- Prospective Students
Dr. Geer earned his doctorate at the University of Oregon and then spent four years in a postdoctoral position at Georgia Tech. He accepted a position at Utah State University in spring of 2008 but spent his first year of the appointment at the prestigious Max Planck Institute for Mathematics in Bonn, Germany. Dr. Geer’s research interests lie in the emerging area of quantum topology, which has applications in theoretical physics, specifically in quantum field theory.
Loosely speaking, topology is the study of space without some of the standard concepts of geometry, including angles and distance. Surprisingly, many geometric features can be studied through the underlying topology. For example, geometric objects called manifolds are used to model space and time in general relativity. Manifolds can be studied with topological objects called knots and, more generally, links (tied up shoes strings). Representation theory is a major discipline of modern mathematics that is concerned with the mathematics of symmetry. Dr. Geer uses representation theory to create and study topological invariants.
“I am attracted to this work because it is a beautiful mix of several areas of mathematics. Also, I really enjoy doing mathematics which is related to modern physics. I find it amazing that a mathematician can sit in his or her office and do abstract mathematics which is miraculously related to the world.”
Dr. Abbass Sharif, a former PhD student of the Department of Mathematics and Statistics who successfully defended his dissertation during the Fall 2012 semester, was announced one of the four winners of the 2013 Student Paper Competition of the Statistical Computing and Statistical Graphics Sections of the American Statistical Association (ASA). The official competition web site at http://stat-computing.org/awards/student/ indicates: .Students are encouraged to submit a paper in this area, which might be original methodological research in statistical computing, some novel computing application in statistics, or any other suitable contribution (for example, a software-related project).. Dr. Sharif.s entry (with his former PhD advisor, Dr. Symanzik, as a co-author) is titled .Multivariate Visual Data Mining Tools for Functional Actigraphy Data. and it is based on one of the chapters of his dissertation. Actigraphy, a technology for measuring a subject.s overall activity level almost continuously over time, has gained a lot of momentum over the last few years. An actigraph, a watchlike device that can be attached to the wrist or ankle of a subject, uses an accelerometer to measure human movement every minute or even every 15 seconds. Actigraphy data is often treated as functional data. In his entry, Dr. Sharif introduced four techniques to visually detect clusters in raw functional actigraphy data for patients with different depression levels.
Overall, 28 submissions for this competition were received in 2013. Past winners of this competition originated from universities such as Stanford, Berkeley, and Harvard . to mention only three. Dr. Sharif is the first winner from Utah State University in this competition.
Immediately after his PhD defense, Dr. Sharif started as an Assistant Professor at the University of Southern California in Los Angeles in January 2013.