Student Differential Geometry Seminar — Spring 2020: The Inhomogeneous ˉ∂-Equation
- Jordan Rainone and El Mehdi Ainasse.
- Fridays, 1:00 PM to 2:00 PM – starting Friday, January 31st 2020.
- Mathematics Building, Room 5-127 (5th floor).
Welcome to the webpage for the Spring 2020 iteration of the SDGS! This semester, we decided to go for the inhomogenous -equation and its (complex) geometric applications.
More precisely, the goal of this seminar is three-fold: (1) studying bits and pieces of several complex variables (SCV) with an analytic introduction to the -operator, (2) covering some basics in complex differential geometry with a geometric take on the -operator, and then (3) exploring applications of the ( theory) of the -operator to various geometric problems.
Any suggestions are welcome!
Here are some links to relevant materials in different forms:
- Tasty Bits of Several Complex Variables, A whirlwind tour of the subject, By: Jiří Lebl. Version 3.2, October 1st, 2019, 182 pages.
- Complex Analytic and Differential Geometry. By: Jean-Pierre Demailly. Version of Thursday June 21, 2012.
- Holomorphic Function Theory in Several Variables - An Introduction. By: Christine Laurent-Thiébaut.
- Analytic and algebraic geometry : common problems, different methods, volume 17 of IAS/PARK CITY Mathematics Series. American Mathematical Soc., 2010. By: Jeffery D. McNeal and Mircea Mustata.
- ESTIMATES FOR THE OPERATOR. By: Jeffery D. McNeal and Dror Varolin.
- A Survey on the Extension Theorems. By: Takeo Ohsawa.
- Bo Berndtsson’s notes.
- Notes for the course “MATH 710: TOPICS IN MODERN ANALYSIS II – -METHODS” (taught by Mattias Jonsson), taken by Matt Stevenson.
- MSRI Summer School notes (cf. below.)
- SEVERAL COMPLEX VARIABLES. By: ZBIGNIEW BLOCKI.
- Complex analysis, the -Neumann problem, and Schrödinger operators. By: Friedrich Haslinger.
- Dror’s notes for the “CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS” program held at ICTS, Banglore.
- Dror Varolin’s SCGP talks.
- MSRI Summer School lectures. (cf. below.)
MSRI Summer School — The ˉ∂-Problem in the Twenty-First Century:
|Jae Ho Cho||01/31/2020||An introduction to the -method|
|Pranav Upadrashta||02/07/2020||Basic properties of holomorphic functions of several variables|
|Willie Rush Lim||02/14/2019||Plurisubharmonic functions|
|Roberto Albesiano||02/28/2020||estimates for the -operator|
|El Mehdi Ainasse||03/06/2020||Hörmander’s theorem and its twisted versions|
|Marlon de Oliveira Gomes||03/13/2020||The geometry of bundles and notions of positivity|
|Jordan Rainone||04/03/2020||estimates for on Riemann surfaces and applications|
|Conghan Dong||04/17/2020||estimates for the -equation on Kähler manifolds|
|Conghan Dong||04/24/2020||Applications of techniques on complex manifolds|
|El Mehdi Ainasse||04/24/2020||Berndtsson’s Nakano-positivity theorem and optimal extension theory|
|Roberto Albesiano||05/1/2020||The Kodaira embedding theorem|