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Seminars
Upcoming Seminars:
Select which seminar you are interested in:
- CSC Seminar
- Discrete Math Seminar
- Number Theory Seminar
- Operations Research Seminar
- Seminar on Teaching Mathematics
- Global Warming Spring 2011 Seminar Series: A Science Perspective
Discrete Math Seminars
Discrete Math seminar: Shonda Gosselin
Tuesday, May 14 - 2:30pm to 3:30pm
Title: Algebraic hypergraph decompositions
Abstract:
We examine edge decompositions of complete uniform hypergraphs whose parts are permuted transitively by a permutation of the vertex set. We present an algebraicmethod for constructing such a hypergraph decomposition which is related tothe well known Paley graph construction. The construction is derived from apartition of the cosets of a group and a function from the power set of thevertex set into this group. Several examples will be constructed using different groups and we discuss the symmetry and other properties of the hypergraphs we obtain.
Abstract:
We examine edge decompositions of complete uniform hypergraphs whose parts are permuted transitively by a permutation of the vertex set. We present an algebraicmethod for constructing such a hypergraph decomposition which is related tothe well known Paley graph construction. The construction is derived from apartition of the cosets of a group and a function from the power set of thevertex set into this group. Several examples will be constructed using different groups and we discuss the symmetry and other properties of the hypergraphs we obtain.
Discrete Math Seminar: Steven Melczer
Tuesday, May 21 - 2:30pm to 3:30pm
Title: Classifying Lattice Walks in the Quarter Plane
Abstract: The enumeration of walks in restricted regions is an elegant and active area in combinatorics. Recently, much work has been done attempting to classify these walks by analytic properties of their generating functions. We discuss this classication and its usefulness, with a focus on walks in the quarter plane using small steps. In particular, we recap previous results in this area and outline a method of classifying the final walks of this type not yet proven by other means.
Abstract: The enumeration of walks in restricted regions is an elegant and active area in combinatorics. Recently, much work has been done attempting to classify these walks by analytic properties of their generating functions. We discuss this classication and its usefulness, with a focus on walks in the quarter plane using small steps. In particular, we recap previous results in this area and outline a method of classifying the final walks of this type not yet proven by other means.
Discrete Math seminar: Andrew Poelstra
Tuesday, May 28 - 2:30pm to 3:30pm
Title: RamseyScript and Double Arithmetic Progressions
Abstract: Ramsey Theory is the study of very persistent structures: structures which
are monochromatic under any finite coloring of some set. For example, every
finite coloring of the naturals contains monochromatic solutions to the
equation x + y = z. Equivalently, there is a least integer N(r) such that
every r-coloring of {1, 2, ..., N(r)} has a monochromatic solution. There
are no good bounds for N(r) and exact values are only known for small r
through computational search.
We introduce the program RamseyScript, which does computational searches
for this and similar problems for integer colorings, sequences, words on
finite alphabets and permutations. It is operated through a simple script
language and obviates much single-purpose code.
We also discuss an open Ramsey problem: does every finite coloring of the
natural numbers contain double arithmetic progressions? We discuss the
history of the problem and present evidence toward a solution gathered
through RamseyScript.
Abstract: Ramsey Theory is the study of very persistent structures: structures which
are monochromatic under any finite coloring of some set. For example, every
finite coloring of the naturals contains monochromatic solutions to the
equation x + y = z. Equivalently, there is a least integer N(r) such that
every r-coloring of {1, 2, ..., N(r)} has a monochromatic solution. There
are no good bounds for N(r) and exact values are only known for small r
through computational search.
We introduce the program RamseyScript, which does computational searches
for this and similar problems for integer colorings, sequences, words on
finite alphabets and permutations. It is operated through a simple script
language and obviates much single-purpose code.
We also discuss an open Ramsey problem: does every finite coloring of the
natural numbers contain double arithmetic progressions? We discuss the
history of the problem and present evidence toward a solution gathered
through RamseyScript.
Discrete Math seminar: Brian Alspach
Thursday, Jun 6 - 2:30pm to 3:30pm
Title: The Coxeter Group Project: A Progress Report
Abstract: If one forms a Cayley graph on the symmetric group using only transpositions
for the connection set, then the graph is bipartite. In 2006, Araki proved that if such a
Cayley graph is connected, then for any two vertices u and v in different parts, there is
a Hamilton path whose terminal vertices are u and v. Of course, the symmetric group is
a Coxeter group. The speaker has embarked on a project of extending Araki's Theorem
to Cayley graphs on other families of Coxeter groups. This talks is a summary of what
has been achieved so far.
Abstract: If one forms a Cayley graph on the symmetric group using only transpositions
for the connection set, then the graph is bipartite. In 2006, Araki proved that if such a
Cayley graph is connected, then for any two vertices u and v in different parts, there is
a Hamilton path whose terminal vertices are u and v. Of course, the symmetric group is
a Coxeter group. The speaker has embarked on a project of extending Araki's Theorem
to Cayley graphs on other families of Coxeter groups. This talks is a summary of what
has been achieved so far.
Discrete Math seminar: Robert Samal
Tuesday, Jun 18 - 2:30pm to 3:30pm