Jordan Watts' Homepage

## My Papers, Research, & Talks

My Erdös number is 4!

My research interests include applications of geometry and topology to data, generalisations of smooth structures (*e.g.* diffeology, differential spaces, stacks, orbifolds) and Lie groupoids with applications to Lie group actions, symplectic geometry, and Hamiltonian group actions.

## Papers

# Published:

- Susan Tolman and Jordan Watts, Tame circle actions, Trans. Amer. Math. Soc., Vol. 369 (2017), 7443-7467.
- Yael Karshon and Jordan Watts, Basic forms and orbit spaces: a diffeological approach, SIGMA Symmetry Integrability Geom. Methods Appl., Vol. 12 (2016), 026, 19 pages
- Jordan Watts, The differential structure of an orbifold, Rocky Mountain J. Math., Vol. 47 (2017), 289-327
- Jiayong Li and Jordan Watts, The orientation-preserving diffeomorphism group of S^2 deforms to SO(3) smoothly, Transformation Groups, Springer, Vol. 16, No. 2, 2011, pp. 537-553
- Tsasa Lusala, Jędrzej Śniatycki, and Jordan Watts, Regular points of a subcartesian space, Canad. Math. Bull., Vol. 53 (2), 2010, pp. 340-346

# Submitted:

- Derek Krepski and Jordan Watts, Differential cocycles and Dixmier-Douady bundles, 23 pages.
- Suzanne Craig, Naiche Downey, Lucas Goad, Michael J. Mahoney, Jordan Watts, Orbit spaces of linear circle actions, 15 pages.
- Jordan Watts, Symplectic quotients and representability: the circle action case, 19 pages.
- Jean-Pierre Magnot and Jordan Watts, The diffeology of Milnor's classifying space, 28 pages.
- Jordan Watts and Seth Wolbert, Diffeological coarse moduli spaces of stacks over manifolds, 15 pages.

# Preprints:

- Jordan Watts, The orbit space and basic forms of a proper Lie groupoid
- Augustin Batubenge, Patrick Iglesias-Zemmour, Yael Karshon, and Jordan Watts, Diffeological, Frölicher, and differential spaces

# Theses:

- Jordan Watts, Diffeologies, Differential Spaces, and Symplectic Geometry, PhD Thesis, Department of Mathematics, University of Toronto, 108 pages, 2012
- Jordan Watts, The Calculus on Subcartesian Spaces, MSc Thesis, Department of Mathematics & Statistics, University of Calgary, 116 pages, 2006

## Selected Talks

__Symplectic Quotients & Representability__- Slides
*Groupoidfest 2017*; University of Colorado Boulder, Boulder, Colorado, USA; March 2017*Colloquium*; Queens University, Kingston, Ontario, Canada; March 2017 (invited)*Colloquium*; University of Denver, Denver, Colorado, USA; March 2017 (invited)*Algebra and Logic Seminar*; University of Denver, Denver, Colorado, USA; January 2017 (invited)*Geometry, Groups and Dynamics/GEAR*; University of Illinois (Urbana-Champaign), Urbana, Illinois, USA; September 2016*Geometry & Topology Seminar*; University of Illinois Chicago, Chicago, Illinois, USA; September 2016 (invited)

__Tame Circle Actions__- Slides
*2016 AMS Sectional Spring Central Meeting*; North Dakota State University, Fargo, North Dakota, USA; April 2016 (invited)*Stratifications, Differentiable Structures, and Poisson Geometry*; University of Colorado Boulder, Boulder, Colorado, USA; March 2016*2015 CMS Winter Meeting*; Montreal, Quebec, Canada; December 2015.

__The Differential Structure of an Orbifold__- Slides
*Groupoidfest 2015*, University of Memphis, Memphis, Tennessee, USA; October 2015 (invited).*Colloquium*, Dalhousie University, Halifax, Nova Scotia, Canada; June 2015 (invited).*Symplectic & Poisson Geometry Seminar*, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA; May 2015.*Kempner Colloquium*; University of Colorado Boulder, Boulder, Colorado, USA; March 2015 (invited).*Colloquium*; University of Manitoba, Winnipeg, Manitoba, Canada; January 2015 (invited).

__Coarse Moduli Spaces of Stacks over Manifolds__- Slides
*2014 CMS Summer Meeting*; Winnipeg, Manitoba, Canada; June 2014 (invited).*UIUC-WUSTL Symplectic Geometry Seminar 2014*; Washington University, St. Louis, Missouri, USA; April 2014 (invited).*Topology Seminar*; University of Illinois at Urbana-Champaign, Urbana, Illinois, USA; February 2014.

__Basic Differential Forms on a Proper Lie Groupoid__- Slides
*New Geometries for Physics: Workshop on Diffeology*; Aix en Provence, France; June 2014 (invited).*AMS Joint Mathematics Meetings 2014*; Baltimore, Maryland, USA; January 2014.*Gone Fishing*; Temple University, Philadelphia, Pennsylvania, USA; September 2013 (invited).

__Differential Forms on Symplectic Quotients__- Slides
*AMS Joint Mathematics Meetings 2015*; San Antonio, Texas, USA; January 2015 (invited).*Symplectic and Poisson Geometry Seminar*; University of Illinois at Urbana-Champaign, Urbana, Illinois, USA; August 2013.*Geometry and Topology Seminar*; McMaster University, Hamilton, Ontario, Canada; March 2012 (invited).*Geometry and Topology Seminar*; University of Western Ontario, London, Ontario, Canada; March 2012 (invited).*Geometry and Topology Seminar*; University of Waterloo, Waterloo, Ontario, Canada; February 2012 (invited).

## Unpublished Stuff

- Differential spaces, vector fields, and orbit-type stratifications (survey on how to use Śniatycki's theory of vector fields on subcartesian spaces to obtain orbit type stratifications in the setting of a Hamiltonian group action, September 2013)
- Holonomy (notes for a lecture in the "Calabi Conjecture Seminar" series, June 2010)
- Cohomologically Free Symplectic Group Actions (a report for the course Hamiltonian Group Actions, University of Toronto, 2010)
- An Introduction to Poisson Manifolds (a report for the course Introduction to Symplectic Geometry, University of Toronto, 2007)