Algebra & Discrete Mathematics Seminar

Algebra & Discrete Mathematics Seminar

Spring 2025 Schedule
  • Spring 2025 Location: Minard 118
  • Time: Tuesday 10:00 --10:50 am
  • Organizer: Jessica Striker
Fall 2024 Schedule
  • Fall 2024 Location: Minard 212
  • Time: Tuesday 10:00 --10:50 am
  • Organizer: Jessica Striker
Spring 2024 Schedule
  • Spring 2024 Location: Minard 302
  • Time: Tuesday 10:00 --10:50 am
  • Organizer: Jessica Striker
Fall 2023 Schedule
  • Fall 2023 Location: Minard 212
  • Time: Tuesday 10:00 --10:50 am
  • Organizer: Jessica Striker

19 September 2023

No seminar

26 September 2023

Jessica Striker (NDSU): Hourglass plabic graphs and symmetrized six-vertex configurations, Part 2

Abstract: In this talk, we discuss the title objects and explore their intriguing connections to tableaux dynamics, alternating sign matrices, and plane partitions. We will also discuss the reason we defined these objects, namely, that they index a rotation-invariant SL4-web basis, a long-sought structure. This is joint work with Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, and Joshua P. Swanson.

10 October 2023

Joshua P. Swanson (University of Southern California): Type B q-Stirling numbers

Abstract: The Stirling numbers of the first and second kind are classical objects in enumerative combinatorics which count the number of permutations or set partitions with a given number of blocks or cycles, respectively. Carlitz and Gould introduced q-analogues of the Stirling numbers of the first and second kinds, which have been further studied by many authors including Gessel, Garsia, Remmel, Wilson, and others, particularly in relation to certain statistics on ordered set partitions. Separately, type B analogues of the Stirling numbers of the first and second kind arise from the study of the intersection lattice of the type B hyperplane arrangement. We combine the two directions and introduce new type B q-analogues of the Stirling numbers of the first and second kinds. We will discuss connections between these new q-analogues and generating functions identities, inversion and major index-style statistics on type B set partitions, and aspects of super coinvariant algebras which provided the original motivation for the definition. This is joint work with Bruce Sagan.

Thursday, 12 October 2023

Stephan Pfannerer (Technische Universitat Wien): Promotion and growth diagrams for r-fans of Dyck paths

Abstract: Using crystal graphs one can extend the notion of Schützenberger promotion to highest weight elements of weight zero. For the spin representation of type B_r these elements can be viewed as r-fans of Dyck paths. We construct an injection from the set of r-fans of Dyck paths of length n into the set of chord diagrams on [n] that intertwines promotion and rotation. This is done in two different ways: 1) as fillings of promotion–evacuation diagrams 2) in terms of Fomin growth diagrams This is joint work with Joseph Pappe, Anne Schilling and Mary Claire Simone.

Location: Minard 208

Time: 11:00am

7 November 2023

Ben Adenbaum (Dartmouth): Involutive Groups from Graphs

Abstract: We present a generalization of the toggle group, when thought of as a proper edge coloring of the Hasse diagram of the associated poset. Beyond general structure results, we focus on the case where the associated graph is a tree. This talk is based on joint work with Jonathan Bloom and Alexander Wilson.

28 November 2022

Tim Ryan (NDSU): The Picard group

Abstract: The Picard group is a fundamental invariant of an algebraic variety. In this introductory talk, we will describe the Picard group starting with basic concepts. After defining it, we will explain a classical result, the Lefschetz hyperplane theorem, and a classical object, the Noether-Lefschetz locus of surfaces of degree d. These ideas will be central to next week’s colloquium and seminar by César Lozano Huerta.

Note: this talk is supplemental and is NOT required to understand either of next week’s talks, though I aim to make it helpful.

5 December 2023

César Lozano Huerta (Universidad Nacional Autónoma de México - Oaxaca): The Noether-Lefschetz loci formed by determinantal surfaces in projective 3-space

Abstract: Solomon Lefschetz showed that the Picard group of a general surface in P3 of degree greater than three is ℤ. That is, the vast majority of surfaces in P3 have the smallest possible Picard group. The set of surfaces of degree greater than 3 on which this theorem fails is called the Noether-Lefschetz locus. This locus has infinite components and their dimensions are somehow mysterious.In this talk, I will calculate the dimension of infinite Noether-Lefschetz components that are simple in a sense, but still give us an idea of the complexity of the entire Noether-Lefschetz locus. This is joint work with Montserrat Vite and Manuel Leal.