Summer School on Positive Operator Semigroups
Budapest, 4 September - 8 September 2023
Description
Positive operator semigroups are a topic at the intersection of operator theory, PDE theory, and dynamical systems. They are, among various other applications, particularly useful to study the behaviour of evolution equations on networks.
The summer school is aimed at advanced Master's students and PhD students. It will consist of a general introduction to positive semigroups, a tour through some very recent developments in the theory in order to provide the students with an entry point to current research, and a discussion of several applications of the theory to concrete evolution equations.
Lecturers
Confirmed lecturers:
Organizers
- Eszter Sikolya (Budapest)
- Jochen Glück (Wuppertal)
Location
The summer school will take place at the following location:
Lecture hall: 0.81 Ortvay Hall
Eötvös Loránd University
Faculty of Science, Institute of Mathematics
Pázmány Péter sétány 1/A
1117 Budapest
Please note: The building was changed from 1/C (which was mentioned in former announcements of the summer school) to 1/A.
Link to the position of the building at Google maps
Exercise Sheets
- Sheet for Exercise Sessions A-D (András Bátkai and Marjeta Kramar Fijavž)
- Sheet for Exercise Sessions E-F (Wolfgang Arendt)
- Sheet for Exercise Sessions G-H (Rainer Nagel)
- Sheet for Exercise Session I (Sahiba Arora)
- Sheet for Exercise Session J (Petra Csomós)
Schedule (preliminary)
The preliminary schedule of the workshop is as follows:
Monday, September 4
| 08:45 - 09:00 | Opening session (in the lecture hall 0.81 Ortvay Hall) |
| 09:00 - 09:45 | Lecture 1 (Kramar Fijavž): Positive Matrices, Powers, and Spectrum |
| 09:45 - 10:45 | Exercise Session A |
| 10:45 - 11:15 | Coffee Break |
| 11:15 - 12:00 | Lecture 2 (Bátkai): Banach Lattices |
| 12:00 - 14:00 | Lunch break |
| 14:00 - 14:45 | Lecture 3 (Kramar Fijavž): Irreducible and Imprimitive Matrices, Asymptotics |
| 14:45 - 15:45 | Exercise Session B |
| 15:45 - 16:15 | Coffee Break |
| 16:15 - 17:00 | Lecture 4 (Bátkai): Positive Operators |
| 17:00 - 18:00 | Exercise Session C |
Tuesday, September 5
| 09:00 - 09:45 | Lecture 5 (Kramar Fijavž): Applications of positive matrices |
| 09:45 - 10:45 | Exercise Session D |
| 10:45 - 11:15 | Coffee Break |
| 11:15 - 12:00 | Lecture 6 (Bátkai): Ppositive Exponential Functions and Applications |
| 12:00 - 14:00 | Lunch break |
| 14:00 - 14:45 | Lecture 7 (Arendt): Positive Semigroups on Banach Lattices I |
| 14:45 - 15:45 | Exercise Session E |
| 15:45 - 16:15 | Coffee Break |
| 16:15 - 17:00 | Lecture 8 (Arendt): Positive Semigroups on Banach Lattices II |
Wednesday, September 6
| 09:00 - 09:45 | Lecture 9 (Arendt): Positive Semigroups on Banach Lattices III |
| 09:45 - 10:45 | Exercise Session F |
| 10:45 - 11:15 | Coffee Break |
| 11:15 - 12:00 | Lecture 10 (Nagel): Koopman Semigroups and Ergodic Theory I |
| 12:00 - 14:00 | Lunch break |
| Afternoon | Workshop trip |
Thursday, September 7
| 09:00 - 10:00 | Exercise Session G |
| 10:00 - 10:45 | Lecture 11 (Nagel): Koopman Semigroups and Ergodic Theory II |
| 10:45 - 11:15 | Coffee Break |
| 11:15 - 12:00 | Exercise Seesion H |
| 12:00 - 14:00 | Lunch break |
| 14:00 - 14:45 | Lecture 12 (Arora): Eventual Positivity I |
| 15:00 - 15:45 | Lecture 13 (Arora): Eventual Positivity II |
| 15:45 - 16:15 | Coffee Break |
| 16:15 - 17:15 | Exercise Session |
| 18:30 | Summer school dinner |
Friday, September 8
| 09:00 - 09:45 | Lecture 14 (Csomós): Numerical Analysis and Positive Semigroups I |
| 09:45 - 10:45 | Exercise Session J |
| 10:45 - 11:15 | Coffee Break |
| 11:15 - 12:00 | Lecture 15 (Csomós): Numerical Analysis and Positive Semigroups II |
| 12:00 - 17:00 | Voluntarily: students have the option to continue individual discussions at their own discretion |
Reimbursement information
Here we summarize infos on how the reimbursement process works:
Reimbursement for lecturers
Lecturers from outside Budapest will be reimbursed by the COST Action 18232:
- Travel expenses to Budapest will be reimbursed based on the ticket prices.
- Local expenses in Budapest (e.g., accommodation and public transport) will be reimbursed by a daily allowance.
- To claim your reimbursement, please use the eCOST portal (you will need to create an account there in case that you do not already have one).
Reimbursement for students (funded partially by COST and partially by the University of Wuppertal)
The reimbursement works as follows:
- Travel expenses to Budapest will be reimbursed by the COST Action 18232 based on the ticket prices.
To claim the reimbursement for your travel tickets to Budapest, please use the eCOST portal (you will need to create an account there in case that you do not already have one). - Local transport expenses in Budapest will be covered by the University of Wuppertal based on the ticket prices. You don't need to take any further actions regarding this. (However, it might take a while until the reimbursement gets tranferred to your bank account, since our reimbursement office currently has a very high work load.)
Co-organized by
