• Joshua Cooper , University of South Carolina.
  • Title: + Probing the Structure of Graph Nullspaces with Zero Loci
    The adjacency nullity of graphs’ and hypergraphs’ adjacency matrices is something of a mystery, though there are nice results for some narrow classes of graphs such as trees. There is, however, rich structure in their nullspaces (and, for hypergraphs, their nullvarieties), visible by partitioning nullvectors according to their zero loci: vertex sets which are indices of their zero coordinates. This set system is the lattice of flats of a ``kernel matroid'', a subsystem of which are the ``stalled'' sets closed under skew zero forcing (SZF), a graph percolation/infection model known to have connections with rank and nullity. These set systems have interesting descriptions in terms of matchings, vertex covers, and edges’ influence on rank – especially for trees. For a wide variety of graphs, the lattice of SZF-closed sets is also a matroid, a fact which can be used to obtain a polynomial-time algorithm for computing the skew zero forcing number. This contrasts with the general case, where we show that the corresponding decision problem is NP-hard. We also define skew zero forcing for hypergraphs, and show that, for linear hypertrees, the poset of SZF-closed sets is dual to the lattice of ideals of the hypergraph's nullvariety; while, for complete hypergraphs, the SZF-closed sets and the zero loci of nullvectors are more loosely related.
• Sergi Elizalde , Dartmouth College
  • Title: + Descents on noncrossing and nonnesting permutations
    Stirling permutations were introduced by Gessel and Stanley to give a combinatorial interpretation of certain polynomials related to Stirling numbers, which count set partitions with a given n\ umber of blocks. A natural extension of Stirling permutations are noncrossing (also called quasi-Stirling) permutations, which are in bijection with labeled rooted plane trees. Archer et al. introduced these permutations, and conjectured\ that there are $(n+1)^{n-1}$ such permutations of size $n$ having $n$ descents.
    In this talk we prove this conjecture and, more generally, we find the generating function for noncrossing permutations by the number of descents. We show that some of the properties of descents \ on usual permutations and on Stirling permutations also hold for noncrossing permutations.
    Finally, we consider a nonnesting analogue, and we show that the polynomial giving the distribution of the number of descents on nonnesting permutations is a product of an Eulerian polynomial and\ a Narayana polynomial. It follows that, rather unexpectedly, this polynomial is palindromic.
• Patricia Klein , Texas A&M University.
  • Title: + Generalizations of vertex decomposition
    The Stanley--Reisner correspondence relates abstract simplicial complexes to squarefree monomial ideals in polynomial rings. Much can be learned about the squarefree monomial ideal, and the variety it defines, by studying the corresponding simplicial complex. For example, Reisner's criterion gives a way to assess Cohen--Macaulayness of a variety determined by a squarefree monomial ideal by studying the homology of its simplicial complex. Vertex decomposition is a technique of breaking down a simplicial complex into smaller simplicial complexes in a manner that tracks a good deal of information about the homology of the complex. More precisely, if a simplicial complex is vertex decomposable, then its associated ideal determines a Cohen--Macaulay variety. We will review basic definitions and properties of vertex decomposition and then consider generalizations of vertex decomposition to not-necessarily-monomial ideals in polynomial rings and to complexes of polytopes associated to toric varieties.
• Bernard Lidicky , Iowa State University.
  • Title: + Applications of Flag Algebras
    Flag algebras is a tool developed by Razborov for solving problems in extremal graph theory and combinatorics. The tool is very general and it lead to breakthrough results on many long standing open problems. It was applied in the area of graphs, hypergraphs, permutations, Ramsey numbers, discrete geometry and phylogenetic trees to name a few areas. The method provides results in the limit, which can be translated to large structures with small error terms. The method is also closely related to the notion of dense graph limits. In the talk we give a brief introduction to the method and show some applications.
• Andrew Suk , University of California San Diego
  Title: + On higher dimensional point sets in general position
  An old question of Erdos asks: Given a set of $N$ points in $R^d$ with no $d+2$ members on a common hyperplane, what is the size of the largest subset of points in general position (i.e., no $d+1$ members on a hyperplane)? In 2018, Balogh and Solymosi showed that one can use the hypergraph container method to tackle this problem in the plane. In this talk, I will show how to use the container method to tackle Erdos' question in any dimension. This is joint work with Ji Zeng.
• Sheila Sundaram , Independent
  Title: + Positivity problems in combinatorial representation theory
  In this talk I will survey some positivity questions which arise in considering representations of the symmetric group. The first set of questions comes from the character table itself, which presents interesting conjectures. The second set of questions arises from poset homology. Here I will discuss various enumerative conjectures, some that are long-standing and others that are new.

Schedule and Abstracts (Central Standard Time)

All the academic activities will be held on the first floop of Blocker Building on the Texas A&M Campus. This is where the Math Dept locates.
The registration and break room are at BLOC 140/141.
The plenary talks will be given in BLOC 169
For contributed talks, session A is at BLOC 169 and session B is at BLOC 164.
Here is an interactive campus map .

Updated April 14: PROGRAM: Schedule and Abstracts of All Talks

Location, Transportation, Parking

All the activities will be held at the third floor of Blocker Building on the campus of Texas A&M University.

The Northside Garage (NSG) is located directly across from the Blocker Building (BLOC) and has space for visitor parking. (One needs to pay if park here.) During the weekend, you can also park for free at any un-reserved space in a numbered lot, such as Lot 47 and Lot 51. (On the northwest side of the campus, near Univesity Drive and the Bon Fair Memorial)

The interactive campus map also lists available parking lots. Move to the rigth side to see the parking lots 47 and 51.

For details, see Special Parking Regulations at TAMU

Night and weekend parking is available 5 pm to 6 am for valid permit holders in unrestricted/unnumbered spaces in most lots except lots 30, 40, 72, 99 and 122. Night and weekend parking at West Campus Garage begins at 4pm.

No permit is required in unrestricted or plain marked spaces on Saturday, Sunday, or days when the University is officially closed. Exceptions include Lot 30, 40, 72, 99, 122, the golf lot, special event parking and athletic events. Notifications are posted at the entrance to the lot(s) affected during these events.

Texas A&M University is located in College Station, Texas, which by automobile lies about 1 hour and 30 minutes northwest of Houston, 1 hour and 45 minutes east of Austin, and 3 hours south of Dallas. Easterwood Airport in College Station is served by American Airlines (connecting to Dallas). There is also a shuttle service from Bush Intercontinental Airport and Hobby Airport in Houston and a shuttle service from Austin-Bergstrom Airport.