—  Mathematics & Statistics

The TACO Seminar | Fall 2024

Wednesdays, 2:45–3:45. Zoom or Cuneo Hall 218

The TACO seminar focuses on topics in Topology, Algebra, Combinatorics, and Operators.

Organizers:  Emily Peters, Carmen Rovi

IES (the institute for environmental sustainability) is located at the corner of W. Sheridan and N. Kenmore Avenues, Chicago, IL (map)

Some of the talks will be on zoom. If you would like to attend a zoom talk please contact one of the organizers

September 11: Sergio A. Fernandez de Soto Guerrero (TU Graz) Triangulations of Flow Polytopes and their Duals via Tropical Geometry

Abstract: Flow polytopes are a type of polytopes that were born in the study of optimization. In recent years there is a great interest in these objects and how to triangulate them, because there are a large number of famous lattices that can be realized as the dual of the triangulation of flow polytopes, but the realization depends on the flow polytope. That is why we will talk about the possibility of using tropical geometry to give a general framework to make a realization of any lattice that arises from this type of triangulation for any flow polytope.

October 2: Alex Moon Kohnert Properties of Northeast Diagrams

Abstract: Kohnert polynomials and posets are combinatorial objects with deep representation theoretic meaning, generalizing both Schubert polynomials and Demazure characters, i.e., key polynomials. I will being this talk by exploring what Kohnert posets and polynomials are in general, then I will discuss some recent results centering on the Kohnert properties of northeast diagrams. I will present some conditions for the boundedness and rankedness of a northeas Kohnert poset and present a surprising connection between certain minimal elements and key diagrams. There will be a worksheet.

This is a joint work with Aram Bingham, Beth Anne Castellano, Kimberly Hadaway, Reuven Hodges, Yichen Ma, and Kyle Salois that originated at this yeas GRWC.

October 9: Hugh Thomas Flows in graphs via representation theory of gentle algebras

The flow polytope of an oriented graph is a geometrical object which encodes the ways that material can flow through a network. A recent paper by von Bell, Braun, Bruegge, Hanely, Peterson, Serhiyenko and Yip (arXiv:2203.01896) made an important and unexpected connection between the flow polytopes of (some) oriented graphs and the representation theory of (some) gentle algebras. We deepen the connection and relax the conditions on the oriented graphs. In my talk, I will give an introduction to both flow polytopes and gentle algebras -- I won't assume that either is already familiar. This is joint work with Abram, Bastidas, Brauner, Dequêne, Morales, and Park.

November 20: Anthony Lazzeroni Filtrations of quasi-symmetric functions in non-commuting variables.

In this talk we will connect the theory of the Hopf algebra of r-quasisymmetric functions, a one-parameter Hopf algebra that generalizes the Hopf algebra of symmetric functions and the Hopf algebra of quasisymmetric functions, to the noncommutative analog of the Hopf algebra of r-quasisymmetric functions. This is accomplished by defining a powersum basis for both of these Hopf algebras and defining a one parameter equivalence relation on these functions. We then quotient the noncommutative analog of the Hopf algebra of r-quasisymmetric function by this equivalence relation on powersum functions. This provides a one parameter Hopf algebra connecting the two theories.