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February 2018

Harm Derksen, University of Michigan, Matrix Invariants and Complexity

February 19, 2018 | 3:00 pm - 4:00 pm EST

We consider the action of the group SL_n x SL_n on the space of m-tuples of n x n matrices by simultaneous left-right multiplication. Visu Makam and the speaker recently proved that invariants of degree at most mn^4 generate the invariant ring. This…

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Nathan Reading, NC State, To scatter or to cluster?

February 26, 2018 | 3:00 pm - 4:00 pm EST

Scattering diagrams arose in the algebraic-geometric theory of mirror symmetry. Recently, Gross, Hacking, Keel, and Kontsevich applied scattering diagrams to prove many longstanding conjectures about cluster algebras. Scattering diagrams are certain collections of codimension-1 cones, each weighted with a formal power series. In this…

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March 2018

Karola Mészáros, Cornell University, Product formulas for volumes of flow polytopes

March 26, 2018 | 3:00 pm - 4:00 pm EDT

The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed netflow at each vertex. We will examine flow polytopes arising from permutation matrices, alternating sign matrices…

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April 2018

Sergi Elizalde, Dartmouth College, Cyclic descents of standard Young tableaux

April 16, 2018 | 3:00 pm - 4:00 pm EDT

Cyclic descents of a permutation were defined by Cellini, by allowing the permutation to wrap around as if the last entry was followed by the first. A natural question is whether a similar, well-behaved notion of cyclic descents exists for…

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Ying Zhou, Brandeis University, Tame Hereditary Algebras have finitely many m-Maximal Green Sequences

April 23, 2018 | 3:00 pm - 4:00 pm EDT

Keller introduced the concept of maximal green sequences. Brustle-Dupont-Perotin proved that tame quivers have finitely many maximal green sequences. We have generalized the result to m-maximal green sequences. This talk will include a gentle introduction to tame path algebras, their indecomposable modules, silting objects…

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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 | 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 | 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 | 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 | 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 | 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 | 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 | 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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