Speaker :- Dr. Sahil Gehlwat

Title of the Talk :- Singular hyperbolic Riemann surface foliation

Date, Time and venue :- 16 April 2025, 12:00 PM at Seminar Hall, Dept of Mathematics.

About the speaker :- Dr. Sahil Gehlawat did his PhD and Masters from IISc Bangalore. My area of specialization is Complex Analysis. He is currently a postdoc fellow in TIFR CAM Bangalore. Before that, he was a postdoc fellow at the University of Lille, France, and HRI Prayagraj as well

Abstract :- We consider singular holomorphic foliations $\mathcal{F}$ of dimension 1 on a complex manifold $M$ with all leaves being hyperbolic Riemann surfaces. Consider the Poincare metric $\lambda_{L}$ on each leaf. It is conjectured to vary smoothly along the transverse directions. There has been a lot of work on achieving this regularity of this leafwise Poincare metric for certain special cases (most of this is for foliations with discrete singular sets). The study of the regularity of this metric is equivalent to studying the Verjovsky's modulus of uniformization map $\eta$, which is a positive map defined away from the singular set $E$ of the foliation $\mathcal{F}$. In this talk, we study this map $\eta$ for foliations without any restriction on the dimension of the singular set. We will give some sufficient conditions for the continuity of the map $\eta$ on the non-singular set, and also the continuous extension on the singular set.