Within mathematics, topologists have begun taking advantage of technological advances to develop and apply new tools to practical problems. The field of applied topology is emerging, tackling problems from robotics, sensor networks, digital imaging, and using topological ideas as a groundwork from which to build solutions. In particular, the viewpoint of applied topology aims to bring the notion of shape more clearly into discussion: what does a particular data set look like? What are its relevant features? How do the local shapes of a data set fit into a global picture? As our world becomes increasingly data-rich, being able to address these questions becomes increasingly valuable.
We are proposing to re-shape our own research trajectories by exploring this new field. We aim to become conversant in this new language, and undertake a shift from our purely theoretical backgrounds as mathematicians to a more interdisciplinary outlook. As we encounter different disciplinary perspectives, we further aim to articulate to some degree how disciplinary languages shape ideas.
In particular, we are proposing to spend the 2010-2011 academic year engaged in learning applied topology, including learning some computational software programs. We aim to arrange for a visiting scholar to spend some time with us during the spring term and to give a colloquium talk for our students during the visit. We are proposing to spend the summer of 2011 on a research problem arising from a non-mathematical field (probably bacterial genomics) which can be attacked using the tools of applied topology.