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.
Open positions
Members
Faculty
Algebra and algebraic geometry
Coding theory and cryptography
Combinatorics
Lie theory and representation theory
Number theory
News
- 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 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 arxiv and individual homepages.
Scientific events
Upcoming
Seminars
Upcoming seminars
- 29.4. 16:15 Oula Kekäläinen: MSc thesis presentation: Generalization of Descartes' rule of signs to multivariate polynomials with real exponents – M3 (M234)
- 7.5. 15:15 Rodrigo Martín Sánchez-Ledesma (Complutense U. Madrid / INDRA): Overview and extension of root-based attacks against PLWE instances – M2 (M233)
The Polynomial Learning With Errors problem (PLWE) serves as the background of two of the four cryptosystems standardised in July 2022 by the National Institute of Standards and Technology to replace non-quantum resistant current primitives like those based on RSA, finite field based Diffie-Hellman and its elliptic curve analogue. Although PLWE is highly believed to be quantum resistant, unlike other post-quantum proposals like multivariate and some code based ones, this fact has not yet been established. Moreover, several vulnerabilities have been encountered for a number of specific instances. In a search for more flexibility, it becomes fully relevant to study the robustness of PLWE based on other polynomials, not necessarily cyclotomic. In 2015, Lauter et al. found a good number of attacks based on different features of the roots of the polynomial. In the present talk we present an overview of the approximations made against PLWE derived from these work, along with several new attacks which refine those by Lauter exploiting the order of the trace of roots over finite extensions of the finite field under the three scenarios laid out by Lauter et al, allowing to generalize the setting in which the attacks can be carried out. This is joint work with I. Blanco-Chacón and R. Durán.
- 13.5. 14:15 Dr. Benjamin Jany (TU Eindhoven): TBA – M2 (M233)
- 13.5. 16:15 Lilja Metsälampi: Midterm review – M3 (M234)
- 27.5. 11:15 Patricija Sapokaitė: Midterm review – M3 (M234)
- 3.6. 13:15 Prof. Sueli I. R. Costa (Unicamp, Brazil): TBA – M2 (M233)
- 13.6. 11:15 Okko Makkonen : Midterm review: TBA – M3 (M234)
- ANTA Seminar
- There are also number theory seminars at both at Turku and Helsinki.
Algebra and Discrete Mathematics at Aalto is supported by
Page content by: webmaster-math [at] list [dot] aalto [dot] fi
