Roger Casals

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

My research is supported by an NSF Career and the Alfred P. Sloan Foundation.
The seminar listing at UC Davis, and the NCSGS.

Selected Articles

  1. Microlocal Theory of Legendrian Links
    and Cluster Algebras
    ,
    Roger Casals, Daping Weng,
    arXiv version (2022), 1–119.

  2. Infinitely Many Lagrangian Fillings,
    Roger Casals, Honghao Gao,
    Annals of Math. 195 (2022), 207–249.

  3. Legendrian Weaves,
    Roger Casals, Eric Zaslow,
    Geometry & Topology (2022), 1–116.

  4. Non-simplicity of isocontact embeddings,
    Roger Casals, John Etnyre,
    Geom. Funct. Anal. (GAFA) 30 (2020), 1–33.

  5. Geometric Criteria for Overtwistedness,
    Roger Casals, Emmy Murphy, F. Presas,
    J. Amer. Math. Soc. 32 (2019), 563–604.

  6. Legendrian Fronts for Affine Varieties,
    Roger Casals, Emmy Murphy,
    Duke Math. Journal 168 (2019), 225–323.

  7. Existence h-principle for Engel structures,
    R. Casals, J.L. Pérez, A. Pino, F. Presas,
    Inventiones Math. 210 (2017), 417–451.

  8. Almost contact 5-folds are contact,
    R. Casals, D. Pancholi, F. Presas,
    Annals of Math. 182 (2015), 429–490.

List of Publications

  1. Microlocal Theory of Legendrian Links and Cluster Algebras with D. Weng (2022), 1–119. Submitted.

  2. Stein Traces and Characterizing Slopes with J. Etnyre and M. Kegel (2021), 1–37. Submitted.

  3. Positroid Links and Braid Varieties with E. Gorsky, M. Gorsky and J. Simental (2021), 1–57. Submitted.

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

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

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

  7. Infinitely Many Lagrangian Fillings, with H. Gao, Annals of Math. 195 (2022), 207–249.

  8. Legendrian Weaves, with E. Zaslow, Geometry & Topology (2022), 1–116.

  9. Full Ellipsoid Embeddings and Toric Mutations with R. Vianna, Selecta Math. (N.S.) 28 (2022), 1–62.

  10. Lagrangian Skeleta and Plane Curve Singularities, JFPTA Viterbo 60 Volume 24 (2021), 1–43.

  11. Branched covering simply-connected 4-manifolds, with MSP Open Book Ser. (2021), 1–11.

  12. The Legendrian Whitney Trick with D. Pancholi and F. Presas, Geometry & Topology 25 (2021), 3229–3256 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Some Talk Slides

  1. Nottingham Online Algebraic Geometry (May 21)

  2. AMS Spring Central Sectional Meeting (Apr 21)

  3. MSU Geometry Seminar (Mar 21)

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

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

  6. Isolated Plane Curve Singularities (Nov 20)

  7. Northwestern Geometry & Physics Seminar (Oct 20)

  8. Western Hemisphere virtual symplectic seminar (Jul 20)

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

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

Recent Teaching

  1. Fall 2021: Contact and Symplectic Topology MAT-280

  2. Fall 2020: Mathematical Quantum Mechanics MAT-265

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

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

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

  6. Fall 2019: Differential Equations MAT-22B

  7. Winter 2019: Combinatorics MAT-145

Media And Outreach