Karl Fredrickson


From 2011-2014 I was a Visiting Assistant Professor in the math department at UCR. As of 2015 I am on the job market and living in Seattle.

Email: karlfredrickson@gmail.com


Research Interests

I am interested in complex algebraic geometry, particularly in toric varieties, Calabi-Yau varieties, and mirror symmetry. My Ph.D. thesis (under the direction of Mark Gross at UCSD) was about applying the Gross-Siebert theory of mirror symmetry to study Calabi-Yau complete intersections in Grassmannians. Currently I am studying extremal transitions of Calabi-Yau manifolds and their relation to toric varieties and mirror symmetry constructions.


Publications and Preprints

• Toric degenerations of Calabi-Yau manifolds in Grassmannians (Ph.D. thesis), link to PDF

• Mirror transitions and the Batyrev-Borisov construction, link to PDF
Accepted to Contributions to Algebra and Geometry, November 2014

• Resolution of degenerate mirror families via toric morphisms (preprint), arxiv.org link
Supplemental Macaulay2 code

• Extremal transitions from nested reflexive polytopes, link to PDF
Communications in Mathematical Physics, Volume 335, Issue 3 (2015), Page 1381-1395
Note: in the published version the top line of p. 1390 should say "proper transform", not "total transform".

• Generalized compactifications of Batyrev hypersurface families (preprint), link to PDF
This is a newer version that the one on the arXiv, and includes a calculation of all possible examples for four-dimensional smooth Fano polytopes, based on the Python program at http://github.com/kfredson/primitiverelations. I would like to fill in Section 4.4 on hypersurface flops before I put a new version on the arXiv. If you are interested in working together on this, send me an email!
Benjamin Nill was the co-author of an intermediate version of this paper and contributed some of the proofs that are still in the current version (in particular the proof of Proposition 2.3).


For employers, here is my:

Research Statement

Teaching Statement

CV


Other stuff:

Current resume

Programming projects