When: every Wednesday 10am-11am
Where: KU Leuven, Belgium - Room B02.18 in the Department of Mathematics
Organisers: Sean Dewar, Alison La Porta, Signe Lundqvist.
Topics: Anything related to Rigidity Theory, Matroid Theory, and Discrete Geometry.
James Cruickshank, Bill Jackson, Tibor Jordán, Shin-ichi Tanigawa.
Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach
(3rd June 2026) Sebastian Seeman
Sections 1 and 2: Introduction to the survey paper
(10th June 2026) Sebastian Seeman
Section 2 continued
(17th June 2026) Sebastian Seeman
Sections 2.4 and 2.5: Graph extension operations and linked vertex pairs
(17th June 2026) Emiliano Lewski
Section 3: Rigidity and global rigidity in dimensions at most two
(24th June 2026) Emiliano Lewski
Section 3 continued
(1st July 2026) Bence Sógor
Section 4: Rigidity and global rigidity in higher dimensions
(8th July 2026) Bence Sógor
Section 4 continued
(22nd July 2026) Matthias Orth
Section 5.1.2: Simplicial circuits and Fogelsanger's theorem
Abstract: After defining abstract simplicial complexes and their associated graphs, I will introduce the k-simplicial matroid and simplicial k-circuits. We will look at edge contractions and see that these contractions do not preserve the property of being a simplicial k-circuit. However, a decomposition result due to Fogelsanger gives, by an inductive proof using contractions, vertex splitting, and gluing, that the graph of a simplicial k-circuit is rigid in (k+1)-dimensional Euclidean space. Finally, we will see a recent characterization due to Cruickshank, Jackson, and Tanigawa, of globally rigid graphs associated to simplical k-circuits.
(29th July 2026) Daniel Garamvolgyi (special guest)
Reconstructing point sets from unlabeled distance measurements
Abstract: Suppose that there is some point set in Euclidean space that we want to reconstruct up to isometry, but we are only given an unordered list of the distances of some point pairs. Under what conditions is this reconstructibility problem feasible? I will give a survey of old and new results around this question, focusing on the case of generic point sets.
(5th August 2026) Matthias Orth
Section 5.2.2: Rigidity and connections with commutative algebra
Abstract: In combinatorial commutative algebra, a central object of study are Stanley-Reisner rings (also known as face rings) associated with abstract simplicial complexes. We will see how properties of the simplicial complexes relate to those of their Stanley-Reisner rings. In particular, certain graded parts of the artinian reduction of these rings can be related to stress spaces of the graph of the simplicial complex. Furthermore, if the Stanley-Reisner ring is Cohen-Macaulay, then rigidity of the associated graph is equivalent to the injectivity of a multiplication map between some graded parts. The necessary algebraic background (systems of parameters, Cohen-Macaulay rings) will be provided. We can also briefly touch upon related topics such as the lower and upper bound theorems for (simplicial) convex polytopes as well as algebraic shifting.