Jo Nelson

Assistant Professor, Department of Mathematics at Rice University

Email: jo.lastname [at] rice [dot] edu Office: 450 Hermann Brown Hall
Rice Topology Seminar Rice Colloquium
Calculus III, Fall 2018 Geometric Topology, Fall 2018
My research involves the interactions between symplectic and contact topology. 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 defining equivariant and nonequivariant formulations of contact (cylindrical) homology. I am also exploring applications to dynamics and symplectic embedding problems.

I wrote the survey article From Dynamics to Contact and Symplectic Topology and Back, which was published in the 2016 Institute for Advanced Study Newsletter. 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 2015 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) Equivariant contact homology for hypertight contact forms, 83 pages, draft available upon request.

(with M. Hutchings) Axiomatic S^1 Morse-Bott theory, 47 pages, arXiv:1711:09996, submitted.

Automatic transversality for contact homology II: Computations, 65 pages, arXiv:1708.07220, submitted.

(with K. Christianson)* Symplectic embeddings of 4-dimensional polydisks into balls, to appear in Alg. Geom. Topol. 27 pages, arXiv:1610.00566.

(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 a Ritt Assistant professor at Columbia University (2017-2018), an NSF MSPRF postdoc at Barnard College, Columbia University (2013-2014, 2016-2017), a Member at the Institute for Advanced Study from 2014-2016, and at the Simons Center for Geometry and Physics in the spring of 2014.

My research involves the interactions between symplectic, contact and complex geometry. Currently, I am working on foundational results in defining contact invariants via pseudoholomorphic curves, often with Michael Hutchings.

I obtained my PhD in 2013 under the supervision of Mohammed Abouzaid while at the University of Wisconsin - Madison. Before that I spent 2006-2007 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, zombies, knitting, speaking german (poorly at this point), and traveling.

Here are some exciting workshops and conferences of the recent past:
2017 Eilenberg Lectures by Paul Seidel
2016 Eilenberg Lectures by Denis Auroux

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