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.

- A Lagrangian filling for every cluster seed,

*Roger Casals, Honghao Gao*,

*Inventiones Math.***237**(2024), 1–60.

- Cluster structures on braid varieties,

*R. Casals, E. Gorsky, M. Gorsky,*,

I. Le,J. Simental, L. Shen

*J. Amer. Math. Soc.*(2024), 1–111.

- Microlocal Theory of Legendrian Links

and Cluster Algebras,

*Roger Casals, Daping Weng*,

*Geometry & Topology***28**(2024), 1–119.

- Infinitely Many Lagrangian Fillings,

*Roger Casals, Honghao Gao*,

*Annals of Math*.**195**(2022), 207–249.

- Legendrian Weaves,

*Roger Casals, Eric Zaslow*,

*Geometry & Topology***26**(2022), 1–157.

- Non-simplicity of isocontact embeddings,

*Roger Casals, John Etnyre*,*Geom. Funct. Anal.*(GAFA)**30**(2020), 1–33.

- Geometric Criteria for Overtwistedness,

*Roger Casals, Emmy Murphy, F. Presas*,

*J. Amer. Math. Soc.***32**(2019), 563–604.

- Legendrian Fronts for Affine Varieties,

*Roger Casals, Emmy Murphy*,

*Duke Math. Journal***168**(2019), 225–323.

- Existence h-principle for Engel structures,

*R. Casals, J.L. Pérez, A. Pino, F. Presas*,

*Inventiones Math.***210**(2017), 417–451.

- Almost contact 5-folds are contact,
*R. Casals, D. Pancholi, F. Presas*,

*Annals of Math.***182**(2015), 429–490.

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

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

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

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

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

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

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

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

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

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

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

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

- 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

- Fall 2024: Differential Topology MAT-239
- Fall 2024: Introduction to Abstract Mathematics MAT-108
- Spring 2024: Algebraic Topology II MAT-215B
- Spring 2024: Abstract Linear Algebra MAT-67
- Spring 2023: Morse Theory MAT-240B
- Spring 2023: Calculus MAT-21C
- Fall 2021: Contact and Symplectic Topology MAT-280
- Fall 2020: Mathematical Quantum Mechanics MAT-265

- Contact and Symplectic Topology,
*Notices Amer. Math. Soc.*(2021).

- Article in The Aggie, an Egghead Blog post and press release.
- Interview in El Mundo, RSME interview in their Magazine, and article on the Fundación BBVA.
- Interview in El Español and RTVE excerpt.
- Interview in Spanish National Radio, and Interview in Tiempo.
- Short video on the Vicent Caselles award and Award Ceremony on the Vincent Caselles.