Christian Geske


Graduate Fellow
Research Interests: 
Topology of Singular Spaces

Summer 2018: With the time made available by RTG funding, I have put two papers up on the ArXiv. One is titled “Algebraic Intersection Spaces” for which I am the sole author. It offers a potential extension to the theory of intersection spaces - an alternative way to achieve duality for singular spaces - that applies to a wider class of singular spaces than previously available. I intend to soon submit this paper to the Journal of Topology and Analysis. The other paper is titled “On the Signed Euler Characteristic Property for Subvarieties of Abelian Varieties” and is coauthored by Eva Elduque and Laurentiu Maxim. It provides a topological proof using stratified Morse theory for the signed Euler characteristic property that closed subvarieties of abelian varieties are known to satisfy. 

I have also received RTG funding to cover a portion of a trip to the Institute of Mathematics of the Romanian Academy, where I gave a talk on the first paper “Algebraic Intersection Spaces”.

Summer 2016:  Because I did not have to teach this spring owing to RTG funding and having just selected Laurentiu Maxim as my advisor at the start of the semester, I was able to dedicate a significant portion of my time to gathering the background knowledge necessary to understand and contribute to my advisor’s research. Since Professor Maxim was on sabbatical, this involved progressing through several books on the subject of singularity theory (Dimca’s Sheaves in Topology and Singularities and Topology of Hypersurfaces) and on occasion givings talks on the material in the weekly topology/singularities seminar. At the same time, the absence of teaching duties allowed me to spend more time with my courses, one of which (Topics in Ring Theory) has particular relevance to my field. The RTG funding allowed me to get the jumpstart necessary to quickly enter research level mathematics, something I would not have had had I been a teaching assistant.