The classical Frobenius problem asks for the largest integer not representable as a non-negative integer linear combination of a relatively prime integer n-tuple. This problem and its various generalizations have been studied extensively in combinatorics, number theory, algebra, theoretical computer science and probability theory. In this talk, we will consider a reformulation of this problem […]
CLAREMONT CENTER for MATHEMATICAL SCIENCES Fall 2019 Poster Session Click here for poster abstracts.
We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the boundary measurement of the photon currents allows unique and […]
In Euclidean geometry, the sum of two sides of any triangle is greater than the third side. We introduce this idea to labeling of graphs. A (p,q)-graph G=(V,E) is said to be in Euclid(0) if there exists a bijection f: V(G) --> {1,…,p} such that for each induced C3 subgraph with vertices {v1,v2,v3} with f(v1)<f(v2)<f(v3) we […]
Title: Biquandle Brackets and Knotoids Abstract: Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein […]
Cells make fate decisions in response to dynamic environmental and pathological stimuli as well as cell-to-cell communications. Recent technological breakthroughs have enabled to gather data in previously unthinkable quantities at single cell level, starting to suggest that cell fate decision is much more complex, dynamic, and stochastic than previously recognized. Multiscale interactions, sometimes through cell-cell […]
An “Adinkra” is a graphical tool to describe a branch of particle physics known as supersymmetry. Understanding the mathematics of Adinkras shines a light on the underlying physics, as well as helps to explore new areas of mathematics. After describing the basic structure of Adinkras, I will discuss some of these interesting interactions between mathematics […]
Single-cell genomics is a catch phrase for numerous new technologies and methods that allow for probing cells at genome scale. I will explain what this means and describe some examples […]
The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as "diagram algebras", meaning that they have basis elements depicted as certain kinds of graphs, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk, we will explore […]
Title: Understanding Structure in the Single Variable Knot Polynomials Abstract: We examine the dimensionality and internal structure of the aggregated data produced by the Alexander, Jones, and Z0 polynomials using topological data analysis and dimensional reduction […]
The beauty of mathematics is often encountered when one discovers that two apparently very different phenomena actually share a common origin. I will discuss such a surprising connection between two apparently unrelated mathematical objects. One is purely combinatorial: the number of ways one can drive from USC to the Claremont Colleges. The other one is […]
Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. Determining the regime […]
