webnotice

Abstract:We define the codegree of a given graph as the maximum number of neighbors that any two distinct vertices have in common.

Abstract: Webs are graphical objects that give a tangible, combinatorial way to compute and classify tensor invariants. Recently, Gaetz, Pechenik, Pfannerer, Striker, and Swanson (arXiv:2306.12501) found a rotation-invariant web basis for SL₄, as well as its quantum deformation U_q(sl₄), and a bijection between move equivalence classes of SL₄-webs and fluctuating tableaux such that web rotation corresponds to tableau promotion. They also found a bijection between the set of plane partitions in an a×b×c box and a benzene move equivalence class of SL₄-webs by determining the corresponding oscillating tableau. In this talk, I will similarly find the oscillating tableaux corresponding to plane partitions in certain symmetry classes by characterizing them via certain lattice words. A dynamical action on tableaux, called promotion, corresponds to rotation of SL₄-webs. I will show how promotion of certain subtableaux aligns with rotation of their respective webs. I will also show that this correspondence maps through a projection to either SL₂ or SL₃ webs. Moreover, this projection is exactly a partial evaluation of webs. This talk will be given through the lens of the combinatorics of webs and tableaux. Some of this work is joint with Jessica Striker.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Abstract: Cosmological correlation functions probe the quantum origins of structure in the universe and are a prototype for many calculations in physics. I will share recent work on the complexes, fans and polytopes associated to these functions based on arXiv:2602.21194 and ongoing work. Two structures lie at the heart of this story: (1) incidence relations between chains and anti-chains, (2) a notion of "nested sets of nested sets". Both structures can be studied for an arbitrary lattice, but building sets of the boolean lattice are my main motivation.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Abstract:We prove a conjecture by DeVos, Kwon and Oum on the unavoidable minors of matroids of high branch-depth. We also consider the properties of collections of crossing low order separations known as anemones. This is joint work with Jim Geelen and Rutger Cambell.

Abstract: It is well-known that every planar graph has a planar drawing with straight-line segments, even if vertices are restricted to lie on a grid with linear coordinates.  In this talk, we will study the question of finding planar graph drawings where the height H of the grid is as small as possible.   Dujmovic et al gave an FPT-algorithm that finds the minimum height.  However, it is not particularly adaptable to closely related problems, such as finding rectilinear drawings of minimum height.    We therefore study a new and completely different approach to test whether a graph has a drawing of height H.     Since such graphs have pathwidth O(H), a natural approach is to appeal to Courcelle's theorem.  This requires phrasing the problem in so-called monadic second-order logic (MSOL), but MSOL supports neither arbitrarily large integers nor permutations, making it difficult to use for graph drawing problems.   In this talk, we show that with some detours we can phrase the question of whether G has a straight-line drawing of height H in a radically different way ("no face has a fish") that can be easily expressed in MSOL.

Abstract: Causal Set Theory (CST) is a theory of quantum gravity where spacetime is taken to be a locally finite poset, called a causal set.  A central problem in CST is to determine physically relevant properties from the purely combinatorial information of the causal set.  In 2014 Glaser and Surya demonstrated that the distribution of interval sizes of a causal set sprinkled into a region of Minkowski space contains information about the dimension of the underlying spacetime.  In 2026 Surya showed that this distribution can be used to define a “closeness” function on causal sets that distinguishes by dimension and global topology.  In this talk we present work motivated by these results which investigates the more general notion of convex sets, instead of intervals, of a poset.  First, we will introduce a generating polynomial for convex sets in a finite poset and explore some of its properties.  We will then show that this polynomial is a complete invariant for the family of series-parallel posets.  Lastly, we discuss early results on the utility of this polynomial in CST.  The pre-seminar will introduce relevant background on CST.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Abstract: Praeger-Xu graphs are a family of multicovers of cycles, known for some of their surprising properties. A fundamental observation is that these graphs can be constructed from De Bruijn graphs. In this presentation, we will generalize the definition of De Bruijn graphs to create a broader family of multicovers. Finally, we will compute the automorphism group and show some applications of our constructions. This is a joint work with Ci Xuan Wu.