Nathan Clement

Clement
Nathan
Graduate Fellow
papers_url: 
https://arxiv.org/abs/1612.09010
person_type: 
Graduate
working_with: 
Arinkin
updates: 

Spring 2016:  His research concerns moduli spaces of Higgs bundles in some low-dimensional examples.

Summer 2016:

Goal:  Prove existence of certain moduli spaces of logarithmic Higgs Bundles on P1 and demonstrate isomorphisms between them.  This should yield two dimensional examples of Hitchen Fibrations. Extend this result to the case of vector bundles with logarithmic connections on P1.

Results:  Major progress was made on the Higgs Bundle case and a paper (my thesis) is in preparation.  Specifically, I now understand, using results of Carlos Simpson and others, the C-points of my moduli problems and the associated isomorphisms.  Further treatment is required to deal with points valued in non-reduced rings.

 Future plans:  By the end of Summer 2016 I plan to finish writing up the Higgs Bundle case and begin work on the case of connections.

display: 
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