2009-10 REGS Dissertation Completion Fellowship recipients
Jason Elliot
Jason Elliot received his fellowship in his fifth year of graduate study at the University of Illinois. During his first summer here he began working with Derek Robinson while being funded by a REGS grant. They began working on applications of homological algebra and topology to group theory, particularly group extensions. This work ultimately led to Elliot's dissertation topic. Since moving to Champaign, Elliot has also become a proud father of a baby girl.
In his thesis he investigates group extensions that have a certain universal property, namely every central group extension embeds into one. These "universal" extensions have applications to nilpotent groups and to capable groups, which are both defined in terms of central extensions. Jason successfully defended his Thesis in November 2010.
Kevin Milans
Milans was born in Maryland. He obtained a Bachelor's Degree in Computer Science from Carnegie Mellon University, where he began to juggle as a hobby. Subsequently, he attended graduate school at the University of Illinois where he earned a Master's Degree in Computer Science under the direction of Professor Jeff Erickson and he successfully defended his thesis in mathematics on April 29, 2010. In August 2010 he moved to the University of South Carolina to begin a two-year postdoctoral fellowship working with the discrete mathematics group. He also enjoys biking and playing guitar.
Milan's Ph.D. thesis, completed under the direction of Professor Douglas B. West, explored several topics in graph theory and extremal combinatorics. For example, Ramsey theory tells us that edge-colored graphs that are sufficiently large and dense contain monochromatic copies of a target subgraph G. When G is sparse, does there exist a sparse host graph whose edge-colorings always contain a monochromatic copy of G? Milan's thesis will explore this question as well as a combinatorial game variant. Other topics include extremal coloring problems and an extremal problem on trees that finds an application in computability theory.
NSF-MCTP — Mentoring Through Critical Transition Points
National Science Foundation