Roger Casals
University of California Davis
Department of Mathematics
,
casals -at- math.ucdavis.edu
My research is supported by an
NSF Career
and the
Alfred P. Sloan Foundation
.
The
seminar listing
at UC Davis, and the
NCSGS
.
Selected Articles
Microlocal Theory of Legendrian Links
and Cluster Algebras
,
Roger Casals, Daping Weng
,
arXiv version
(2022), 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
(2022), 1–116.
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.
List of Publications
Microlocal Theory of Legendrian Links and Cluster Algebras
with
D. Weng
(2022), 1–119. Submitted.
Stein Traces and Characterizing Slopes
with
J. Etnyre
and
M. Kegel
(2021), 1–37. Submitted.
Positroid Links and Braid Varieties
with
E. Gorsky
,
M. Gorsky
and
J. Simental
(2021), 1–57. Submitted.
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.
Infinitely Many Lagrangian Fillings
, with
H. Gao
,
Annals of Math.
195
(2022), 207–249.
Legendrian Weaves
, with
E. Zaslow
,
Geometry & Topology
(2022), 1–116.
Full Ellipsoid Embeddings and Toric Mutations
with
R. Vianna
,
Selecta Math. (N.S.)
28
(2022), 1–62.
Lagrangian Skeleta and Plane Curve Singularities
,
JFPTA Viterbo 60 Volume
24
(2021), 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.
(2021), 1–11.
The Legendrian Whitney Trick
with
D. Pancholi
and
F. Presas
,
Geometry & Topology
25
(2021), 3229–3256 .
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.
Some Talk Slides
Nottingham Online Algebraic Geometry
(May 21)
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)
Recent Teaching
Fall 2021:
Contact and Symplectic Topology
MAT-280
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
Media And Outreach
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.