Projects
Explicit Methods in Quadratic Form Theory. University of Antwerp
Hochschild cohomology and deformation theory of triangulated categories. University of Antwerp
Orthogonal Polynomials and Matrix Computations. Applications of Recurrence Relations. KU Leuven
Univariate and multivariate polynomials play a fundamental role in pure and applied mathematics.
In this text orthogonal polynomials and their corresponding recurrence relations are studied
and connected to matrix computations
and applied in polynomial interpolation and approximation and in polynomial system solving.
For univariate orthogonal polynomials on the complex unit circle, efficient algorithms for ...
The Reidemeister spectrum and the R-infinity property for residually nilpotent groups KU Leuven
Any automorphism of a group G determines an equivalence relation of twisted conjugacy on G. The equivalence classes are called Reidemeister classes and their number is the Reidemeister number of the automorphism. These notions originate from topological fixed point theory, where they correspond to fixed point classes, but nowadays these appear also in many other branches of mathematics, such as algebraic geometry, cryptography, ... . The ...
Back to the roots of data-driven dynamical system identification KU Leuven
To obtain data-driven dynamic models for simulation, prediction, monitoring, classification or control tasks, in applications e.g. in Industry 4.0 and eHealth, most identification methods ‘solve’ an optimization problem, relying on some nonlinear iterative algorithm. Undeniably, too many heuristics prevail: What do we mean by ‘solved’? Where did the algorithm converge to? Is the model globally optimal, unique and reproducible?
To tackle ...
Cryptanalysis of post-quantum cryptosystems KU Leuven
Polymathy and Interdisciplinarity in Premodern Islamic Epistemic Cultures Ghent University
KNOW is the first comprehensive study of polymathy and interdisciplinarity in premodern Islam. The project sets out to write a history
of knowledge that takes the interaction between disciplines as its primary subject. The project’s historical framework is the postformative period, 1200-1800 CE, which saw the rise of new institutions of learning, the proliferation of libraries, the formation and
integration of disciplines and ...
Efficiency and security aspects of post-quantum cryptography KU Leuven
This thesis will advance the state of the art in two types of post-quantum cryptography, namely, isogeny-based cryptography and multivariate cryptography. A particular emphasis will be put on cryptanalysis and efficiency of both systems leveraging methods from algebraic geometry and number theory.
ManiFactor: Factor analysis for maps into manifolds KU Leuven
A central topic in data science is constructing a data-driven surrogate
model that approximates an unknown multivariate target function f.
The key goal of a surrogate model is to predict the outputs of the
target function both accurately and efficiently. A practical data-driven
surrogate model of f can be constructed numerically from
approximate input-output pairs by a learning algorithm, is
computationally cheap ...