Jo Nelson

Assistant Professor, Department of Mathematics at Rice University

Email: jo.lastname [at] rice [dot] edu Office: 402 Hermann Brown Hall, x5209
Topology Seminar Contact Topology Learning Seminar
Rice Colloquium Horizons in Mathematics
Curves and Surfaces, Fall 2019 Geometric Topology, Fall 2019
😭 🦠 UPDATES 🦠 😭 :
The Dubrovnik 2020: Holomorphic curves and low-dimensional topology conference is postponed to 2022 due to the ongoing COVID-19 pandemic. I have cancelled all my upcoming travel for the foreseeable future and encourage others to practice similar social distancing measures in the interest of public safety. Be safe. 💜
My research involves the interactions between symplectic and contact topology and is supported by NSF DMS-1840723. Presently, I am working on using geometric techniques to define and compute various flavors of contact homology and related product structures. I'm interested in the relationships between symplectic and contact homology theories. I am also exploring applications to dynamics and symplectic embedding problems.

My research group consists of Dr. Morgan Weiler (RTG Lovett Instructor) and Leo DiGiosia (PhD Candidate).

A video of my research lecture on ``Equivariant and Nonequivariant Contact Homology" at the 2019 IAS Symplectic Geometry/Dynamics Seminar

My Meet our Faculty profile from Fall 2019 by the Wiess School of Natural Sciences, Rice University.

My survey article From Dynamics to Contact and Symplectic Topology and Back, was published in the 2016 Institute for Advanced Study Newsletter.

Here are my 2019 colloquium slides, Reeb dynamics and contact invariants.

Here are my 2020 undergraduate colloquium slides, Contact encouters in the third dimension.

Videos of my expository lectures on the origins of cylindrical contact homology at the 2019 IMPA Winter school on Symplectic Topology.

Publications and arXiv postings.

(with M. Weiler) Embedded contact homology of Seifert Fiber Spaces, in preparation.

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

(with M. Hutchings) S^1-equivariant contact homology for hypertight contact forms, 88 pages, arXiv:1906.03457, submitted.

(with M. Hutchings) Axiomatic S^1 Morse-Bott theory, 48 pages, to appear in Algebraic & Geometric Topology.

Automatic transversality for contact homology II: filtrations and computations, Proceedings of the London Mathematical Society. Volume 120, Issue 6, 853-917 June 2020.

(with K. Christianson)* Symplectic embeddings of 4-dimensional polydisks into balls, Algebraic & Geometric Topology 18 (2018) 2151-2178.

(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, a Visitor at the Institute for Advanced Study from 2013-2014, 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. I am working on foundational results in defining contact invariants via pseudoholomorphic curves, often with Michael Hutchings and more recently with Morgan Weiler. More recently I've started thinking about pair of pants products in various formulations of contact homology and relationships to loop spaces.

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, swimming, knitting, speaking german (poorly at this point), and traveling (although I've started to overdo it).

Here are some exciting workshops and conferences I was involved with in the (not so) 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