6 papers
Monodromy of plane curve singularities and quiver mutation
Roger Casals
The main result of this article shows that the quiver mutation class of a malleable real Morsification uniquely determines the integral monodromy module of a plane curve singularit…
On wall-crossing coordinates in Cerf theory
Roger Casals
We relate Bruhat numbers in real Morse theory to cluster variables in braid varieties. This provides instances of wall-crossing coordinates in the study of Cerf diagrams.
Boundedness criteria for real quivers of rank 3
Roger Casals, Kenton Ke
We study the boundedness of a mutation class for quivers with real weights. The main result is a characterization of bounded mutation classes for real quivers of rank 3.
Spectral Networks and Betti Lagrangians
Roger Casals, Yoon Jae Nho
We introduce and develop the theory of spectral networks in real contact and symplectic topology. First, we establish the existence and pseudoholomorphic characterization of spectr…
Positive microlocal holonomies are globally regular
Roger Casals, Wenyuan Li
We establish a geometric criterion for local microlocal holonomies to be globally regular on the moduli space of Lagrangian fillings. This local-to-global regularity result holds f…
A binary invariant of matrix mutation
Roger Casals
We construct a binary mutation invariant for skew-symmetric integer matrices. The invariant is not an integer congruence invariant for matrices of odd size: we provide examples of…