The Department of Mathematical Sciences Newsletter (2023)

Samuel Gunningham’s work is broadly in the field of Geometric Representation Theory. His research utilizes ideas and tools from all over geometry, topology, mathematical physics, and related areas. Many of the phenomona he is interested in can be understood through the lens of topological field theory (TFT). In physics, TFTs arise when you consider a quantum field theory such that there is no dependence of the spacetime metric (often this will require some “twist” or limit of the original theory). Mathematically, a TFT may be understood as a certain gadget that assigns numerical and linear algebraic data to manifolds (i.e. pieces of spacetime). Deep and mysterious dualities predicted by physics (in particular, by string theory) thus give rise to concrete mathematical predictions which can (hopefully!) be precisely formulated and proved. A rich example of this phenomenon is the (geometric) Langlands program. This program has its origins in number theory, in particular the theory of modular and automorphic forms; physically, it corresponds to so-called S-duality in 4d N=4 super Yang-Mills.

Ian Laga is primarily interested in Bayesian modeling and generalized linear models, and specifically applications related to HIV and hard-to-reach, or key, populations like sex workers and drug users. These populations have increased risk of HIV and other infectious diseases, and governments and organizations like UNAIDS need accurate population size estimates for these key populations to implement prevention and treatment services. The statistical methods used to estimate population sizes are quite diverse, so his research involves small area estimation and geospatial methods, with a current emphasis on the Network Scale-up Method. He is currently involved in collaborative research projects to improve the Network Scale-up Method and estimate the size of various key populations across large areas, like sub-Saharan Africa. He is also broadly interested in anything related to Bayesian computing.

John Smith’s research is focused largely on Bayesian application driven methodology, with a particular interest in modeling, forecasting, and simulation of complex dynamical systems in ecology. Current collaborative research projects in that area include integrating data from the National Ecosystem Observatory Network (NEON) with process-based models for carbon budgets in a Bayesian state space framework, and fitting hierarchical thermal performance curves to estimate traits of common disease vectors (e.g. mosquitoes). Additional research interests include surrogate models for ecological applications, sports forecasting, and adoption of best practices for iterative near-term ecological forecasts.