This school is devoted to providing an audience comprising, primarily, students working towards a PhD in any area of analysis or geometry exposure to fundamental tools from SCV. In recent times, methods from SCV have made inroads into many fields of mathematics – ranging from analytic geometry to operator theory. This observation shapes the choice of topics that comprise the proposed syllabus for this Instructional School, namely:
- The concept of holomorphicity in several variables and the basic theory
- Subharmonicity and plurisubharmonicity
- Zeros of holomorphic functions
- The ∂̅—problem
- The Levi problem
- Invariant metrics
Topics to be covered in terms of modules of 6 lectures each:
| Name of the speaker | No of lectures: duration 1.5hours Each |
Detailed syllabus |
| J. Jaikrishnan (IIT Madras) |
4 lectures | Holomorphic functions of several variables, basic properties such as open mapping theorem, the Schwarz lemma, Hartogs’ separate analyticity theorem |
| Vamsi Pingali (IISc) |
4lectures | Subharmonic functions in one variable, the Dirichlet problem, plurisubharmonic functions – basic theory |
| A.J.Parameswaran (TIFR) |
4lectures | The Weierstrass Preparation and Division theorems |
| Kingshook Biswas (ISI Kolkata) |
4lectures | The basic setup of Hormander’s∂̅ -methods |
| R. Sivaguru (TIFR-CAM) |
4lectures | Domains of holomorphy, the Levi problem |
| G. P. Balakumar (IIT Palakkad) |
4lectures | Invariant metrics such as the Bergman, Caratheodory and Kobayashi metric – properties, relations between them and applications. |
References:
- Steven G. Krantz, Function theory of several complex variables: AMS Publishing, 2001.
- R. Narasimhan, Several complex variables: University of Chicago Press, 1971.
- R.M. Range, Holomorphic functions and integral representations in several complex variables, GTM 108, Springer-Verlag, 1986.
Names of the tutors/course associates:
| Name | Affiliation | Status |
| Dr. Vikramjeet Singh Chandel | IISc | ResearchAssociate |
| Mr. AnwoyMaitra | IISc | PhD student |
| Dr. GopalDatt | IISc | Post Doc |
| Mr. Amardep Sarkar | IISc | PhD student |
| Dr. Diganta Borah | IISER Pune | Assistant Professor |
| Dr. SayaniBera | RKMVU | Post Doc |
| Dr. Ratna Pal | IISER Pune | Post Doc |
| Dr. Pranav Haridas | IIT Madras | Post Doc |
Tentative Timetable:
| Day | Date | Lec.1 9:30 AM – 11 AM |
Tea 11 – 11:30 AM |
Lec. 2 11:30 – 1 PM |
Lunch 1 – 2:30 PM |
Tut. 1 2:30 – 3:30 PM |
Tea 3:30 – 4:00 PM |
Tut. 2 4:00 – 5:00 PM |
Tea 5:00 – 5:30 PM |
| Mon | 11/6 | JJ | AJP | VC/AM | VC/AM | ||||
| Tue | 12/6 | JJ | AJP | VC/AM | VC/AM | ||||
| Wed | 13/6 | JJ | AJP | VC/AM | VC/AM | ||||
| Thu | 14/6 | JJ | AJP | GD/RP | GD/RP | ||||
| Fri | 15/6 | RS | KB | GD/RP | GD/RP | ||||
| Sat | 16/6 | RS | KB | GD/RP | GD/RP | ||||
| Sun | 17/6 | Sunday Recess | |||||||
| Mon | 18/6 | RS | KB | AS/DB | AS/DB | ||||
| Tue | 19/6 | RS | KB | AS/DB | AS/DB | ||||
| Wed | 20/6 | VP | GPB | AS/DB | AS/DB | ||||
| Thu | 21/6 | VP | GPB | PH/SB | PH/SB | ||||
| Fri | 22/6 | VP | GPB | PH/SB | PH/SB | ||||
| Sat | 23/6 | VP | GPB | PH/SB | PH/SB | ||||
Key:
| JJ: J. Jaikrishnan | AM: AnwoyMaitra |
| AJP: A.J.Parameswaran | GD: GopalDatt |
| RS: R. Sivaguru | RP: Ratna Pal |
| KB: Kingshook Biswas | PH: Pranav Haridas |
| VP: VamsiPingali | SB: SayaniBera |
| GPB: G.P.Balakumar | AS: Amardeep S. |
| VC: Vikramjeet Singh Chandel | DB: Diganta Borah |