming seminars
- 2.12. 11:15 Signe Lundqvist (KU Leuven): Scenes over non-generic pictures of hypergraphs – M2 (M233) and https://aalto.zoom.us/j/69981271101
The central problem in scene analysis is finding the space of d-dimensional polyhedral caps with a fixed projection to (d-1)-dimensional space. In particular, we are interested in which sets of points in (d-1)-dimensional space are the projections of non-trivial polyhedral caps, in the sense that the hyperplanes of the polyhedral cap are distinct.
Given the combinatorial structure of the polyhedral cap, studying the space of d-dimensional polyhedral caps with a fixed generic projection becomes a combinatorial problem. Specifically, liftings of generic projections can be studied via a lifting matrix. Whiteley characterised independence in the row-matroid of the lifting matrix for generic projections. The dual problem to studying scenes over generic projections is the problem of studying the space of parallel redrawings of hyperplane arrangements.
In this talk, we will focus on liftability of non-generic projections, or, dually, parallel redrawings of non-generic hyperplane arrangements. For a class of polyhedral caps, we will see that the set of projections that lift to non-generic polyhedral caps with the correct combinatorial structure is given as the zero-set of a single polynomial, called the pure condition. We will see some basic properties of the pure condition, and how to easily compute it.
The talk will be based on joint work with Daniel Bernstein.
Algebra and Discrete Mathematics at Aalto is supported by
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