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 […]
Title: Exploiting metric structure for more accurate classification Speaker: Mike Izbicki, Department of Mathematical Sciences, Claremont McKenna College Abstract: Classification problems often have many semantically similar classes. For example, the famous ImageNet dataset contains classes for 80 different dog breeds, 40 different bird species, and 25 types of vehicles. This semantic structure can be formalized using a metric […]
Title: Modern techniques to approach the invariant subspace problem Abstract: The invariant subspace problem is by far one of the most important problems in operator theory. It has been open for more than half a century, and there are many significant contributions with a huge variety of techniques, making this challenging problem so interesting; however […]
A frame in a Euclidean space is a spanning set, which can be overdetermined. Large frames are used for redundant signal transmission, which allows for error correction. An important parameter of frames is coherence, which is maximal absolute value of the cosine of the angle between two frame vectors: the smaller it is, the closer […]
In this talk I will recount the history of my knot theory-based music project and show an example of my method for creating music from knot homsets.
Title: Modeling the waning and boosting of immunity Speaker: Dr. Lauren Childs Assistant Professor and the Cliff and Agnes Lilly Faculty Fellow Virgina Tech Abstract: Infectious disease often leads to significant loss of life and burden on society. Understanding disease dynamics is essential to the development and implementation of earlier and more effective interventions. Traditionally, perfect, […]
