Wednesday

Mini-course 1. Mathematical Modeling in Ecology: Population Dynamics

Lidia Mrad

Abstract: The aim of this mini-course is to explore some models which have been central to the development of mathematical modeling, and which provide examples of how mathematics can be used in understanding ecological interactions. We focus on dynamical systems, which historically have been bound up with the calculus. However, we assume no knowledge of calculus and build up ideas using computational tools. Models we will study include the logistic growth model, competitive and symbiotic species interaction models, and predator-prey models.

Mini-course 2. What is dimension?

Sean McCurdy

Abstract: We all have the intuition that lines are one-dimensional, planes are two-dimensional, and cubes are three-dimensional. But why? What does that mean? And how do we apply that intuition to sets which are not so “nice”? It turns out, there are many different ways to make our intuitions of “dimension” rigorous. Surprisingly, these different ways don’t always agree! This mini-course invites participants into mathematics as a creative process through the question “What is dimension?” Attempts to answer this question will take us through 5 definitions of “dimension,” with plenty of opportunities for participants to come up with their own definitions along the way. We will see some strange things (fractional dimensions, infinite dimensions, even negative dimensions!) as well as some big ideas in Linear Algebra, Topology, and Analysis. The course will be structured loosely as a dialectic. Each class will develop a new definition of “dimension” and end with an exploration of its strengths and limitations. Problem Sessions for this mini-course will give participants the opportunity to A) further explore the theory in which a given definition of “dimension” is framed, or B) invent new definitions of dimension which fix the limitations. The next class will focus upon seeing where these the new definitions lead.

Informal conversation

Reginald McGee

Talk. Analyzing single-cell data to identify significant interactions in leukemi

Reginald McGee

Abstract: Complex protein interaction networks complicate the understanding of what most promotes the rate of cancer progression. High dimensional data provides opportunities for new insights into possible mechanisms for the proliferative nature of aggressive cancers, but these datasets often require fresh techniques and ideas for exploration and analysis. In this talk, we consider mass cytometry data capturing expression levels of tens of biomarkers in individual cells from acute myeloid leukemia patients. After identifying immune cell subpopulations in this data using an established clustering method, we present a novel statistic for testing differential biomarker across patients and within specific cell phenotypes.

Worktime