Roger Casals

University of California Davis
Department of Mathematics,
casals -at- math.ucdavis.edu

My research is supported by the NSF and the Alfred P. Sloan Foundation.

Research interests: contact and symplectic topology, flexible-rigid dichotomy, h-principles and groups of contactomorphisms.
I am also interested in the relations with algebraic geometry, including mirror symmetry and singularity theory.


Selected Articles

  1. Infinitely Many Lagrangian Fillings,
    joint work with H. Gao (2020).

  2. Non-simplicity of isocontact embeddings,
    joint work with J. Etnyre,
    Geom. Funct. Anal. (2020).

  3. Geometric Criteria for Overtwistedness,
    joint work with E. Murphy and F. Presas,
    J. Amer. Math. Soc. (2019).

  4. Legendrian Fronts for Affine Varieties,
    joint work with E. Murphy,
    Duke Math. Journal (2019).

  5. Existence h-principle for Engel structures,
    with J.L. Pérez, A. del Pino and F. Presas,
    Invent. Math. (2017).

  6. Almost contact 5-folds are contact,
    joint work with D. Pancholi and F. Presas,
    Ann. Math. (2015).

List of Publications

  1. Braid Loops with infinite monodromy on the Legendrian contact DGA, with L. Ng (2021), 1–78. Submitted.

  2. Dynamical Quantization of Contact Structures, with G. Herczeg and A. Waldron (2021), 1–45. Submitted.

  3. Algebraic Weaves and Braid Varieties with E. Gorsky, M. Gorsky and J. Simental (2020), 1–62. Submitted.

  4. Legendrian Weaves, with E. Zaslow (2020), 1–114. Submitted.

  5. Sharp Ellipsoid Embeddings and Toric Mutations with R. Vianna (2020), 1–61. Submitted.

  6. Infinitely Many Lagrangian Fillings, with H. Gao (2020), 1–28. Submitted.

  7. Lagrangian Skeleta and Plane Curve Singularities, JFPTA Viterbo 60 Volume (2021).

  8. Branched covering simply-connected 4-manifolds, with Open Book Ser. (2021).

  9. The Legendrian Whitney Trick with D. Pancholi and F. Presas, Geom. Topol. (2020).

  10. Non-simplicity of isocontact embeddings with J. Etnyre, Geom. Funct. Anal. 30 (2020), 1–33.

  11. Geometric Criteria for Overtwistedness, with E. Murphy and F. Presas, J. Amer. Math. Soc., 32 (2019), 563–604.

  12. Transverse Universal Links, with J. Etnyre, Proc. Sympos. Pure Math 102 (2019), 43–56.

  13. Loose Engel structures with A. del Pino and F. Presas, Compositio Math. 156 (2019), 412–434.

  14. Legendrian Fronts for Affine Varieties, with E. Murphy, Duke Math. Journal 168 (2019), 225–323.

  15. OT Disks and Exotic Symplectic Structures, Proc. Amer. Math. Soc. 148 (2019), 825–834.

  16. Differential algebra of cubic planar graphs, with E. Murphy, Advances in Math. 338 (2018), 401–446.

  17. Classification of Engel Knots, with A. del Pino, Math. Ann. 371 (2018), 391–404.

  18. Symplectomorphisms of exotic discs, with A. Keating and I. Smith, J. École Polytechnique 5 (2018), 289–316.

  19. Existence h-principle for Engel structures, with J.L. Pérez, A. del Pino and F. Presas, Invent. Math. 210 (2017), 417–451.

  20. Higher Maslov Indices, with V.L. Ginzburg and F. Presas, J. Geom. Phys. 115 (2017), 167–177.

  21. Contact topology from the loose viewpoint, with E. Murphy, Gökova Geom. Top. 22 (2016), 81–115.

  22. On the strong orderability of overtwisted 3-folds, with F. Presas, Comment. Math. Helv. 91 (2016), 305–316.

  23. Small positive loops on overtwisted manifolds, with F. Presas and S. Sandon, J. Symp. Geom. 14 (2016), 1013–1031.

  24. Chern-Weil theory and the group of strict contactomorphisms, with O. Spáčil, J. Topol. Anal. 8 (2016), 59–87.

  25. Almost contact 5-folds are contact, with D. Pancholi and F. Presas, Ann. Math. 182 (2015), 429–490.

  26. h-principle for 4-dimensional contact foliations, with A. del Pino and F. Presas, Int. Math. Res. Not. 20 (2015), 176–207.

  27. Contact blow-up, with D. Pancholi and F. Presas, Exp. Math. 33 (2015), 78–100.

  28. A Remark on the Reeb Flow for Spheres, with F. Presas, J. Symp. Geom. 12 (2014), 657–671.

Some Talk Slides

  1. AMS Spring Central Sectional Meeting (Apr 21)

  2. MSU Geometry Seminar (Mar 21)

  3. IBS Legendrians, Cluster algebras, and Mirror symmetry (Jan 21)

  4. Geometry and Representation Theory at home (Dec 20)

  5. Isolated Plane Curve Singularities (Nov 20)

  6. Northwestern Geometry & Physics Seminar (Oct 20)

  7. Western Hemisphere virtual symplectic seminar (Jul 20)

  8. Topología de contacto: cáusticas y reflexiones (Sep 17)

  9. Congreso Bienal de la Real Sociedad Matemática Española (Sep 17)

Recent Teaching

  1. Fall 2020: Mathematical Quantum Mechanics MAT-265

  2. Fall 2020: Introduction to Abstract Mathematics MAT-108

  3. Winter 2020: Algebraic Topology II MAT-215B

  4. Winter 2020: Euclidean and Non-Euclidean Geometry MAT-141

  5. Fall 2019: Differential Equations MAT-22B

  6. Winter 2019: Combinatorics MAT-145

Media And Outreach