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 […]
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 techniques. By examining several families of knots, including over 10 million distinct examples, we find that the Jones data is well described as a three […]
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 […]
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 transitions from absolute (Rayleigh- Plateau) instability is useful in the design of heat and mass exchangers for applications that include cooling systems and desalination. We present a […]
TOPIC: Symmetry Symmetry seems to be an important idea in mathematics, but how do mathematicians think about symmetry? In this workshop, we’ll talk about mathematical objects called groups, see how […]
Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I will discuss different approaches to develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states […]
In this talk, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions of this theory, I will discuss several examples of matroids and explain some connections with optimization. Also, in this talk, I will introduce matroid polytopes, […]
Title: Cobordism Categories and Spaces of Manifolds. Abstract: Cobordisms have been one of the central objects in topology since the pioneering work of Rene Thom, which provided the first link between manifolds and homotopy theory. In more recent years, there has been much focus on cobordism categories. These play a fundamental role in the study […]
I plan to explain how a purely algebraic technique involving Lie Algebra Cohomology can be used to construct standard characteristic classes of vector bundles and foliations (in fact, it could be tweaked to give most characteristic classes in differential and complex geometry).
