The Austral Winter Workshop on Microlocal Analysis and Non-elliptic Fredholm Theory
An Australian Mathematical Winter workshop run by ARC Laureate Professor Andrew Hassell at the Mathematical Sciences Institute, Australian National University. This is a two-week intensive winter workshop, led by Andrew Hassell with two other distinguished researchers from Australia and the USA.
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RegisterDescription
The Austral Winter Workshop on Microlocal Analysis and Non-elliptic Fredholm Theory will be a two-week intensive workshop on modern microlocal analysis, held at the Australian National University, Canberra, Australia in June-July, 2025. The goal of the workshop is to show how, through microlocal propagation estimates, one can find Fredholm realizations of non-elliptic operators typically encountered in partial differential equations, such as wave operators, Klein-Gordon operators, or Helmholtz operators.
Organising committee
- Andrew Hassell (Australian National University)
- Akrti Tyagi (Australian National University)
- Tony Martin (Australian National University)
Lecturers
- Andrew Hassell (Australian National University)
- Qiuye Jia (Australian National University)
- Ethan Sussman (Northwestern University, USA)
Applications
Applications are solicited from interested participants. Please note that there is a strict limit of 40 students for the workshop. Only students whose applications are accepted will be permitted to attend the workshop. The deadline for submission is March 17th.
Please submit your application using the link above.
Poster session
There will be a Poster session in the second week of the workshop.
Information for Visitors
Lecture notes
The week 2 lecture notes have been updated (July 9, 9am). There will still be another update later in the week!
Timetable
All lectures will be held in the Seminar Room 1.33 of the Hanna Neumann Building (Building 145). Each lecture will be 90 minutes long followed by a 30 minute question/problem session. There will be two 2 hour tutorials (problem sessions) each week.
| WEEK 1 | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
| 9.30-11.30 | Lecture 1 | Lecture 3 | Tutorial | Lecture 6 | Lecture 8 | |
| 11.30-2.30 | Lunch provided | Shorter lunch break 11.30-1.30 | Hike to Black Mtn 1-2.30pm (meet at 12..50pm in the foyer of the HN building) | Tidbinbilla excursion (leave 1pm) | ||
| 2.30-4.30 | Lecture 2 | Lecture 4 | Lecture 5 | Lecture 7 (starts 1.30pm) | Tutorial | Tidbinbilla excursion (return 6pm) |
| Afternoon tea (3rd floor, 3.30-4pm) |
| WEEK 2 | Monday | Tuesday | Wednesday | Thursday | Friday |
| 9.30-11.30 | Lecture 9 Helmholtz operator | Lecture 11 Radial point estimates | Tutorial | Lecture 14 Scattering theory | Lecture 16 Schrodinger operator |
| 11.30-2.30 | Shorter lunch break 11.30-1.30 | ||||
| 2.30-4.30 | Lecture 10 Variable order spaces and operators | Lecture 12 Radial pt/ Fredholm estimates | Lecture 13 Fredholm estimates | Lecture 15 (starts 1.30pm) Klein-Gordon operator | Tutorial |
| 4.30-6.00 | Poster session, wine and cheese | Afternoon tea (3rd floor, 3.30-4pm) followed by Colloquium by Ethan at 4pm |
Hanna Neumann Building
Schedule
9.30am-11.30am Seminar Room (1.33) Hanna Neumann Building (Building 145)
Lecture 1: The Scattering Calculus Introduced
- Speaker: Andrew Hassell
2.30pm - 4.30pm
Lecture 2: The Scattering Calculus: Composition, Principal Symbol, Ellipticity
- Speaker: Andrew Hassell
9.30am - 11.30am
Lecture 3: Weighted Sobolev Spaces
- Speaker: Ethan Sussman
2.30pm - 4.30pm
Lecture 4: Microlocalization
- Speaker: Ethan Sussman
9.30am - 11.30am
Tutorial (Problem Session)
- Speaker: Andrew Hassell, Qiuye Jia, Ethan Sussman
2.30-4.30
Lecture 5: Microlocal Propagation I
- Speaker: Andrew Hassell
9.30am - 11.30am
Lecture 6: Microlocal Propagation II
- Speaker: Andrew Hassell
1.30pm - 3.30pm NOTE EARLIER START TIME
Lecture 7: Scattering Calculus on Manifolds with Boundary
- Speaker: Qiuye Jia
9.30am - 11.30am
Lecture 8: Applications to Inverse Problems
- Speaker: Qiuye Jia
2.30 - 4.30pm
Tutorial (Problem Session)
- Speaker: Andrew Hassell, Qiuye Jia, Ethan Sussman
Location
Mathematical Sciences Institute
ANU College of Systems and Society
Seminar Rooms 1.33 & 1.37
Hanna Neumann Building #145, Science Road
The Australian National University
Canberra ACT 2600
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