Jordan Watts' Homepage

## My Research

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!

Preprints of most of my papers can be found on the arXiv.

- Carla Farsi, Laura Scull, and Jordan Watts, Bicategories of action groupoids, Applied Categorical Structures (to appear).
- Gabriele Barbieri, Jordan Watts, and François Ziegler, Remarks on diffeological Frobenius reciprocity, 26 pages (submitted).
- Augustin Batubenge, Yael Karshon, and Jordan Watts, Diffeological, Frölicher, and differential spaces, Rocky Mountain J. Math. (to appear).
- Derek Krepski, Jordan Watts, and Seth Wolbert, Sheaves, principal bundles, and Čech cohomology for diffeological spaces, Israel J. Math. (to appear).
- Jordan Watts and Seth Wolbert, Diffeological coarse moduli spaces of stacks over manifolds, Recent Advances in Diffeologies and their Applications, In: Contemporary Mathematics, Vol. 794 (2024), American Mathematical Society.
- Yael Karshon and Jordan Watts, Smooth maps on convex sets, Recent Advances in Diffeologies and their Applications, In: Contemporary Mathematics, Vol. 794 (2024), American Mathematical Society.
- Jordan Watts, Bicategories of diffeological groupoids, 84 pages (preprint).
- Yael Karshon, David Miyamoto, and Jordan Watts, Diffeological submanifolds and their friends, 15 pages (submitted).
- Jordan Watts, The orbit space and basic forms of a proper Lie groupoid, In: Current Trends in Analysis, its Applications and Computation: Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019; Trends in Mathematics: Research Perspectives; Birkhäuser, 2022.
- 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.
- 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.

## Select Talks:

- When is a Symplectic Quotient a Diffeological Orbifold?: Slides
- Weak Equivalences between Action Groupoids: Slides
- Diffeological Groupoids: Slides
- Sheaves, principal bundles, and Čech cohomology for diffeological spaces: Tablet Notes
- Bredon Cohomology for Transitive Groupoids: Slides
- Data Science & Drought, or How a Mathematician can be Useful in the Real World: Slides
- Classifying Spaces of Diffeological Groups: Slides
- Lie Group Actions and Differentiability Beyond Manifolds: Slides
- Symplectic Quotients & Representability: Slides
- Tame Circle Actions: Slides
- The Differential Structure of an Orbifold: Slides
- Coarse Moduli Spaces of Stacks over Manifolds: Slides
- Basic Differential Forms on a Proper Lie Groupoid: Slides
- Differential Forms on Symplectic Quotients: Slides

## 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)