Jo Nelson

Ritt Assistant Professor, Department of Mathematics at Columbia University



My CV. Email: nelson [at] math [dot] columbia [dot] edu
My Research Statement. Office: 624 Math, MC 4403
My Teaching Statement. Phone: 212-854-2622
Slides from my 2017 talk  
2016 Eilenberg Lectures by Denis Auroux Columbia SGGT Seminar

Exciting workshops and conferences of the recent past:
ALIAS: Augmentations and Legendrians at the IAS
Thursday and February 11-12, 2016.

Moduli Problems in Symplectic geometry
IHÉS Summer School, July 6-17, 2015.
Chair of the organizing committee.
Videos of lectures
Link to notes

Transversality in Contact Homology
AIM, December 8-12, 2014
My research involves the interactions between symplectic, contact and complex geometry. I'm interested in the relationships between symplectic and contact homology theories. Presently, I am working on proving a cohomological McKay correspondence for links of simple singularities in addition to my work with Michael Hutchings on weakening the assumptions under which one can define contact invariants such as local and cylindrical contact homology.

I wrote the survey article From Dynamics to Contact and Symplectic Topology and Back, which was published in the IASNewsletter. Here are slides from my expository talk on Reeb dynamics and contact invariants, and a video of my lecture on an ``Integral Lift of Contact Homology" at the IHÉS Summer School

Publications and arXiv postings.

(with M. Hutchings) Invariance of cylindrical contact homology for dynamically convex contact forms, in preparation.

(with M. Hutchings) An integral lift of cylindrical contact homology without contractible orbits, in preparation.

(with M. Hutchings) Axiomatic Morse-Bott theory, in preparation.

Automatic transversality for contact homology II: Computations, arXiv:1708.07220.

(with K. Christianson)* Symplectic embeddings of 4-dimensional polydisks into balls, arXiv:1610.00566, submitted

(with L. Abbrescia, I. Huq-Kuruvilla, & N. Sultani)* Reeb Dynamics of the Link of the A_n Singularity, Involve Vol. 10 (2017), No. 3, 417-442.

(with M. Hutchings) Cylindrical contact homology for dynamically convex contact forms in three dimensions, J. Symp. Geom. 14, No, 4, 983-1012, 2016.

From Dynamics to Contact and Symplectic Topology and Back, The Institute for Advanced Study Newsletter, Summer 2016,

Automatic transversality for contact homology I: Regularity, Abh. Math. Semin. Univ. Hambg. 85 (2015), no. 2, 125-179.

* denotes a paper written with REU mentees.

Previously I was an NSF MSPRF postdoc at Barnard College, Columbia University (2013-2014, 2016-2017), at the Institute for Advanced Study from 2013-2016, and at the Simons Center for Geometry and Physics in the spring of 2014. Other fun academic facts can be found in my CV.

My research involves the interactions between symplectic, contact and complex geometry. Currently, I am working on weakening the assumptions under which one can claim in dimension 3 that cylindrical contact homology can be defined with Michael Hutchings.

I was a graduate student at the University of Wisconsin - Madison, and my PhD advisor was Mohammed Abouzaid. Before that I spent a year as a foreign exchange student at the Technische Universität Berlin. I earned my bachelors degree in mathematics and minored in German at the University of Illinois at Urbana-Champaign. A long time ago I went to the Illinois Mathematics and Science Academy.

Among other things I enjoy the color purple, creeping, knitting, speaking german (poorly at this point), vegetarian food, and traveling.