Home /  Special Geometric Structures and Analysis (St. Mary's College)

Summer Graduate School

Special Geometric Structures and Analysis (St. Mary's College) June 17, 2024 - June 28, 2024
Parent Program:
Location: St. Mary's College
Organizers Costante Bellettini (University College London), LEAD Eleonora Di Nezza (Institut de Mathématiques de Jussieu; École Normale Supérieure), Song Sun (Zhejiang University; University of California, Berkeley)
Lecturer(s)

Show List of Lecturers

Teaching Assistants(s)

Show List of Teaching Assistants

Speaker(s)

Show List of Speakers

Description
1066 image
a Calabi-Yau manifold

This summer school will serve as an introduction to the SLMath program "Special geometric structures and analysis", which will take place in Fall 2024. There will be two mini-courses: one in Geometric Measure Theory and the other in Microlocal Analysis. The aim is to give the basic notions of two subjects also treated during the program.

School Structure

There will be two lectures and two problem sessions on most days.  Wednesday mornings will be devoted to a session of “Answers & Questions”.

Prerequisites

For both mini-courses, the undergraduate courses of Differential Geometry, Riemannian geometry, Topology and Analysis are pre-requisites. More precisely we expect a student to master the notions of
• differential manifolds (any dimension), tangent space, curvature tensor;
• riemannian metric, Levi-Civita connection, Ricci curvature;
• homotopy, first fundamental group, cohomology classes;

We suggest the following books:

References

[1] do Carmo, Manfredo P. Differential geometry of curves & surfaces. Dover Publications, Inc., Mineola, NY, 2016.
[2] Lee, Jeffrey. Manifolds and differential geometry. Graduate Studies in Mathematics, 107. American Mathematical Society, Providence.
[3] Munkres, James R. Topology. Prentice Hall, Inc., Upper Saddle River, NJ, 2000.
[4] Tao, Terence. Analysis II. Third edition. Texts and Readings in Mathematics, 38. Hindustan Book Agency, New Delhi.

To be more specific, we recommend the interested student to go over:
• Chapters 1, 2, 3, 7, 10 and 13 in [2]. We also suggest the problems 4, 7, 17, 18 at page 51-52, the problems 5, 12, 21 at page 123-125 and the problems 2, 9, 10 at page 634-635.
• Chapters 3, 4, 5 in [4]. We also suggest the exercises 4.6.8, 4.6.10, 4.6.16, 4.7.10, 5.5.3, 5.5.4.
(exercise numbering for Analysis II, editions 1, 3, & 4)

Geometric Measure Theory mini-course
Lectures on geometric measure theory, by Leon Simon, chapters 4-8
Geometric integration theory, by S. Krantz and H. Parks, chapter 8
Measure theory and fine properties of functions, by L. Evans and R. Gariepy, chapters 2-3

Microlocal Analysis mini-course
Lecture notes on pseudodifferential operators, by Richard Melrose
Basics of the b-calculus, by Daniel Grieser
Fredholm property of elliptic operators, by Semyon Dyatlov, chapter 15

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.


 

 

Keywords and Mathematics Subject Classification (MSC)
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
Show All Collapse
Jun 17, 2024
Monday
08:40 AM - 09:00 AM
  Welcome and Introduction to SLMath
09:00 AM - 10:15 AM
  Lecture 1
Xuwen Zhu (Northeastern University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 1
Xuwen Zhu (Northeastern University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Romain Speciel (Stanford University)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Romain Speciel (Stanford University)
Jun 18, 2024
Tuesday
09:00 AM - 10:15 AM
  Lecture 2
Xuwen Zhu (Northeastern University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 2
Xuwen Zhu (Northeastern University)
12:00 PM - 02:00 PM
  BBQ Lunch
02:00 PM - 03:15 PM
  Problem Session
Romain Speciel (Stanford University)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Romain Speciel (Stanford University)
Jun 19, 2024
Wednesday
09:00 AM - 12:00 PM
  Free Morning
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 05:00 PM
  Free afternoon
Jun 20, 2024
Thursday
09:00 AM - 10:15 AM
  Lecture 3
Xuwen Zhu (Northeastern University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 3
Xuwen Zhu (Northeastern University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Romain Speciel (Stanford University)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Romain Speciel (Stanford University)
Jun 21, 2024
Friday
09:00 AM - 10:15 AM
  Lecture 4
Xuwen Zhu (Northeastern University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 4
Xuwen Zhu (Northeastern University)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Romain Speciel (Stanford University)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Romain Speciel (Stanford University)
Jun 24, 2024
Monday
09:00 AM - 10:15 AM
  Lecture 1
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 1
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
12:00 PM - 12:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
Jun 25, 2024
Tuesday
09:00 AM - 10:15 AM
  Lecture 2
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 2
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
Jun 26, 2024
Wednesday
09:00 AM - 10:15 AM
  Problem Session
Aria Halavati (New York University, Courant Institute)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
12:00 PM - 12:15 PM
  Group Photo
12:15 PM - 02:00 PM
  Lunch
02:00 PM - 04:00 PM
  Visit to SLMath with Afternoon Tea
Jun 27, 2024
Thursday
09:00 AM - 10:15 AM
  Lecture 3
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 3
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:00 PM
  Problem Session
Aria Halavati (New York University, Courant Institute)
Jun 28, 2024
Friday
09:00 AM - 10:15 AM
  Lecture 4
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 4
Alessandro Pigati (Università Commerciale ``Luigi Bocconi'')
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Participant Survey
02:00 PM - 03:30 PM
  Session: Questions and Answers
03:30 PM - 04:00 PM
  Afternoon Tea
06:30 PM - 08:30 PM
  Social Event: Pub