AIS - Topics in Complex Analysis in one and higher dimensions (2025)

Speakers and Syllabus

Detailed syllabus

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Dr. Prachi Mahajan, IIT Bombay	6	Holomorphic functions of several variables, basic properties, domains of convergence of power series and Laurent series, domains of holomorphy, pseudoconvexity.
Dr. Vikramjeet Chandel IIT Kanpur	6	Basics of metric geometry, length spaces, geodesics, completeness and Hopf–Rinow theorem, Basics of the Kobayashi and Caratheodary pseudodistances.
Dr. Sabyasachi Mukherjee, TIFR - Mumbai.	6	connections between complex analysis and hyperbolic geometry: uniformization theorem, strong versions of Montel's and Picard's theorems, the notion of Riemann surfaces, basic theory of quasiconformal maps, basic iteration theory of holomorphic maps on Euclidean and hyperbolic Riemann surfaces, iteration theory of rational maps on the Riemann sphere: basic properties of Fatou and Julia sets, local dynamics near periodic points and their relation to global dynamics, and
Dr. Sivaguru Ravisankar, TIFR CAM - Bengaluru	6	CR-Geometry (basics of CR manifolds and holomorphic extension), Function theory on domains in C^n (say, estimates of various objects on finite type domains in C^2, convex finite type domains in C^n, etc).
Dr. Purvi Gupta, IISc	6	Introduction to Pluripotential Theory: Distributions & currents, subharmonic and plurisubharmonic functions, the Dirichlet problem for the complex Monge-Ampere operator, pluripolar sets.
Dr. Anwoy Maitra IIT Madras	6	The visibility property and connection to SCV, goldilocks domains of Bharali–Zimmer and their properties, non-goldilocks domains with visibility property, weak visibility domains.

References:

Klaus Fritzsche & Hans Grauert, From Holomorphic Functions to Complex Manifolds, Springer.
S. Krantz, Function Theory of Several Complex Variables, American Mathematical Society, 2001.
J. Milnor, Dynamics in one complex variable, Princeton University Press.
Klimek, Maciej. Pluripotential theory, London Math. Soc. Monogr. (1991).
Kołodziej, Sławomir. The complex Monge-Ampere equation and pluripotential theory. American Mathematical Soc., 2005
Dror Varolin - Riemann Surfaces by way of complex analytic geometry, American Mathematical Society.
Jean-Pierre Demailly - Complex Analytic and Differential Geometry (Lecture Notes)

Time Table

Day	Date	Lecture 1 (9.30 to 11.00)	Tea (11.05-11.25)	Lecture 2 (11.30–1.00)	Lunch (1.05–2.25)	Tutorial (2.30–3.30)	Tea (3.35-3.55)	Tutorial (4.00-5.00)	Snacks 5.05-5.30
		(name of the speak er		(nameof the speaker		(nameof the speaker + tutors)		(nameof the speaker + tutors)
Mon	9th June	VSC		PM		VSC+T B		PM+JM
Tues	10th June	PM		VSC		PM+JM		VSC+T B
Wed	11th June	VSC		PM		VSC+T B		PM+JM
Thu	12th June	PM		VSC		PM+JM		VSC+T B
Fri	13th June	VSC		PM		VSC+T B		PM+JM
Sat	14th June	PM		VSC		PM+JM		VSC+T B
SUNDAY:OFF
Mon	16th June	SM		SR		SV+SM		RJ+SR
Tues	17th June	SR		SM		RJ+SR		SV+SM
Wed	18th June	SM		SR		SV+SM		RJ+SR
Thu	19th June	SR		SM		RJ+SR		SV+SM
Fri	20th June	SM		SR		SV+SM		RJ+SR
Sat	21st June	SR		SM		RJ+SR		SV+SM
SUNDAY:OFF
Mon	23rd June	AM		PG		AM+JM		PG+AB
Tues	24th June	PG		AM		PG+AB		AM+JM
Wed	25th June	AM		PG		AM+JM		PG+AB
Thu	26th June	PG		AM		PG+AB		AM+JM
Fri	27th June	AM		PG		AM+JM		PG+AB
SAT	28th June	PG		AM		PG+AB		AM+JM

Tutorial Assistants:

S.No.	Name	Affiliation
1	Jiju Mammen	IIT-Palakkad
2	T.Bharathi	IIT-Palakkad
3	S. Viswanathan	ICTS
4	Annapurna Banik	TIFR-CAM
5	Ravisankar Jaiswal	TIFR-CAM

Full forms for the abbreviations of speakers and tutors:

VSC: Vikramjeet Singh Chandel PM: Prachi Mahajan
SM: Sabyasachi Mukherjee SR: Sivaguru Ravisankar PG: Purvi Gupta
AM: Anwoy Maitra
JM: Jiju Mammen TB: T. Bharathi
SV: S. Viswanathan AB: Annapurna Banik
RJ: Ravi Shankar Jaiswal

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AIS - Topics in Complex Analysis in one and higher dimensions (2025)

Speakers and Syllabus

Detailed syllabus

Time Table

AIS TCAOHD (2025)