Absolute concentration robustness is a property that allows signaling networks to sustain a consistent output in the face of protein concentration variability from cell to cell.  This property is structural and can be determined from the topology of the network alone.  In this talk, I discuss this concept first for deterministic systems, and then set out to describe their stochastic behavior.  In the long term, the corresponding stochastic processes undergo an extinction event that eliminates the robustness. However, these systems have a transiently robust behavior that may be sufficient to carry out the necessary signal transduction in cells.  This work has been recently funded by NSF and graduate students are invited to inquire about working with me on this topic.

What happens to an embedded curve in the plane if we decrease its length as fast as possible?  In this talk I will discuss the beautiful answer to this simple question, which involves techniques and ideas from multivariable calculus and plane geometry.  Generalizing this situation to higher dimensions leads to a number of interesting open questions in geometry, topology, and analysis.

Hindman’s theorem states that if one colors every natural number either red or blue, then there will be an infinite set X of natural numbers such that all finite sums of distinct elements from X have the same color. The original proof of Hindman’s theorem was a combinatorial mess and the slickest proof is via ultrafilters. In this talk, I will introduce the notion of an ultrafilter on a set, which is simply a division of the subsets of the set into two categories, “small" and “large", satisfying some natural axioms. We will then give the proof of Hindman’s theorem using ultrafilters that are idempotent with respect to a natural addition operation on the set of ultrafilters on the set of natural numbers. Finally, we will introduce an open conjecture of Erdos related to Hindman’s theorem, its reformulation in terms of ultrafilters, and some recent progress made on the problem by myself and my collaborators.

Cohomology is a basic and powerful tool that arises in many fields of geometry and topology.  I will motivate this technique and demonstrate its use in some simple examples.

The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments.
 
I ran a student internship program at Los Alamos National Laboratory for over 20 years. Recently, I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers.
 
I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can
help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life.
 
The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime.
 
Please join us for an engaging discussion on how to make the choices that
will lead to a great career.