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

Convener(s)


Name:	Dr. G.P. Balakumar	Dr. J. Jaikrishnan
Mailing Address:	Assistant Professor, Department of Mathematics, Indian Institute of Technology Palakkad	Assistant Professor, Department of Mathematics, Indian Institute of Technology Palakkad Kanjikode, Palakkad
Email:	gpbalakumar at iitpkd.ac.in	jaikrishnan at iitpkd.ac.in

This AIS (Advanced Instructional School) is meant to provide an introduction to a range of topics that have become fundamental to pursue research in complex analysis in one or several variables and allied areas. To ensure that this workshop is actually accessible to PhD students whose research area broadly lies in Complex Analysis and is relatively self-contained, presupposing only the knowledge of standard topics covered in the three AFS’ (Annual Foundation Schools), the first week will be devoted to a brisk review of SCV (Several Complex Variables); particularly, since it is not part of any of the topics covered in the AFS’. Likewise, the second week will include a rapid review of complex dynamics. Further exposition of topics associated with this as well as that in SCV, will be rendered by active young researchers in these areas in the latter half of this workshop.

Dates:

Monday, June 9, 2025 - 09:00 to Saturday, June 28, 2025 - 21:00

Venue:

Venue Address:

Indian Institute of Technology Palakkad
Kanjikode, Palakkad
Kerala – 678623.

Venue State:

Kerala

Venue City:

Palakkad

PIN:

678623

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

Selected Applicants:

Sr.n	SID	Full Name	Gender	Affiliation	Position in College/ University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D. Degree Date
1	61992	Mr. Nirmal Rawat	Male	IIT Bhubaneswar	PhD	IISER Thiruvananthapuram	2023
2	61998	Dr Anish Kumar	Male	Dr. Shyama Prasad Ranchi	Asst. Prof	Central University of South Bihar	2018
3	62084	Ms. Ramanpreet Kaur	Female	Indian Institute of Science Education and Research (IISER) Mohali	Postdoctoral fellow	M.Sc	2017	24/02/2024
4	62118	Mr. Ashish Kumar Trivedi	Male	University of Delhi	PhD	Hindu College, University of Delhi.	2023
5	62120	Mr. Rahul Gogoi	Male	University of Delhi	PhD	Tezpur University	2023
6	62121	Mr. Ayush Kumar	Male	University of Delhi	PhD	Hindu College, University of Delhi	2023
7	62167	Mr. Pushpender	Male	University of Delhi	Ph.D.	Kirori Mal College, University of Delhi	2023
8	62177	Ms Pinki ‎ ‎	Female	University of Delhi	PhD	MSc	2022
9	62271	Mr Harikrishnan S	Male	IISER Thiruvananthapuram	BSMS Student	IISER Thiruvananthapuram	Awaiting Result
10	62305	Ms. Priya Birendra Kumar Singh	Female	Indian Institute Of Science Education and Research, Pune	PhD	Sardar Vallabhbhai National Institute of Technology, Surat	2023
11	62327	Mast. Devarajan Iyer	Male	Shiv Nadar Institute of Eminence	PhD	University of Hyderabad	2023
12	62331	Mr. Sureshkrishnan K	Male	Inidian Institute Of Technology Roorkee	PhD	M.sc	2020
13	62336	Mr. Bharath Krishna S	Male	Indian Institute of Science Education and Research Thiruvananthapuram	Integrated PhD student	Indian Institute of Science Education and Research Thiruvananthapuram	2024
14	62408	Mr. Shantanu Panja	Male	University of Kalyani	PhD Scholar	National Institute Of Technology Rourkela	2020
15	62414	Mr. Thirupathi P	Male	Indian Institute of Science Education and Research - Thiruvananthapuram	PhD	Islamiah College - Vanniyambadi	2019
16	62516	Mr. Bhaskar Paul	Male	Indian Institute of Technology Bhilai	PhD Student	Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math	2021
17	62625	Mr. Sourasish Karmakar	Male	IISER Kolkata	PhD Student	IISER Kolkata	2024
18	62758	Ms Pratiksha Pakhetra	Female	University of Jammu	PhD	University of Jammu	2022
19	62896	Mr. Dipon Kumar Mondal	Male	IIT Bhubaneswar	Ph.D.	University of Hyderabad	2021
20	62952	Mr. Ganesh V	Male	IISER Tirupati	PhD	University of Madras	2021
21	63057	Ms Mary Cinderella P S	Female	Indian Institute of Science Education and Research	PhD	Central University of Tamilnadu	2021
22	63124	Mr. Subham Chatterjee	Male	Sidho-Kanho-Birsha University	Ph.D Student	Sidho-Kanho-Birsha University, M.Sc.(Mathematics)	2020
23	63125	Mr. Soumyadip Majee	Male	Sidho-Kanho-Birsha University	PhD	Sidho-Kanho-Birsha University, M.Sc.(Mathematics)	2020
24	63142	Mr. Nitai Mandal	Male	Sidho-Kanho-Birsha University	PhD Student	University of Kalyani	2020
25	63389	Mr. Mayank Jangid	Male	Indian Statistical Institute, Kolkata	M.Math Student	Indian Statistical Institute, Kolkata	Awaiting Result
26	63522	Mr Aakash Ramankutty	Male	Indian Institute Of Technology Hyderabad	PhD	University Of Hyderabad	2024
27	63828	Ms Keerthana Reddy	Female	Indian Institute of Technology, Madras.	PhD	IIT Madras	2020
28	63894	Mr. Saptaak Dey	Male	Visva-Bharati	Ph. D. student	University of Kalyani - M.Sc.	2019
29	64123	Mr Aryan Kumar Prasad	Male	National Institute of Science Education and Research (NISER)	Int MSc-PhD Student	NISER
30	64178	Mr. Ujjal Hazra	Male	Indian Institute of Technology Bhubaneswar	PhD	West Bengal State University	2021
31	64179	Mr. Suman Karak	Male	Indian Institute of Science Education and Research Kolkata	PhD Student	NIT Rourkela	2023
32	64211	Mr Kaustav Roy	Male	Indian Institute of Technology Palakkad	PhD Student	Jadavpur University	2020
33	64212	Mr Chinnapparaj R	Male	Indian Institute of Technology	PhD student	Ayya Nadar Janaki Ammal College	2016
34	64293	Mr. Subhajit Ghosh	Male	Indian Institute of Science Education and Research Kolkata (IISER Kolkata)	PhD	University of Calcutta,Ballygunge Science College.	2023
35	64338	Mr Sanju Mandal	Male	Jadavpur University	Ph.D. Student	University of Calcutta	2020
36	64357	Mr. Shreedhar Bhat	Male	TIFR-Centre for Applicable Mathematics	Postdoctoral Researcher	IIT Madras	2019	10/08/2024
37	64452	Ms Winne Bareh	Female	North Eastern Hill University, Shillong.	PhD	University M.Sc	2023
38	64469	Mr Joson Josh Amaro Martires Henriques	Male	The Institute of Mathematical Sciences Chennai	PhD student	Indian Institute of Science Education and Research Pune	2024
39	64601	Ms. Goirika Saha	Female	Indian Association For The Cultivation Of Science	PhD	Vidyasagar University	2020
40	64608	Ms. Moumita Manna	Female	IIT Bhubaneswar	PhD Student	Banaras Hindu University	2020
41	64649	Mr. Ritam Sinha	Male	Ramakrishna Mission Vivekananda Centenary College, Rahara	PhD	Ramakrishna Mission Vivekananda Centenary College, Rahara(WBSU)	2022
42	64663	Ms Poonam Babani Rane	Female	BITS Pilani, K K Birla Goa Campus	PhD	Maharashtra Institute of Technology, WPU Pune	2023
43	64676	Mr Shubhankar Mandal	Male	Indian Institute of Technology Bhilai	Research Associate-1	National Institute of Technology Rourkela	2016	16/09/2024
44	64687	Ms Maitree Pal	Female	Indian Association for the Cultivation of Science	PhD student	Jadavpur University	2022
45	64752	Mr. Om Sai	Male	Indian Statistical Institute Kolkata	M.Math Student	Indian Statistical Institute Kolkata
46	64791	Mr Subith G	Male	iiser Trivandrum	Phd	Calicut University	2020
47	64836	Mr. Saurav Kumar	Male	Indian Institute of Science Education and Research Bhopal	PhD	IISER Bhopal	Awaiting Result
48	64885	Mr. Nilaksh Pundir	Male	Indian Statistical Institute Kolkata	Msc Student	Indian Statistical Institute	Awaiting Result
49	64890	Mr Gourab Paul	Male	IISER Kolkata	PhD	Jadavpur University	2021
50	64938	Mr. Ritesh Pal	Male	Babasaheb Bhimrao Ambedkar University, Lucknow	Ph.D.	Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur	2021
51	64979	Mr Mehta Nihar Kamleshbhai	Male	Institute of Infrastructure Technology Research and Management	PhD	M.Sc	2024
52	65019	Ms. Kothai Velayutham	Female	Indian Institute of Technology, Hyderabad	PhD	Pondicherry University	2023

How to Reach:

TBA

School Short Name:

tcaohd

Last Date Application:

Monday, March 31, 2025

School Type:

AIS