Adventures in the Theoretical Sciences, ITS Summer school
Katherine Quinn lecture
Thursday, June 11 and Friday, June 12
11:00AM - 1:00PM (EDT)
As effective theories in physics have evolved in time, they have undergone a fundamental transformation in terms of their mathematical complexity: from one-line, hand-written expressions to complex, nonlinear models involving countless parameters. Such an evolution reflects not only the increasingly powerful computational tools at our disposal, but the broader class of mathematical models we use to understand the world around us. Importantly, such multi-parameter models exhibit a kind of universality; they have a hierarchical structure in their parameter importance and predictive power.
In these lectures, I will introduce the formalism of information geometry, an area of mathematics used to translate the problem of understanding patterns in models and data into finding geometric structure in high-dimensional manifolds. Using this framework, we will explore universal properties of complex, nonlinear models through illustrative examples in fields ranging from statistical physics to systems biology, chemistry, and cosmology.