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May 2018

Emily Barnard, Northeastern University, Graph Associahedra and the Poset of Maximal Tubings

May 7, 2018 | 3:00 pm - 4:00 pm EDT

Given a graph G on n vertices, Postnikov defined a graph associahedron  P_G as an example of a generalized permutohedron, a polytope whose  normal fan coarsens the braid arrangement. Combinatorially, each face of  P_G corresponds to certain collections of compatible…

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September 2018

Sami Assaf, University of Southern California, Inversions for reduced words

September 10, 2018 | 3:00 pm - 4:00 pm EDT

The number of inversions of a permutation is the number of pairs (i < j) for which w_i > w_j. This important statistic that arises in many contexts, including as the minimum number of simple transpositions needed to express the…

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Bojko Bakalov, NC State, An operadic approach to vertex algebras and Poisson vertex algebras

September 24, 2018 | 3:00 pm - 4:00 pm EDT

Following Beilinson and Drinfeld, we describe vertex algebras as Lie algebras in a certain pseudo-tensor category. More precisely, starting from a vector superspace V with a linear operator on it, we introduce the operad of n-ary chiral operations on V. When V is…

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October 2018

Michael Strayer, University of North Carolina at Chapel Hill, Finite and infinite minuscule and d-complete posets from Kac-Moody representations

October 1, 2018 | 3:00 pm - 4:00 pm EDT

The finite minuscule and d-complete posets generalize Young and shifted Young diagrams.  They have many nice combinatorial properties; for example, minuscule posets are Gaussian and Sperner, and d-complete posets have the hook length and jeu de taquin properties.  Infinite analogs…

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Darij Grinberg, University of Minnesota, Multiline queues and their generating functions

October 15, 2018 | 3:00 pm - 4:00 pm EDT

Multiline queues were introduced by Ferrari and Matrin as a tool for understanding the steady state of the Totally Asymmetric Simple Exclusion Process (TASEP) on a ring. Since then, they have attracted independent interest as combinatorial objects. A queue can be described as a…

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Rekha Biswal, Laval University, Affine structure and tableaux models for E_7 crystals

October 22, 2018 | 3:00 pm - 4:00 pm EDT

A Kirillov-Reshetikhin(KR) module is a certain finite dimensional U_q'(\mathfrak{g}) module that is determined by its Drinfeld polynomials. KR modules are an important class of modules for quantum groups with many applications to Mathematical physics. KR modules are conjectured to have many nice properties, one…

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November 2018

Naihuan Jing, NC State, Yangian algebras of classical types

November 5, 2018 | 3:00 pm - 4:00 pm EST

Yangians are one of the main examples of quantum groups introduced by Drinfeld and have found applications in combinatorics, representation theory and algebraic geometry. It is well-known that the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation.…

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December 2018

Saúl Blanco Rodríguez, Indiana University, Cycles in the pancake and burnt pancake graph

December 3, 2018 | 3:00 pm - 4:00 pm EST

The pancake graph has the elements of the symmetric group as vertices and there is an edge between two permutations if there is a prefix reversal that transforms one permutation into the other. One can similarly define the burnt pancake graph using signed permutations instead of…

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January 2019

Travis Scrimshaw, University of Queensland, Towards a uniform model for higher level Kirillov-Reshetikhin crystals

January 28, 2019 | 2:00 pm - 3:00 pm EST

Kirillov-Reshetikhin (KR) modules are a special class of finite-dimensional modules for affine Lie algebras that have deep connections with mathematical physics. One important aspect is that they are conjectured to have crystal bases, which is known except for affine type…

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February 2019

Yeeka Yau, University of Sydney, Coxeter systems for which the Brink-Howlett automaton is minimal

February 18, 2019 | 3:00 pm - 4:00 pm EST

In their celebrated 1993 paper, Brink and Howlett proved that all finitely generated Coxeter groups are automatic. In particular, they constructed a finite state automaton recognising the language of reduced words in a Coxeter group. This automaton is not minimal…

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March 2019

Jason Elsinger, Florida Southern College, On the irreducible characters and representations of orbifold lattice vertex algebras

March 4, 2019 | 3:00 pm - 4:00 pm EST

Given a positive-definite even lattice Q, one can construct a lattice vertex algebra V. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the subalgebra of fixed points, known as an orbifold, corresponding to an isometry…

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Adam Marcus, Princeton University, Ramanujan colorings

March 29, 2019 | 2:00 pm - 3:00 pm EDT

An important construction for (the information theoretic version of) semantic security is a "Biregular Irreducible Function" (BRI). These can be constructed from a complete biregular graph on $2^k d \times 2^k d$ by by coloring it with $2^k$ colors in…

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April 2019

Juan Villarreal, Virginia Commonwealth University, Logarithmic singularities in vertex algebras

April 15, 2019 | 3:00 pm - 4:00 pm EDT

In this talk we want to consider a different kind of singularities in logarithmic vertex algebras. In vertex algebras many properties arise from the locality of their fields. In particular, this implies the expansion of their brackets into a base of delta function and…

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Aram Dermenjian, University of Quebec at Montreal, Facial weak order in hyperplane arrangements

April 22, 2019 | 3:00 pm - 4:00 pm EDT

We discuss the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first introduced on the braid arrangements by Krob, Latapy, Novelli, Phan and…

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September 2019

Corey Jones, Ohio State University, Vanishing of categorical obstructions for permutation orbifolds

September 9, 2019 | 3:00 pm - 4:00 pm EDT

Modular tensor categories are rich mathematical structures. They are important in the study of 2D conformal field theory, arising as categories of modules for rational vertex operator algebras. The orbifold construction A-> A^{G}  for a finite group G is a fundamental method for producing…

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Emily Gunawan, University of Connecticut, Cambrian combinatorics on quiver representations

September 30, 2019 | 3:00 pm - 4:00 pm EDT

Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice (of triangulations of a polygon). We give a new geometric way…

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October 2019

Yan Zhuang, Davidson College, Counting permutations by peaks, descents, and cycle type

October 7, 2019 | 3:00 pm - 4:00 pm EDT

We present a general formula describing the joint distribution of two permutation statistics—the peak number and the descent number—over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formula involves a certain kind of plethystic substitution…

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Duff Baker-Jarvis, Wake Forest University, QSym and the Shuffle Compatibility of Permutation Statistics

October 21, 2019 | 3:00 pm - 4:00 pm EDT

The fundamental basis of the Hopf algebra of quasisymmetric functions, QSym, can be thought of in terms of shuffling permutations.  We can think of QSym as having a basis indexed by equivalence classes of permutations, where we identify permutations with…

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Jason Brown, Dalhousie University, Independence Polynomials and Their Roots

October 28, 2019 | 3:00 pm - 4:00 pm EDT

Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G. In addition to encoding useful information about the graph (such as the number of vertices, the number of edges and the independence…

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December 2019

Thomas McConville, University of North Carolina at Greensboro, Chapoton triangles from multidimensional Catalan objects

December 9, 2019 | 3:00 pm - 4:00 pm EST

Chapoton triangles are polynomials in two variables defined by Coxeter-Catalan objects. These polynomials are related by some remarkable identities that only depend on the rank of the associated (finite) Coxeter system. The multidimensional Catalan numbers enumerate the number of standard Young tableaux of a…

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