Roger Casals

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.
    
    

1. Spectral Networks and Betti Lagrangians with Y.J. Nho, 1–150.
   
   
2. Positive microlocal holonomies are globally regular with W. Li, 1–35.
   
   
3. Demazure weaves for reduced plabic graphs, with I. Le, M. Sherman-Bennett, D. Weng, 1–79.
   
   
4. Conjugate Fillings and Legendrian Weaves with W. Li, 1–100.
   
   
5. Comparing cluster algebras on braid varieties, with P. Galashin, M. Gorsky, L. Shen, J. Simental, M. Sherman-Bennett, 1-67.
   
   
6. Positroid Links and Braid Varieties with E. Gorsky, M. Gorsky and J. Simental, 1–57.
   
   
7. Boundedness of Mutation Classes of Rank 3 Quivers with K. Ke, 1–14.
   
   
8. A Lagrangian filling for every cluster seed, with H. Gao, Invent. Math. (2024), 1–60.
   
   
9. Cluster structures on braid varieties with E. Gorsky, M. Gorsky, I. Le, J. Simental, L. Shen, J. Amer. Math. Soc. (2024), 1–111.
   
   
10. A binary invariant of matrix mutation, J. Comb. Algebra (2024), 1–16.
    
    
11. Microlocal Theory of Legendrian Links and Cluster Algebras with D. Weng, Geometry & Topology 28 (2024), 1–100.
    
    
12. Algebraic Weaves and Braid Varieties with E. Gorsky, M. Gorsky and J. Simental, Amer. J. Math. (2024), 1–75.
    
    
13. On Newton polytopes of Lagrangian augmentations with O. Capovilla-Searle, Bulletin of the LMS56 (2024), 1–28.
    
    
14. Stein Traces and Characterizing Slopes with J. Etnyre and M. Kegel, Math. Ann.389 (2024), 1–46.
    
    
15. Infinitely Many Lagrangian Fillings, with H. Gao, Annals of Math. 195 (2022), 207–249.
    
    
16. Legendrian Weaves, with E. Zaslow, Geometry & Topology 26 (2022), 1–157.
    
    
17. Full Ellipsoid Embeddings and Toric Mutations with R. Vianna, Selecta Math. (N.S.) 28 (2022), 1–62.
    
    
18. Braid Loops with infinite monodromy on the Legendrian contact DGA, with L. Ng, J. Topology 15(4) (2022), 1–82.
    
    
19. Lagrangian Skeleta and Plane Curve Singularities, JFPTA Viterbo 60 Volume 24(2) (2022), 1–43.
    
    
20. 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.
    
    
21. The Legendrian Whitney Trick with D. Pancholi and F. Presas, Geometry & Topology 25 (2021), 3229–3256.
    
    
22. Dynamical Quantization of Contact Structures, with G. Herczeg and A. Waldron, Adv. Theor. Math. Phys. (2021), 1–45.
    
    
23. Non-simplicity of isocontact embeddings with J. Etnyre, Geom. Funct. Anal. (GAFA) 30 (2020), 1–33.
    
    
24. Geometric Criteria for Overtwistedness, with E. Murphy and F. Presas, J. Amer. Math. Soc., 32 (2019), 563–604.
    
    
25. Transverse Universal Links, with J. Etnyre, Proc. Sympos. Pure Math 102 (2019), 43–56.
    
    
26. Loose Engel structures with A. del Pino and F. Presas, Compositio Math. 156 (2019), 412–434.
    
    
27. Legendrian Fronts for Affine Varieties, with E. Murphy, Duke Math. Journal 168 (2019), 225–323.
    
    
28. OT Disks and Exotic Symplectic Structures, Proc. Amer. Math. Soc. 148 (2019), 825–834.
    
    
29. Differential algebra of cubic planar graphs, with E. Murphy, Advances in Math. 338 (2018), 401–446.
    
    
30. Classification of Engel Knots, with A. del Pino, Math. Annalen 371 (2018), 391–404.
    
    
31. Symplectomorphisms of exotic discs, with A. Keating and I. Smith, J. École Polytechnique 5 (2018), 289–316.
    
    
32. Existence h-principle for Engel structures, with J.L. Pérez, A. del Pino and F. Presas, Inventiones Math. 210 (2017), 417–451.
    
    
33. Higher Maslov Indices, with V.L. Ginzburg and F. Presas, J. Geom. Phys. 115 (2017), 167–177.
    
    
34. Contact topology from the loose viewpoint, with E. Murphy, Gökova Geom. Top. 22 (2016), 81–115.
    
    
35. On the strong orderability of overtwisted 3-folds, with F. Presas, Comment. Math. Helv. 91 (2016), 305–316.
    
    
36. Small positive loops on overtwisted manifolds, with F. Presas and S. Sandon, J. Symp. Geom. 14 (2016), 1013–1031.
    
    
37. Chern-Weil theory and the group of strict contactomorphisms, with O. Spáčil, J. Topol. Anal. 8 (2016), 59–87.
    
    
38. Almost contact 5-folds are contact, with D. Pancholi and F. Presas, Annals of Math. 182 (2015), 429–490.
    
    
39. h-principle for 4-dimensional contact foliations, with A. del Pino and F. Presas, Int. Math. Res. Not. 20 (2015), 176–207.
    
    
40. Contact blow-up, with D. Pancholi and F. Presas, Exp. Math. 33 (2015), 78–100.
    
    
41. A Remark on the Reeb Flow for Spheres, with F. Presas, J. Symp. Geom. 12, 657–671.
    
    

1. Official website: Legendrian Links and the Microlocal Theory of Sheaves


2. Material for lectures: A microlocal introduction to Legendrian submanifolds (draft in progress)

• MCA Prize 2025 at the Mathematical Congress of the Americas 2025.
  
  
• José Luis Rubio de Francia Prize by the Spanish Royal Mathematical Society.
  
  
• Vicent Caselles Prize by the Spanish Royal Mathematical Society and the BBVA Foundation.
  
  
• Sloan Research Fellowship by the Alfred P. Sloan Foundation.
  
  
• NSF Career Award by the National Science Foundation.
  
  

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


2. Fall 2024: Differential Topology MAT-239


3. Spring 2024: Abstract Linear Algebra MAT-67


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


5. Spring 2023: Calculus MAT-21C


6. Spring 2023: Morse Theory MAT-240B


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


8. Fall 2020: Mathematical Quantum Mechanics MAT-265

• Contact and Symplectic Topology, Notices Amer. Math. Soc. (2021).
  
  
• On rays of light by G. Watry, Article in The Aggie, an Egghead Blog post and press release.
  


• RSME interview in La Gaceta Magazine, Interview in El Mundo, and article on the Fundación BBVA.
  
  
• Interview in El Español, RTVE excerpt, and Interview in Tiempo.