We will discuss the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries, which is referred to as the 0-norm of the vector. Our main results are new improved bounds on the minimal 0-norm of solutions […]
Title: Collective Behavior in Locust Swarms from Data to Differential Equations Prof. Jasper Weinburd Department of Mathematics Harvey Mudd College Abstract: Locusts are devastating pests that infest and destroy crops. Locusts forage and migrate in large swarms which exhibit distinctive shapes that improve efficiency on the group level, a phenomenon known as collective […]
No applied math talk
Title: TBA Abstract: TBA
In this talk we discuss some problems related to finding large induced subgraphs of a given graph G which satisfy some degree-constraints (for example, all degrees are odd, or all degrees are j mod k, etc). We survey some classical results, present some interesting and challenging problems, and sketch solutions to some of them. This […]
Title: A tribute to Professor Ellis Cumberbatch (1934-2021) Abstract: The math colloquium on December 1st will be devoted to remembrances of our beloved CGU colleague Professor Ellis Cumberbatch, a pillar of the Claremont mathematics community, who passed away in September. Three brief talks by his friends and collaborators, Professor John Ockendon (University of Oxford), Dr. […]
Let d >= 2 be a natural number. We determine the minimum possible size of the difference set A-A in terms of |A| for any sufficiently large finite subset A of R^d that is not contained in a translate of a hyperplane. By a construction of Stanchescu, this is best possible and thus resolves an […]
Title: Where do Putnam problems come from? Speaker: Andrew Bernoff, Department of Mathematics, Harvey Mudd College Abstract: The William Lowell Putnam Exam is the preeminent mathematics competition for undergraduate college students in the United States and Canada. I recently finished a three year stint on the competition’s problem committee. This talk is a personal reflection on […]
The set of subsets {1, 3}, {1, 3, 4}, {1, 3, 4, 6} is a symmetric chain in the partially ordered set (poset) of subsets of {1,...,6}. It is a chain, because each of the subsets is a subset of the next one. It is symmetric because the collection has as many subsets with less […]
Title: Using Stitching for faster sampling Speaker: Mark Huber, Department of Mathematics, Claremont McKenna College Abstract: Point processes are used to model location data, such as the locations of trees in a forest, or cities in a plain. Repulsive point processes modify the basic model in order to obtain points that are farther apart from each other than would […]
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed k, the method finds a convex polytope with k vertices, called archetype points, such that the polytope is contained in the convex hull of the data and the mean squared distance between the data and the polytope […]
A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d. Power permutations are used in cryptography, and the exponent d must be chosen so that the permutation is highly nonlinear, that is, not easily approximated by linear functions. The Walsh spectrum […]
