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

## Meeting times

• Fridays, 1:00 PM to 2:00 PM – starting Friday, January 31st 2020.

## Location

• Mathematics Building, Room 5-127 (5th floor).
• Zoom starting April 3rd, 2020.

## Description

Welcome to the webpage for the Spring 2020 iteration of the SDGS! This semester, we decided to go for the inhomogenous $$\bar{\partial}$$-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 $$\bar{\partial}$$-operator, (2) covering some basics in complex differential geometry with a geometric take on the $$\bar{\partial}$$-operator, and then (3) exploring applications of the ($$L^2$$ theory) of the $$\bar{\partial}$$-operator to various geometric problems.

Any suggestions are welcome!

## References

Here are some links to relevant materials in different forms:

## Schedule

SpeakerDateTopic
Jae Ho Cho01/31/2020An introduction to the $$\bar{\partial}$$-method
Pranav Upadrashta02/07/2020Basic properties of holomorphic functions of several variables
Willie Rush Lim02/14/2020Plurisubharmonic functions
Emily Schaal02/21/2020Pseudoconvexity
Roberto Albesiano02/28/2020$$L^2$$ estimates for the $$\bar{\partial}$$-operator
El Mehdi Ainasse03/06/2020Hörmander’s theorem and its twisted versions
Marlon de Oliveira Gomes03/13/2020The geometry of bundles and notions of positivity
Jordan Rainone04/03/2020$$L^2$$ estimates for $$\bar{\partial}$$ on Riemann surfaces and applications
Conghan Dong04/17/2020$$L^2$$ estimates for the $$\bar{\partial}$$-equation on Kähler manifolds
Conghan Dong04/24/2020Applications of $$L^2$$ techniques on complex manifolds
El Mehdi Ainasse04/24/2020Berndtsson’s Nakano-positivity theorem and optimal $$L^2$$ extension theory (Slides)
Roberto Albesiano05/1/2020The Kodaira embedding theorem