My research interests include data analysis (especially related to drought 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. Click on one of my research topics below to learn more about it.

• Generalisations of Smooth Structures
• Differential Forms on Singular Spaces
• Proper Groupoids
• Symplectic Quotients
• Classifying Spaces of Diffeological Groups
• Data Science and Drought

Papers

My Erdös number is 4!

• Jordan Watts, The orbit space and basic forms of a proper Lie groupoid, Trends in Mathematics, Research Perspectives: Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019, Birkh"auser (to appear).
• Jordan Watts and Seth Wolbert, Diffeological coarse moduli spaces of stacks over manifolds, 16 pages (submitted).
• Carla Farsi, Laura Scull, and Jordan Watts, Classifying spaces and Bredon (co)homology for transitive groupoids, Proc. Amer. Math. Soc., Vol. 148 (2020), 2717-2737.
• Suzanne Craig, Naiche Downey, Lucas Goad, Michael J. Mahoney, Jordan Watts, Orbit spaces of linear circle actions, Involve, Vol. 12 (2019), 941-959.
• Derek Krepski and Jordan Watts, Differential cocycles and Dixmier-Douady bundles, J. Geom. Phys., Vol. 130 (2018), 168-183.
• Augustin Batubenge, Patrick Iglesias-Zemmour, Yael Karshon, and Jordan Watts, Diffeological, Frölicher, and differential spaces, 21 pages (submitted).
• Jean-Pierre Magnot and Jordan Watts, The diffeology of Milnor's classifying space, Topol. Appl., Vol. 232 (2017), 189-213.
• Susan Tolman and Jordan Watts, Tame circle actions, Trans. Amer. Math. Soc., Vol. 369 (2017), 7443-7467.
• Jordan Watts, The differential structure of an orbifold, Rocky Mountain J. Math., Vol. 47 (2017), 289-327.
• Jordan Watts, Symplectic quotients and representability: the circle action case, 19 pages (preprint).
• 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, Diffeologies, Differential Spaces, and Symplectic Geometry, PhD Thesis, Department of Mathematics, University of Toronto, 108 pages, 2012.
• 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.
• Jordan Watts, The Calculus on Subcartesian Spaces, MSc Thesis, Department of Mathematics & Statistics, University of Calgary, 116 pages, 2006.

Selected Talks

• Bredon Cohomology for Transitive Groupoids
  • Slides
  • CMS Annual Summer Meeting 2019; University of Regina, Regina, Saskatchewan, Canada; June 2019 (invited)
• Data Science & Drought, or How a Mathematician can be Useful in the Real World
  • Slides
  • Graduate Student Seminar; Central Michigan University, Mount Pleasant, Michigan, USA; November 2018 (invited)
• Classifying Spaces of Diffeological Groups
  • Slides
  • 12th International ISAAC Congress; University of Aveiro, Aveiro, Portugal; July 2019 (invited)
  • LG&TBQ 2019; University of Michigan, Ann Arbor, Michigan, USA; June 2019 (invited)
  • CMS Annual Summer Meeting 2019; University of Regina, Regina, Saskatchewan, Canada; June 2019 (invited)
  • Souriau 2019; Université Paris-Diderot, Paris, France; May 2019 (invited)
  • Colloquium; University of Toledo, Toledo, Ohio, USA; March 2019 (invited)
  • 2018 AMS Sectional Fall Central Meeting; University of Michigan, Ann Arbor, Michigan, USA; October 2018
  • Topology Seminar; University of Colorado Boulder, Boulder, Colorado, USA; April 2018 (invited)
• Lie Group Actions and Differentiability Beyond Manifolds
  • Slides
  • Colloquium; Central Michigan University, Mount Pleasant, Michigan, USA; January 2018 (invited)
  • Groupoidfest 2017; University of Colorado Boulder, Boulder, Colorado, USA; March 2017
  • Colloquium; University of Denver, Denver, Colorado, USA; March 2017 (invited)
• Symplectic Quotients & Representability
  • Slides
  • Colloquium; Queens University, Kingston, Ontario, Canada; 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)