| Talk_id | Date | Speaker | Title |
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9249
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Tuesday 1/23
4:10 PM
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Bruce Sagan, MSU
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An Introduction to Stanley's Theory of P-Partitions. I
- An Introduction to Stanley's Theory of P-Partitions. I
- 01/23/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Bruce Sagan, MSU
Richard Stanley developed a powerful generalization of the theory of integer partitions where the parts of the partition are arranged on any labeled poset P. In this first lecture we will develop some intuition by computing the generating functions for various families of ordinary integer partitions. This will motivate Stanley's generalization which will be discussed in the second lecture. No background will be assumed.
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9250
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Tuesday 1/30
4:10 PM
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Bruce Sagan, MSU
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An Introduction to Stanley's Theory of P-Partitions, II
- An Introduction to Stanley's Theory of P-Partitions, II
- 01/30/2018
- 4:10 PM - 5:00 PM
- C517 Wells Hall
- Bruce Sagan, MSU
In this second lecture we will describe how Stanley associated to any labelled poset P a set of partitions having a rational generating function. Its denominator only depends on the number of elements of P and the numerator can be computed using an associated set of permutations and the major index statistic. If one bounds the size of the parts, then the major index is replaced by the number of descents.
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9272
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Tuesday 2/13
4:10 PM
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Nick Ovenhouse, MSU
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Cluster Expansions Using Snake Graphs
- Cluster Expansions Using Snake Graphs
- 02/13/2018
- 4:10 PM - 5:00 PM
- C517 Wells Hall
- Nick Ovenhouse, MSU
We will begin by outlining the construction of a cluster algebra associated to any surface with boundary (and marked points). Then we will discuss a formula, due to Schiffler, which explicitly gives an arbitrary cluster variable as a Laurent monomial in the initial variables, using the perfect matchings of an associated graph, called a "snake graph".
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12277
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Tuesday 2/20
4:10 PM
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Alexander Wilson, MSU
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Determining the Regularity of Formal Languages
- Determining the Regularity of Formal Languages
- 02/20/2018
- 4:10 PM - 5:00 PM
- C517 Wells Hall
- Alexander Wilson, MSU
The concept of a regular language is very useful for computers parsing data and generally in theoretical computer science. We will define a formal language, what makes a formal language regular, and methods to decide whether a language is regular.
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12278
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Tuesday 2/27
4:10 PM
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Oliver Pechenik, University of Michigan
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Taking the long way home: Orbits of plane partitions
- Taking the long way home: Orbits of plane partitions
- 02/27/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Oliver Pechenik, University of Michigan
Plane partitions are piles of cubes stacked in the corner of a room. P. Cameron and D. Fon-der-Flaass (1995) studied a simple action on such piles, whose dynamics are nonetheless quite mysterious. In particular, repeating this action will always eventually return the original pile, but sometimes the voyage is much longer than expected. Motivated by some deep problems in algebraic geometry, H. Thomas and A. Yong (2009) introduced a suite of combinatorial algorithms on certain grids of numbers. In particular, there is a beautiful K-theoretic promotion operator, which again has some mysteriously large orbits, despite its simple combinatorial definition. We'll see how these two mysteries are in fact the same mystery, and use this relation to explain special cases of both actions. (Based on joint work with Kevin Dilks and Jessica Striker)
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13311
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Tuesday 3/27
4:10 PM
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John Machacek, MSU
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A hypergraphic combinatorial Hopf algebra
- A hypergraphic combinatorial Hopf algebra
- 03/27/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- John Machacek, MSU
We will give a brief introduction to combinatorial Hopf algebras using a Hopf algebra structure on hypergraphs as the main example. Combinatorial reciprocity results that can be obtain by combining Aguiar-Bergeron-Sottile character theory and antipode formulas will be emphasized. In particular, we will see a generalization of Stanley's theorem on acyclic orientations.
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13312
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Tuesday 4/3
4:10 PM
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John Machacek, MSU
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Hypergraphic polytopes
- Hypergraphic polytopes
- 04/03/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- John Machacek, MSU
We will define and study hypergraphic polytopes. These polytopes make up a proper subset of all generalized permutahedra and include all graphic zonotopes. We will show how the normal fan of hypergraphic polytopes can be understood in terms of acyclic orientations of hypergraphs. This will provide additional understanding of the antipode of the hypergraphic Hopf algebra from last week.
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13326
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Tuesday 4/10
4:10 PM
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Daniel Johnston, Grand Valley State University
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On Rainbow Turán Numbers
- On Rainbow Turán Numbers
- 04/10/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Daniel Johnston, Grand Valley State University
For a fixed graph F, we consider the maximum number of edges in a properly edge-colored graph on n vertices which does not contain a rainbow copy of F, that is, a copy of F all of whose edges receive a different color. This maximum, denoted by ex^*(n; F), is the rainbow Turán number of F, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstr\"ate [Combinatorics, Probability and Computing 16 (2007)]. In this talk, we look ex^*(n; F) when F is a forest of stars, and consider bounds on ex^*(n; F) when F is a path with m edges, disproving a conjecture in the aforementioned paper for m = 4. This is based on joint work with Cory Palmer, Puck Rombach, and Amites Sarkar.
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13331
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Tuesday 4/24
4:10 PM
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Linhui Shen, MSU
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Cluster Duality for Grassmannians and Cyclic Sieving
- Cluster Duality for Grassmannians and Cyclic Sieving
- 04/24/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Linhui Shen, MSU
The Grassmannian Gr(k,n) parametrizes k-dimensional subspaces in C^n. Due to work of Scott, the homogenous coordinate ring C[Gr(k,n)] of Gr(k,n) is a cluster algebra of geometric type. In this talk, we introduce a periodic configuration space X(k,n) equipped with a natural potential function W. We prove that the topicalization of (X(k,n), W) canonically parametrizes a linear basis of C[Gr(k,n)], as expected by a duality conjecture of Fock-Goncharov. We identify the tropical set of (X(k,n), W) with the set of plane partitions. As an application, we show a cyclic sieving phenomenon involving the latter. This is joint work with Jiuzu Hong and Daping Weng.
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