# Student Differential Geometry Seminar — Spring 2020: The Inhomogeneous ¯∂-Equation

## Organizers

- Jordan Rainone and El Mehdi Ainasse.

## Meeting times

- Mondays, 4:30 PM to 5:30 PM – starting Monday, January 27th 2020 (tentatively).

## Location

- TBD.

## Description

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 (L^2 theory) of the ¯∂-operator to various geometric problems.

Any suggestions are welcome!

## References

Here are some links to relevant materials in different forms:

### Introductory articles:

### Books:

- 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.

### Papers:

### Lecture notes:

- Bo Berndtsson’s notes.
- Notes for the course “MATH 710: TOPICS IN MODERN ANALYSIS II – L^2-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.

### Videos:

- Dror Varolin’s SCGP talks.
- MSRI Summer School lectures. (cf. below.)

### MSRI Summer School — The ¯∂-Problem in the Twenty-First Century:

## Schedule

Speaker | Date | Topic | Suggested References |
---|---|---|---|

TBD | 01/23/2020 | TBD | TBD |

TBD | 02/03/2020 | TBD | TBD |

TBD | 02/10/2019 | TBD | TBD |

TBD | 02/17/2020 | TBD | TBD |

TBD | 02/24/2020 | TBD | TBD |