Title Promoter Affiliations Abstract
"Subgraphs and codes in distance-regular graphs in incidence geometry" "Frank De Clerck" "Department of Mathematics: Algebra and Geometry" "My project includes the application of techniques in algebraic graph theory, to obtain new bounds and non-existence results in geometry. Conversely, finite geometries can yield new (distance-regular) graphs with certain properties, and algebraic techniques can yield a characterization of them. In particular, I intend to further examine a proposed construction relying on substructures in a specific dual polar graph."
"Study of m-systems in finite projective spaces en associated incidence geometries" "Frank De Clerck" "Department of Mathematics: Algebra and Geometry" "From m-systems one can construct incidence geometries in particular, by using generalised linear representation. It is already known that in certain cases this method leads to semipartial geometries, and it is likely that in other similar cases, weaker properties can be found. We also endeavour to obtain more results on existence and non-existence of m-systems in some specific polar spaces."
"Intertwining Extremal Combinatorics and Finite Geometry" "Leo Storme" "Department of Mathematics: Analysis, Logic and Discrete Mathematics" "Extremal combinatorics investigates finite objects such as graphs or set systems with extremal properties. Finite geometry investigates finite incidence structures. For decades there have been interesting interactions between both areas: (1) Finite geometry provides examples of graphs and hypergraphs with extremal properties for extremal combinatorics. (2) Problems in extremal combinatorics on families of finite sets generalize naturally to questions on families of subspaces in finite vector spaces.This proposal will investigate some of these connections: (1) Low degree Boolean functions on vector spaces. (2) The investigation of q-analogs of hypergraph Turán problems. (3) Pseudorandom clique-free graphs and Ramsey numbers.These particular topics have broad relevance with applications in combinatorics and computer science."
"Structurable algebras, representation theory and related point-line geometries" "Tom De Medts" "Department of Mathematics: Algebra and Geometry" "The goal of the project is to investigate connections between algebraic structures (linear algebraic groups, Jordan pairs, structurable algebras, Lie algebras) and geometric structures (especially point-line geometries, but also so-called root filtration spaces). We will often rely on the representation theory of the underlying groups."
"Exceptional Groups and Exceptional Geometries in the Theory of Tits Buildings" "Hendrik Van Maldeghem" "Department of Mathematics: Algebra and Geometry" "The aim is (1) to write some books on buildings and geometries, focusing on the exceptional types, making use of the Freudenthal-Tits Magis Square, and (2) continue and intensify my research around the same Magic Square. "
"Buildings of exceptional type: their geometries and their representations." "Hendrik Van Maldeghem" "Department of Mathematics: Algebra and Geometry" "My project is about buildings, abstract geometric objects introduced to get a grip on certain classes of groups. Classical examples are projective and polar spaces. Exceptional examples are buildings of type G2, F4, E6, E7 and E8, widely studied in mathem"
"A functorial approach to projective representations of Tits-buildings and the associated groups of Lie type." "Hendrik Van Maldeghem" "Department of Mathematics: Algebra and Geometry" "The aim of the project is to take the axioms of Mazzocca-Melone describing Veronese varieties as a solid base for a functor mapping classical Tits-buildings to other classical or exceptional Tits-buildings of higher rank. This we, we lay the foundations for a systematic treatment of representations of Tits-buildings."
"Affine buildings and CAT(0)-spaces" "Hendrik Van Maldeghem" "Department of Mathematics: Algebra and Geometry" "The theory of buildings (developed by Jacques Tits) studies certain (incidence) geometric objects with close ties to Algebra and Geometric Group Theory. In our project we want to study the class of affine buildings and various closely related objects using these different points of view."