Monthly group meetings
of the Advances in Applied Algebraic Geometry Group at KU Leuven
of the Advances in Applied Algebraic Geometry Group at KU Leuven
The A3G group at KU Leuven is led by Fatemeh Mohammadi.
The purpose of the monthly group meetings is to keep scientific exchange within the group lively and to discuss general organization issues coming up in the group.
Each meeting includes one to two informal presentations on current research, problematics that arise there, or suggestions for new projects.
The monthly group meetings are currently organized by Daniel Windisch.
For a list of the current and former group members, see here.
Dates and Presentations
22.06.2026, 14:00 - 15:30, Room Math 02.18
Ryoshun Oba (Sorbonne): Characteristic p method in generic Lefschetz theory
In resolving g-conjecture and Hibi-Ohsugi conjecture (unimodality of h-vector of homology spheres and h*-vector of IDP reflexive polytopes respectively), Adiprasito, Papadakis and Petrotou established the Hard Lefschetz property for the generic Artinian reductions of face rings and Ehrhart rings. The key idea is to work in characteristic 2 and replace the positive definiteness in the Hodge-Riemann bilinear form with anisotropy, which is derived from the Parseval-Rayleigh-type identity on the volume map. We extend these techniques to any graded Gorenstein rings and give a condition for generic Lefschetz theory to work. This condition immediately implies the generic Lefschetz property for broad classes of rings: toric face rings, determinantal rings, Pfaffian rings, to name a few. Moreover, I present an example of a Gorenstein domain without the generic Lefschetz property. This is based on joint work with Karim Adiprasito, Eric Katz, Stavros Papadakis, and Vasiliki Petrotou.
27.05.2026, 14:00 - 15:30, Room Math 05.100
Daisie Rock: Pixelation
I will introduce a type of categorical approximation called pixelation. This talk will be mostly hand waving about the abstract definitions and theorems. However, a running example will ground us all the way through. We will touch on applications to representation theory and algebraic geometry and speculate about applications to persistent homology. (arXiv:2603.25432)
21.04.2026, 14:00 - 15:30, Room Math 05.100
Erdenebayar Bayarmagnai: Orbits of polynomial maps and their geometric structure
We study orbits of polynomial endomorphisms of $\mathbb{C}^n$ from an algebraic-geometric perspective. Under a dimension-preserving or a linearity assumption, we show that the Zariski closure of an orbit decomposes into finitely many irreducible components of equal dimension, together with a zero-dimensional part. We further discuss several consequences of this result and present algorithms for computing orbit closures under suitable conditions.
George Kenison: The Minimality and Positivity Problems for Second-Order Holonomic Sequences
A recursively defined sequence is holonomic if it satisfies a linear recurrence relation with polynomial coefficients. This talk will discuss two open decision problems, those of Positivity and Minimality, that are open even for the class of holonomic sequences that satisfy three-term (or second-order) recurrence relations. Time permitting, we will draw connections to the convergence of polynomial continued fractions, Diophantine approximation, and equality testing procedures.
10.03.2026, 14:00 - 15:30, Room Math 05.100
Akihiro Higashitani: Toric degenerations of Grassmannians using matching fields
Abstract: Toric degenerations of Grassmannians Gr(r,n) have been intensively studied in recent years, motivated by connections to several areas of mathematics. One approach to constructing such degenerations is via a SAGBI basis of the Plücker algebra, where matching fields play a key role in this context. These constructions give rise to toric varieties (lattice polytopes), for which the theory of combinatorial mutations provides a powerful tool. In this talk, I will discuss the SAGBI construction, the role of matching fields, and how combinatorial mutation equivalence can be used to establish key results.
04.02.2026, 14:30 - 16:00, Room Math 02.18
George Kenison: Reachability and Invariants for Linear Loops
Abstract: In this introductory talk, we will discuss computational problems related to linear loops (loops whose update assignments are all linear in the loop variables). These problems will come in several flavours such as, does a linear loop reach a specified target? and does the orbit of a linear loop stay within a permitted domain? We will give a broad overview of several open problems as well as their connections to problems in dynamical systems and algebraic geometry.
14.01.2026, 14:00 - 15:30, Room Math 02.18
Sebastian Seemann: Vandermonde cells and positive geometries
Abstract: We will define Vandermonde cells and provide 2 definitions of positive geometries. We will discuss examples and how Vandermonde cells fit into each framework.
03.12.2025, 14:00 - 15:30, Room Math 02.18
Sean Dewar: The Cayley-Menger variety and secant varieties
04.11.2025, 13:30 - 15:00, Room CS 05.128
Signe Lunqvist: Rigid realizations of graphs and scenes