CombinaTexas Conferences

CombinaTexas 2020/21

CombinaTexas, a combinatorics conference in the South-Central United States, is an annual regional conference on Combinatorics, Graph Theory, and Computing. It is dedicated to the enhancement of both the educational and research atmospheres of the community of combinatorialists and graph theorists in Texas and the surrounding states. The aim of the CombinaTexas series is to increase communication between mathematicians in the region, promote the research of the regional combinatorics community, and provide a forum for presentation and discussion of developments in the field of combinatorics.

For more information about the CombinaTexas series, click here.

Basic Information

Texas A&M University,
College Station, TX,
February 20-21, 2021.
The conference will be done through ZOOM.

Registration

Registration is closed on Feb 13.
Information on the ZOOM link of the conference will be sent to regsitered participants on Feb 18.
Check the email account that you provided in the registration form. Contact the organizer cyan@math.tamu.edu if the link is broken.

Plenary Speakers

• Miklos Bona , University of Florida .
  • Title: + Permutation patterns and nonrational generating functions
    The solution of an enumeration problem is very often a generating function $F$. Some problems are too difficult for us to find the explicit form of $F$. This is almost always so in the theory of pattern avoiding permutations In this talk, we will introduce a method that leads to negative results that are rare in this part of combinatorics. When our method applies, it shows that $F$ is not a rational function, which provides at least some explanation of the fact that the original enumeration problem is difficult. As an example, we will prove that for the overwhelming majority of permutation patterns, the generating function of the corresponding generating function is not rational.
• Tri Lai , University of Nebraska-Lincoln.
  • Title: + Tilings of Semi-hexagons, Plane Partitions, Young Tableaux, and Classical Group Characters.
    We will talk about the fundamental connections between the tilings of semi-hexagons and various mathematical objects, including plane partitions, Young tableaux, and classical group characters. This is based on joint works with Sam Hopkins, Alejandro Morales, and Igor Pak.
• Chun-Hung Liu , Texas A&M University.
  • Title: + Clustered coloring for Hadwiger-type conjectures
    Hadwiger (Hajos, and Gerards and Seymour, respectively) conjectured that the vertices of every graph with no K_{t+1} minor (topological minor, and odd minor, respectively) can be colored with t colors such that any pair of adjacent vertices receive different colors. These conjectures are stronger than the Four Color Theorem and are either open or false in general. A weakening of these conjectures is to consider clustered coloring which only requires every monochromatic component to have bounded size instead of size 1. It is known that t colors are still necessary for the clustered coloring version of those three conjectures. Joint with David Wood, we prove a series of tight results about clustered coloring on graphs with no subgraph isomorphic to a fixed complete bipartite graph. These results have a number of applications. In particular, they imply that the clustered coloring version of Hajos’ conjecture is true for bounded treewidth graphs in a stronger sense. They also lead to the first linear upper bound for the clustered coloring version of Hajos’ conjecture and the currently best upper bound for the clustered coloring version of the Gerards-Seymour conjecture.
• Nathan Reading , North Carolina State University
  Title: + Lattice congruences of the weak order: Algebra, combinatorics, and geometry
  The talk will begin with a crash course on congruences on a finite lattice and the corresponding lattice quotients. To make the case that combinatorialists should care about congruences and quotients, we’ll flip through some examples of lattice quotients of the weak order. I will sketch a complete combinatorial model for congruences on (and quotients of) the weak order on permutations and talk about how it generalizes to other Coxeter groups. The talk will conclude with a discussion of the connections to geometry, representation theory, and string theory and a mention of current and future work.
• Stephanie van Willigenburg , University of British Columbia
  Title: + The e-positivity of chromatic symmetric functions
  The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity.
  In this talk we approach the question of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not e-positive.
  This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.
• Josephine Yu , Georgia Institute of Technology
  Title: + Topics in Real Tropical Geometry
  I will introduce tropical geometry and discuss some recent developments and future directions at the intersection of tropical geometry and real algebraic or convex geometry.

Schedule and Abstracts (Central Standard Time)

Schedule and Abstracts of Plenary Talks
Schedule and Abstracts of Contributed Talks
List of Registered Participants (by Feb 13, 2021)
Information of the ZOOM links will be distributed to registered participants on Feb 18.

Saturday, February 20, 2021

Sunday, February 21, 2021

Resources

A map of Texas A&M, and driving directions from the College Station airport.

A list of former CombinaTexas conferences.

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Acknowledgement:

This conference is supported in part by the Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program. PI members may use IMA/PI funds to support personnel's travel to this conference."

This conference is also supported in part by National Science Foundation, the Combinatorics Foundation, and Department of Mathematics at Texas A&M University.

Organizers

Laura Matusevich (Texas A&M University)
Jacob White (University of Texas Rio Grande Valley)
Catherine Yan (Texas A&M University)