Department of Mathematics
Carolina Center for Interdisciplinary Applied Mathematics
Social Network Analysis at Carolina
Department of Applied Physical Sciences
Duke Network Analysis Center
Research: Our current research focus is in networks. We use mathematical models and statistical principles to develop and apply computational tools for the study of real-world data. Networks appear across many disciplines and our group activities have included collaborations with Archeology, Biostatistics, Epidemiology, Finance, Geography, Infectious Diseases, Neuroscience, Physics, Political Science, Psychology, Public Policy, Sociology, and Statistics. With “nodes” representing actors of interest and “edges” connecting the nodes representing relationships or similarities, the concept of a network can be flexibly used across many applications. Most people are familiar with the concept of a network in terms of hyperlinked web pages or online social networks, and online networks are indeed an area of broad interest (including some of our own work); but networks can be successfully applied to a much wider variety of connected systems.
Group: Our research group currently includes postdoctoral scholars Saray Shai and Dane Taylor; graduate students Sam Heroy, Hsuan-Wei “Wayne” Lee and Natalie Stanley; and undergraduates Austen Kelly, Nic Larsen, Zichao Li, Charlie Ramsey and Sean Xiao. Each is working on some aspect of the study of networks, including developments in community detection, modeling network dynamics, model interactions in networked materials, and diffusive processes with applications to disease and health behaviors. Our group activities are fundamentally collaborative, with a variety of ongoing collaborations with students and faculty from other departments and universities.
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Biographical Sketch: After a childhood spent mostly in Minnesota, I moved east to attend college at Cornell University where I majored in Engineering Physics. I then took a Churchill Scholarship to study in the Cavendish Laboratory at Cambridge with an M.Phil. in Physics. Returning to the States, I continued my studies at Princeton, leading to an M.A. and Ph.D. in Applied and Computational Mathematics. Following a postdoctoral instructorship in applied mathematics at MIT, and a tenure-track assistant professorship in Mathematics at Georgia Tech, I moved to Chapel Hill to join the Department of Mathematics and the Institute for Advanced Materials, Nanoscience and Technology (now folded into the new Department of Applied Physical Sciences) at UNC.
Pronunciation: If you really want to get it right, my last name is pronounced the same way as Alphonse Mucha’s (sound file). My own Americanized pronunciation comes out sounding like the vowel and ‘k’ in the word “book” (/’mʊk-a/).