BRIEF RESEARCH DESCRIPTION
My area of research is Several Complex Variables (SCV). Mathematical problems and
techniques in this area make contact with a broad range of disciplines, from analysis to geometry to
partial differential equations. My own interests in SCV, and the techniques that I am most familiar
with, are closer to analysis. In recent times, I have also worked on problems of a
geometric nature (although the solutions thereof feature a considerable amount of analysis) with
several wonderful collaborators. Take a look at my
list of publications to see whom I have been collaborating with.
A broad classification of the types of problems I am working on at the moment is as follows:
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Dynamics of holomorphic correspondences: A holomorphic correspondence is a special type
of relation between a pair of complex manifolds of the same dimension (of which holomorphic maps
are a special case). A compact hyperbolic Riemann surface admits only finitely many
holomorphic self-maps. Thus, the iterative dynamics of any such map is uninteresting.
However, the class of holomorphic correspondences on a hyperbolic Riemann surface is very
rich. Thus, the dynamical system arising from iterating a holomorphic correspondence (that is
not a self-map) exhibits very interesting and complex behaviour. The study of this
type of complexity is a rather new field, with lots of scope for exploration.
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The Kobayashi geometry of domains: This aspect of my research involves the geometric
properties that domains in Cn acquire when viewed as metric spaces equipped
with the Kobayashi distance. My core interest is to obtain a complete theory for the boundary regularity
of complex geodesics in convex domains. This has—in joint work with collaborators—led to
investigations of when and how the above-mentioned domains exhibit weak forms of negative curvature.
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Rigidity of holomorphic mappings: "Rigidity" here refers to the phenomenon wherein every member of a
specified family of holomorphic maps turns out to obey severe structural constraints (and is thus easy to
describe, often explicitly). This type of rigidity usually arises due to metrical or topological properties of the
target space in question (and on the way these properties interact with holomorphicity).
RESEARCH SUPERVISION
CURRENT Ph.D. STUDENTS
FORMER Ph.D. STUDENTS
(in reverse-chronological order of graduation)
FORMER M.S. STUDENTS
(in reverse-chronological order of graduation)
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