Talk_id  Date  Speaker  Title 
4655

Tuesday 1/31 4:10 PM

WeiHsuan Yu, MSU

New bounds for equiangular lines and spherical twodistance sets
 New bounds for equiangular lines and spherical twodistance sets
 01/31/2017
 4:10 PM  5:00 PM
 C304 WH
 WeiHsuan Yu, MSU
The set of points in a metric space is called an sdistance set if pairwise distances between these points admit only s distinct values. Twodistance spherical sets with the set of scalar products {alpha, alpha}, alpha in [0,1), are called equiangular. The problem of determining the maximal size of sdistance sets in various spaces has a long history in mathematics. We determine a new method of bounding the size of an sdistance set in twopoint homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical twodistance set in R^n is n(n+1)/2 with possible exceptions for some n = (2k+1)^23, k a positive integer. We also prove the universal upper bound ~ 2 n a^2/3 for equiangular sets with alpha = 1/a and, employing this bound, prove a new upper bound on the size of equiangular sets in an arbitrary dimension. Finally, we classify all equiangular sets reaching this new bound.

4648

Tuesday 2/7 4:10 PM

Bruce Sagan, MSU

Matrices with given row and column sums, I
 Matrices with given row and column sums, I
 02/07/2017
 4:10 PM  5:00 PM
 C304 WH
 Bruce Sagan, MSU
This is an expository talk and no background will be assumed. Given two integral vectors R = (r_1,...,r_m) and S = (s_1,...,s_n) we wish to know whether there exists an m x n matrix A whose ith row has sum r_i and whose jth column has sum s_j for all i, j. Such matrices have applications via the Transportation Problem. We will discuss the fundamental results in this area, including the GaleRyser Theorem.

4649

Tuesday 2/14 4:10 PM

Bruce Sagan, MSU

Matrices with given row and column sums, II
 Matrices with given row and column sums, II
 02/14/2017
 4:10 PM  5:00 PM
 C304 WH
 Bruce Sagan, MSU
In this continuation of the first talk, I will discuss new results by Brualdi and myself where we impose various symmetry conditions on the desired matrix A via the action of the dihedral group of the square.

4692

Tuesday 2/21 4:10 PM

Emad Zahedi, MSU

On Distance Preserving and Sequentially Distance Preserving Graphs
 On Distance Preserving and Sequentially Distance Preserving Graphs
 02/21/2017
 4:10 PM  5:00 PM
 C304 WH
 Emad Zahedi, MSU
A graph H is an isometric subgraph of G if d_H(u,v) = d_G(u,v), for every pair u,v in V(H), where d denotes distance. A graph is distance preserving (dp) if it has an isometric subgraph of every possible order. We consider how to add a vertex to a dp graph so that the result is a dp graph. This condition implies that chordal graphs are dp. A graph is sequentially distance preserving (sdp) if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i at least 1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sdp. In closing, we discuss our results, other work and open problems concerning dp graphs.

4693

Tuesday 2/28 4:10 PM

Emad Zahedi, MSU

On Distance Preserving and Sequentially Distance Preserving Graphs
 On Distance Preserving and Sequentially Distance Preserving Graphs
 02/28/2017
 4:10 PM  5:00 PM
 C304 WH
 Emad Zahedi, MSU
A graph H is an isometric subgraph of G if d_H(u,v) = d_G(u,v), for every pair u,v in V(H), where d denotes distance. A graph is distance preserving (dp) if it has an isometric subgraph of every possible order. We consider how to add a vertex to a dp graph so that the result is a dp graph. This condition implies that chordal graphs are dp. A graph is sequentially distance preserving (sdp) if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i at least 1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sdp. In closing, we discuss our results, other work and open problems concerning dp graphs.

4707

Tuesday 3/14 4:10 PM

Nick Ovenhouse, MSU

Cluster Algebras and Compatible Poisson Brackets
 Cluster Algebras and Compatible Poisson Brackets
 03/14/2017
 4:10 PM  5:00 PM
 C304 WH
 Nick Ovenhouse, MSU
We will discuss basic definitions and examples of cluster algebras and Poisson brackets, and the relationship between the two.

4720

Tuesday 3/21 4:10 PM

Nicholas Ovenhouse, MSU

LogCanonical Coordinates for Poisson Brackets
 LogCanonical Coordinates for Poisson Brackets
 03/21/2017
 4:10 PM  5:00 PM
 C304 WH
 Nicholas Ovenhouse, MSU
In symplectic geometry, Darboux's theorem gives socalled 'canonical' local coordinates, in which the Poisson bracket (obtained from the symplectic structure) takes a particularly simple form: all brackets of coordinate functions are constants. We investigate whether something analogous is true for Poisson varieties (when the coordinate change is only allowed to be rational functions), and give a negative answer in the case of logcanonical coordinates.

4729

Tuesday 3/28 4:10 PM

Robert Davis, MSU

What polytopes tell us about toric varieties
 What polytopes tell us about toric varieties
 03/28/2017
 4:10 PM  5:00 PM
 C304 WH
 Robert Davis, MSU
Polytopes are among the oldest mathematical objects that have been studied. Often, people want to find their volumes, identify triangulations, and describe their lattice points, and more. But why bother doing this? From a combinatorial perspective, the data often answer counting questions that one might have. However, there is much more depth from an algebrogeometric standpoint: this information is often useful for learning about certain toric varieties.
In the first of these talks, I will give the background needed to understand what a normal projective toric variety is and how to model them using polytopes. In the second talk, I will define several properties that an algebraic geometer may want to know about a toric variety, and explain how to detect these properties from a purely polytopal perspective.

4730

Tuesday 4/4 4:10 PM

Robert Davis, MSU

What polytopes tell us about toric varieties
 What polytopes tell us about toric varieties
 04/04/2017
 4:10 PM  5:00 PM
 C304 WH
 Robert Davis, MSU
Polytopes are among the oldest mathematical objects that have been studied. Often, people want to find their volumes, identify triangulations, and describe their lattice points, and more. But why bother doing this? From a combinatorial perspective, the data often answer counting questions that one might have. However, there is much more depth from an algebrogeometric standpoint: this information is often useful for learning about certain toric varieties.
In the first of these talks, I will give the background needed to understand what a normal projective toric variety is and how to model them using polytopes. In the second talk, I will define several properties that an algebraic geometer may want to know about a toric variety, and explain how to detect these properties from a purely polytopal perspective.
