The Discrete Math Seminar at Iowa State University is held on Thursdays at 2:10-3:00 pm in Carver 401 .
Some old talks are available on YouTube.
The seminar is organized by Grace McCourt and Bernard Lidický.
Aug 28 - Introduce yourself
Sep 4 - Sydney Miyasaki
Title: Phylogenetic Conflicts
Abstract: In computational genetics, the perfect phylogeny model is a simple but fundamental model of how speciation occurs under Darwinian evolution. Reconstructing an evolutionary history from observed characteristics of living species under this model is a well-studied and useful technique in the study of evolutionary lineages. However, this model does not always agree with data. In particular, a certain "three-gamete condition" captures all such disagreements. In this work, we use tools from extremal graph theory, namely flag algebras, to determine the asymptotically maximum number of such three-gamete conflicts that any set of observational data may have. In addition, we provide an asymptotic characterization of such observational data. This talk is based on joint work with Oliver Eulenstein, Anastasia Halfpap, Bernard Lidický, Florian Pfender, Jan Volec.
Sep 11 - Matt Burnam
Title: Spectrum of the q-Laplacian of a graph
Abstract: Given a finite graph G and a real number q, then q-Laplacian of G is the matrix qD + A where D is the diagonal degree matrix and A the adjacency matrix. The q-Laplacian is a generalization of several well-studied graph matrices: the adjacency matrix (q=0), the negative of the Laplacian (q=-1), and the signless Laplacian (q=1). Notably, the signless Laplacian is positive semi-definite and it relates to the line graph of G. We generalize this to the q-Laplacian for q = 1/(n-1). A graph is called K_n-decomposable if its edge set can be partitioned into edge-disjoint copies of K_n. The K_n-line graph of G is the line graph of the hypergraph whose edges are the disjoint copies of K_n. We show that the 1/(n-1)-Laplacian is positive semi-definite for K_n-decomposable graphs, and that its eigenvalues correspond to the eigenvalues of the K_n-line graph of G.
Sep 18 - Bernard Lidický
Title: Hypergraph Turán Problems
Abstract: Hypergraph Turán Problems became more approachable due to flag algebras. In this talk we will first focus on tight cycles without an edge. A tight k-cycle minus an edge C_k^- is the 3-graph on the vertex set [k], where any three consecutive vertices in the string 123...k1 form an edge. We show that for every k >= 5, k not divisible by 3, the extremal density is 1/4. Moreover, we determine the extremal graph up to O(n) edge edits. The proof is based on flag algebra calculations.
Then we describe new developments in solving large semidefinite programs that allows for improving several other bounds on Turán densities.
This talk is based on joint work with Connor Mattes, Florian Pfender and Jan Volec.
Sep 25 - Coy Schwieder
Oct 2
Oct 9 - Alec Helm (University of South Carolina) [Zoom]
Oct 16 - John Byrne (University of Delaware)
Oct 23 - Swaroop Hegde (University of Georgia) [Zoom]
Oct 30 - Tony Vuolo
Nov 6 - Sean Grate
Nov 13 - Jiaxi Nie (Georgia Tech)
Nov 20 - Flo Pfender (CU Denver)
Dec 4 - Dylan King (Caltech)
Dec 11
Nov 14-15 MAA Sectional meeting in Ames at ISU (local, come)
Jan 4-7 Joint Math Meetings
Mar 9-16 57th Southeastern International Conference on Combinatorics, Graph Theory & Computing (Boca)
Mar 27-29 Graduate Students Combinatorics Conference (Chicago)
Jun 22-25 SIAM Conference on Discrete Mathematics
Aug 5-8 MAA Mathfest (Boston)
TBA (April?) The 11th Lake Michigan Workshop on Combinatorics and Graph Theory)
TBA (Summer) Graduate Research Workshop in Combinatorics (GRWC 2026)