Department of Mathematics,

casals -at- math.ucdavis.edu

My research is supported by the NSF and the Alfred P. Sloan Foundation.

I am also interested in the relations with algebraic geometry, including mirror symmetry and singularity theory.

- Infinitely Many Lagrangian Fillings,

joint work with H. Gao (2020).

- Non-simplicity of isocontact embeddings,

joint work with J. Etnyre,

*Geom. Funct. Anal.*(2020).

- Geometric Criteria for Overtwistedness,

joint work with E. Murphy and F. Presas,

*J. Amer. Math. Soc.*(2019).

- Legendrian Fronts for Affine Varieties,

joint work with E. Murphy,

*Duke Math. Journal*(2019).

- Existence h-principle for Engel structures,

with J.L. Pérez, A. del Pino and F. Presas,

*Invent. Math.*(2017).

- Almost contact 5-folds are contact,

joint work with D. Pancholi and F. Presas,

*Ann. Math.*(2015).

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

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

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

- Legendrian Weaves, with E. Zaslow (2020), 1–114. Submitted.

- Sharp Ellipsoid Embeddings and Toric Mutations with R. Vianna (2020), 1–61. Submitted.

- Infinitely Many Lagrangian Fillings, with H. Gao (2020), 1–28. Submitted.

- Lagrangian Skeleta and Plane Curve Singularities,
*JFPTA Viterbo 60 Volume*(2021).

- Branched covering simply-connected 4-manifolds, with
AiM Group,
D. Auckly, R.I. Baykur, S. Kolay, T. Lidman, D. Zuddas

*Open Book Ser.*(2021).

- The Legendrian Whitney Trick with D. Pancholi and F. Presas,
*Geom. Topol.*(2020).

- Non-simplicity of isocontact embeddings with J. Etnyre,
*Geom. Funct. Anal.***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. Ann.***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,
*Invent. 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,
*Ann. 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**(2014), 657–671.

- AMS Spring Central Sectional Meeting (Apr 21)
- MSU Geometry Seminar (Mar 21)
- IBS Legendrians, Cluster algebras, and Mirror symmetry (Jan 21)
- Geometry and Representation Theory at home (Dec 20)
- Isolated Plane Curve Singularities (Nov 20)
- Northwestern Geometry & Physics Seminar (Oct 20)
- Western Hemisphere virtual symplectic seminar (Jul 20)
- Topología de contacto: cáusticas y reflexiones (Sep 17)
- Congreso Bienal de la Real Sociedad Matemática Española (Sep 17)

- Fall 2020: Mathematical Quantum Mechanics MAT-265
- Fall 2020: Introduction to Abstract Mathematics MAT-108
- Winter 2020: Algebraic Topology II MAT-215B
- Winter 2020: Euclidean and Non-Euclidean Geometry MAT-141
- Fall 2019: Differential Equations MAT-22B
- Winter 2019: Combinatorics MAT-145

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

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