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Summer Graduate School

The ∂-Problem in the Twenty-First Century June 11, 2018 - June 22, 2018
Parent Program: --
Location: MSRI: Simons Auditorium, Atrium
Organizers Debraj Chakrabarti (Central Michigan University), Jeffery McNeal (Ohio State University)
Lecturer(s)

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Speaker(s)

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Description

This Summer Graduate School will introduce students to the modern theory of the  inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum

Suggested prerequisites:

Students will be expected to have had graduate-level courses in complex and real analysis. A typical first or second year graduate course at the level of Rudin’s Real and Complex Analysis, for example, would be sufficient. Exposure to some basic functional analysis or PDE would be desirable, but not assumed. The basic results from those areas needed to understand subsequent material in the summer school will be developed in the course

Bibliography (PDF)

Projects

Lecture Notes
Day 1 - McNeal & Chakrabarti
Day 2 - McNealChakrabarti
Day 3 - McNealChakrabarti
Day 4 - McNealChakrabarti
Day 5 - McNealChakrabarti
Day 6 - Chakrabarti
Day 7 - Chakrabarti
Day 8 - Chakrabarti

Supplement Lectures
Lecture 1
Lecture 2

Homework
Day 1
Day 2
Day 3
Day 4
Day 5 - no homework
Day 6
Day 7 - no homework
Day 8 - no homework

Excercises
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8

Schedule for Final Projects
 

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Several Complex Variables

  • Cauchy-Riemann Equations

  • Holomorphic functions

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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Jun 11, 2018
Monday
09:00 AM - 09:15 AM
  Introduction to MSRI
09:15 AM - 09:30 AM
  Introduction
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 12, 2018
Tuesday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 13, 2018
Wednesday
09:00 AM - 10:00 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:00 AM - 10:30 AM
  Break
10:30 AM - 11:30 AM
  Lecture
Debraj Chakrabarti (Central Michigan University)
11:30 AM - 02:00 PM
  BBQ Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 14, 2018
Thursday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 15, 2018
Friday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 18, 2018
Monday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 19, 2018
Tuesday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 20, 2018
Wednesday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 21, 2018
Thursday
09:30 AM - 10:30 AM
  Lecture
Jeffery McNeal (Ohio State University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Lecture
Debraj Chakrabarti (Central Michigan University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Discussion 1
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Discussion 2
Jun 22, 2018
Friday
09:30 AM - 10:30 AM
  Presentations by postdocs and participants
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Presentations by postdocs and participants
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Presentations by postdocs and participants
03:00 PM - 03:30 PM
  Tea Break
03:30 PM - 04:30 PM
  Presentations by postdocs and participants