Research
Low-dimensional Topology and Geometry
Complex projective structures and Branched projective structures on surfaces, Translation structures on surfaces. Hyperbolic Geometry, hyperbolic structures and branched hyperbolic structures. Relationship between hyperbolic structures and their holonomy representation. Teichmüller theory and higher Teichmüller theory. Moduli spaces of geometric structures in low-dimension. Representation spaces of finite genertated groups into Lie groups and character varieties.
Dynamical Systems
Teichmüller dynamics. Ergodic theory. Mapping class group action on the character varieties and classification of the orbits.
Published papers
Complex projective structures with maximal number of Möbius transformations. Joint work with L. Ruffoni. In: Mathematische Nachrichten, Volume 292, Issue 6, (2019). Available here.
Distances on the Moduli space of Complex Projective Structures. Expositiones Mathematicae, Volume 38, Issue 4, (2020). Available online here.
Geometrization of purely hyperbolic representations in PSL(2,R). Advances in Geometry, Volume 21, Issue 1, (2021). Available online here.
Translation surfaces and periods of meromorphic differentials. Joint work with S. Chenakkod and S. Gupta. Preprint available here. Proc. London Math. Soc. (3) 2022, 124 478-557.
Modular orbits on the representation space of compact abelian Lie groups. Joint work with Y. Bouilly. Groups, Geometry and Dynamics vol 17, no 2, pagg 719-749.
Tessellation of surfaces. To be published in Proceedings of The Year-Long Program on Triangle Groups, Belyi Uniformization, and Modularity, Volume 1. Preprint available here.
On the distality and expansivity of certain maps on spheres. Joint work with M. Choudhuri and A. K. Yadav. To appear in Dynamical Systems. Preprint available here.
Monodromy of Schwarzian equations with regular singularities. Joint work with S. Gupta. To appear on Geometry & Topology (2024) . Preprint available here.
Automorphism groups of certain branched structures on surfaces. Milan J. Math. (2024). https://doi.org/10.1007/s00032-024-00393-w. Preprint avialable here.
Simple loop conjecture for discrete representations in PSL(2,R). Joint work with Subhojoy Gupta. To appear on Proceeding - Mathematical Sciences. Preprint available here.
Preprints
Period realization of meromorphic differentials with prescribed invariants. Joint work with Dawei Chen. Preprint available here.
Isoperiodic foliation of the stratum H(1,1;-2). Joint work with Guillaume Tahar and Yongquan Zhang. Preprint available here.
Counterexamples to the simple loop conjecture in higher-dimension. Preprint available on here.
2057UB_FaracoGupta_Monodromy_of_Schwarzian_equations_with_regular_singularities.pdfPlease, come and look at this poster for a quick overview about my most recent collaboration with Subhojoy Gupta! This poster has been recently selected to appear at Short Communications Satellite 2022. Link here.
RGF_II-2.pdfPlease, come and look at this poster for a quick overview about my collaboration with Dawei Chen!
Math Events (old and new)
Spherical surfaces and related topics - June 20-24, 2022
Virtual Math Fest 2020 - July 20-26.
Collaborators and friends
Yohann Bouilly, France
Dawei Chen, Boston College, USA
Manoj Choudhuri, IITRAM, India
Soumya Dey, CMI Chennai, India
Camilla Felisetti, University of Modena and Reggio Emilia, Italy
Subhojoy Gupta, IISc Bangalore, India
Krishnendu Gongopadhyay, IISER Mohali, India
Debanjan Nandi, Weizmann Institute, Israel
Irene Pasquinelli, University of Bristol, UK
Lorenzo Ruffoni, Tufts University, USA
Gunja Sachdeva, BITS Pilani, India
Alessio Savini, University of Geneva, Switzerland
Maxim Smirnov, University of Augsburg, DE
Alok Kumar Yadav, University of Delhi, India