Roger Casals

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

My research is supported by an NSF Career, the Alfred P. Sloan Foundation and the College of L&S Dean's Fellowship.
The seminars at UC Davis, the NCSGS and this upcoming AIM Conference.

Selected Articles

  1. A Lagrangian filling for every cluster seed,
    Roger Casals, Honghao Gao,
    Inventiones Math. 237 (2024), 1–60.

  2. Cluster structures on braid varieties,
    R. Casals, E. Gorsky, M. Gorsky,
    I. Le,J. Simental, L. Shen    ,
    J. Amer. Math. Soc. (2024), 1–111.

  3. Microlocal Theory of Legendrian Links
    and Cluster Algebras    ,
    Roger Casals, Daping Weng,
    Geometry & Topology 28 (2024), 1–119.

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

  5. Legendrian Weaves,
    Roger Casals, Eric Zaslow,
    Geometry & Topology 26 (2022), 1–157.

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

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

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

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

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

List of Publications

  1. A Lagrangian filling for every cluster seed, with H. Gao, Invent. Math. (2024), 1–60.

  2. Cluster structures on braid varieties with E. Gorsky, M. Gorsky, I. Le, J. Simental, L. Shen, J. Amer. Math. Soc. (2024), 1–111.

  3. A binary invariant of matrix mutation, J. Comb. Algebra (2024), 1–10.

  4. Microlocal Theory of Legendrian Links and Cluster Algebras with D. Weng, Geometry & Topology (2024), 1–119.

  5. Algebraic Weaves and Braid Varieties with E. Gorsky, M. Gorsky and J. Simental, Amer. J. Math. (2024), 1–75.

  6. On Newton polytopes of Lagrangian augmentations with O. Capovilla-Searle, Bulletin of the LMS (2024), 1–28.

  7. Stein Traces and Characterizing Slopes with J. Etnyre and M. Kegel, Math. Ann. (2023), 1–46.

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

  9. Legendrian Weaves, with E. Zaslow, Geometry & Topology 26 (2022), 1–157.

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

  11. Braid Loops with infinite monodromy on the Legendrian contact DGA, with L. Ng, J. Topology 15(4) (2022), 1–82.

  12. Lagrangian Skeleta and Plane Curve Singularities, JFPTA Viterbo 60 Volume 24(2) (2022), 1–43.

  13. Branched covering simply-connected 4-manifolds, with
    AIM Group,

    D. Auckly, R.I. Baykur, S. Kolay, T. Lidman, D. Zuddas

    MSP Open Book Ser. 5(4) (2022), 1–11.

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

  15. Dynamical Quantization of Contact Structures, with G. Herczeg and A. Waldron, Adv. Theor. Math. Phys. (2021), 1–45.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Preprints

  1. Positive microlocal holonomies are globally regular with W. Li (2024), 1–35.

  2. Demazure weaves for reduced plabic graphs, with I. Le, M. Sherman-Bennett, D. Weng (2023), 1–79.

  3. Conjugate Fillings and Legendrian Weaves with W. Li (2022), 1–100.

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

Recent Teaching

  1. Fall 2024: Differential Topology MAT-239

  2. Fall 2024: Introduction to Abstract Mathematics MAT-108

  3. Spring 2024: Algebraic Topology II MAT-215B

  4. Spring 2024: Abstract Linear Algebra MAT-67

  5. Spring 2023: Morse Theory MAT-240B

  6. Spring 2023: Calculus MAT-21C

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

  8. Fall 2020: Mathematical Quantum Mechanics MAT-265

Media And Outreach