GilYoung Cheong

I am a second year PhD student in the Department of Mathematics at the University of Michigan. My advisor is Michael Zieve.

I have obtained M.S. in mathematics from Seoul National University in May 2015. My thesis advisor was Atanas Iliev. Before that I have obtained B.A. in mathematics from the University of Wisconsin-Madison in May 2013. I have not written any senior thesis, but I have developed much of my interest in mathematics by working with Melanie Matchett Wood.

Research

    I work on algebraic geometry over finite fields. Recently, I have been interested in varieties with integer coefficients which can be thought of complex manifolds or smooth varieties over finite fields. The complex manifolds asing this way have classical homological information, which can be related to the number of rational points over finite fields due to Grothendieck's trace formula and Artin's comparison theorem of different cohomology theories. Of course, in real life, one encounters situations where such tricks may not be used. For instance, varieties arising in one's problem can be horribly singular. My current goal is to lay out some systemetic approach to break such singular varieties into smooth ones and even into linear ones if certain structure is imposed so that the number of rational points over finite fields can be closely connected to homological information given by the complex manifold.

Teaching/Mentoring

Winter 2017Math 216 (TA, University of Michigan)
Fall 2016Math 116 (University of Michigan)
Summer 2016Mentoring a high school student (Jiwoo Park)
Winter 2016Math 115 (University of Michigan)
Fall 2015Math 115 (University of Michigan)

Talks given

Fall 2016Topological methods for some arithmetic questions (Sept 22, 2016, UM Math Club)

Acknowledgements

This website is shamelessly copied from the one made by Corey Everlove. I would like to thank him for the permission to use his codes.