Roger Casals

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


I am a contact and symplectic topologist at the Department of Mathematics at UC Davis.
My research is supported by an NSF Award and a Research Fellowship at Fundación BBVA.

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., Volume 32 (2019) 563–604.
   
   
4. Legendrian Fronts for Affine Varieties
   joint work with E. Murphy.
   Duke Math. Journal, Volume 168 (2019), 1-136.
   
   
5. Existence h-principle for Engel structures
   joint work with J.L. Pérez, A. del Pino and F. Presas.
   Invent. Math. Volume 210, Issue 2, (2017) 417-451.
   
   
6. Almost contact 5-folds are contact
   joint work with D. Pancholi and F. Presas
   Ann. Math., Volume 182, Issue 2 (2015) 429-490.
   
   

List of Publications

1. Non-simplicity of isocontact embeddings
   joint work with J. Etnyre.
   Geom. Funct. Anal. (2020).
   
   
2. Geometric Criteria for Overtwistedness
   joint work with E. Murphy and F. Presas.
   J. Amer. Math. Soc., Volume 32 (2019), 563-604.
   
   
3. Legendrian Fronts for Affine Varieties
   joint work with E. Murphy.
   Duke Math. Journal, Volume 168 (2019), 1-136.
   
   
4. Loose Engel structures
   with A. del Pino and F. Presas.
   Compositio Math. (2019).
   
   
5. OT Disks and Exotic Symplectic Structures
   Proc. Amer. Math. Soc. (2019).
   
   
6. Differential algebra of cubic planar graphs
   joint work E. Murphy.
   Advances in Math. Volume 338 (2018), 401-446.
   
   
7. Classification of Engel Knots
   joint work A. del Pino.
   Math. Ann. Issue 1, Volume 371 (2018), 391-404.
   
   
8. Symplectomorphisms of exotic discs
   joint work with A. Keating and I. Smith.
   J. École Polytechnique, Volume 5 (2018), 289-316.
   
   
9. Transverse Universal Links
   joint work with J. Etnyre.
   Proc. Sympos. Pure Math (2018).
   
   
10. Existence h-principle for Engel structures
    joint work with J.L. Pérez, A. del Pino and F. Presas.
    Invent. Math. Volume 210, Issue 2, (2017), 417-451.
    
    
11. Higher Maslov Indices
    joint work with V.L. Ginzburg and F. Presas.
    J. Geom. Phys. Volume 115 (2017), 167-177.
    
    
12. Contact topology from the loose viewpoint
    joint with E. Murphy.
    Gökova Geom. Top. Volume 22 (2016), 81-115.
    
    
13. On the strong orderability of overtwisted 3-folds
    joint work with F. Presas
    Comment. Math. Helv. Volume 91, Issue 2, (2016), 305-316.
    
    
14. Small positive loops on overtwisted manifolds
    joint work with F. Presas and S. Sandon
    J. Symp. Geom., Volume 14, Issue 2 (2016).
    
    
15. Chern-Weil theory and the group of strict contactomorphisms
    joint work with O. Spáčil
J. Topol. Anal., Volume 08, Issue 1 (2016).


16. Almost contact 5-folds are contact
    joint work with D. Pancholi and F. Presas
    Ann. Math., Volume 182, Issue 2 (2015) 429-490.
    
    
17. h-principle for 4-dimensional contact foliations
    joint work with A. del Pino and F. Presas
Int. Math. Res. Not., Volume 20 (2015) 176-207.


18. Contact blow-up
    joint work with D. Pancholi and F. Presas,
    Exp. Math., Volume 33, Issue 1, (2015) 78-100.
    
    
19. A Remark on the Reeb Flow for Spheres
    joint work with F. Presas,
    J. Symp. Geom., Volume 12, Number 4, (2014) 657-671.

Preprints

1. Infinitely Many Lagrangian Fillings
   joint work with H. Gao (2020).
   
   
2. The Legendrian Whitney Trick
   joint work with D. Pancholi and F. Presas (2019).
   
   

Teaching

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


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


3. Fall 2019: Differential Equations MAT-22B


4. Winter 2019: Combinatorics MAT-145


5. Working Group: Symplectic Geometry


6. Fall 2018: Introduction to Abstract Mathematics MAT-108


7. Fall 2017: Lie Groups M206


8. Summer 2017: H-Principles School


9. Spring 2017: Real Analysis 18.100A


10. Fall 2016: Riemann Surfaces 18.116


11. Spring 2016: Differential Equations 18.03


12. Fall 2015: Real Analysis 18.100C


13. Fall 2014: Linear Algebra 111


14. Spring 2013: Multivariable Calculus 911

Media Outreach

1. Interview in El Mundo.
   


2. Interview, in the RSME Magazine.
   


3. Interview in Tiempo by Hernando F. Calleja.
   


4. Interview in Spanish National Radio by S. García.
   


5. Short video on the Vicent Caselles award.
   


6. Award Ceremony on the Vincent Caselles.