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 that illustrate the excitement in this new domain. While single-cell genomics technologies draw on methods from a variety of disciplines such asf biology, chemistry and […]
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 […]
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 […]
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 […]
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).
