The problems of stochastics in fluids is one of the most challenging areas in physics, numerics as well as in mathematics. The aim of this summer school is to present a comprehensive series of lectures on various aspects of stochastics in all these areas and their role in mathematical analysis and numerical simulation of different types of flows. The summer school is organized as a multidisciplinary event with topics ranging from theoretical and numerical mathematics up to physics and applications. The emphasize will be on models related to topics originating in environmental, biomedical and industrial applications. The summer course is prepared for graduate students, young scientists, and other interested specialists. Besides of the course lectures, the program will include a one day workshop (on Wednesday, August 23) dedicated to short, more advanced lectures given by attending scientists.

Organized by:

• Tomáš Bodnár – Czech Technical University in Prague, ERCOFTAC PC Czech Republic
• Giovanni Paolo Galdi – University of Pittsburgh, USA
• Šárka Nečasová – Institute of Mathematics, Czech Academy of Sciences

Web:http://prague-sum.com/

Main Topics:

• Random processes in fluids
• Statistical methods
• Statistical approach to turbulenence and diffusion
• Stochastic models of fluids flows
• Numerical simulation of stochastic processes
• Random dynamical systems
• Stochastic Analysis and applications

Invited Speakers (confirmed):

• Franco Flandoli, University of Pisa, Italy
• Michele Coti Zelati, Imperial College London, United Kingdom
• Eduard Feireisl, Czech Academy of Sciences, Czech Republic

More invited speakers to appear soon (including CFD and industrial applications)

Summer School courses:

• Compact minicourses (typically 4 lectures by 50 minutes each) will be presented by the invited speakers (up to 28 lectures in total).
• The lectures will be scheduled in larger blocks within four full days (Monday August 21, Tuesday 22, Thursday 24, Friday 25).

Workshop presentations:

• Workshop is organized on Wednesday, August 23, 2023.
• Shorter talks (up to 30 minutes), given by invited or contributing speakers.
• Talks will be selected from the proposed contributions based on their quality and suitability with respect to the main topic of the summer course.
• Remaining presentation, including those of the students of the summer school, will be presented in the form of posters.
• All the young researchers profiting from the ERCOFTAC support will be obliged to present their own work (poster or talk) during the Workshop day.

Relation to ERCOFTAC:

• The participants coming from ERCOFTAC member institutions are eligible for substantial (25%) discount from all registration fees.This will be advertised on the Summer School web page.
• The support from ERCOFTAC will be acknowledged in all important official printed and electronic documents related to the Summer School.
• The announcement of the event will be placed on the ERCOFTAC web page.
• The Summer School web will point to the ERCOFTAC (and Czech PC) web page.

History of the event

The above presented Summer School is already seventh in the series started in 2011. The previous events were:

• Fluid-Structure Interaction for Biomedical Applications: August 29 - September 2, 2011
• Non-Homogeneous Fluids and Flows: August 27 - August 31, 2012
• Particles in Flows: August 25 - August 31, 2014
• Fluids under Pressure: August 29 - September 2, 2016
• Waves in Flows: August 27 - August 31, 2018
• Fluids Under Control: August 23 – 27, 2021

Now it has developed into a regular (bi-annual) series of thematic summer schools running under a common label “Prague-Sum”. All the information, presentations, course materials as well as the photos from those events are made openly available to public at the dedicated permanent web page http://prague-sum.com/

The events in 2011, 2014, 2016, 2018 and 2021 were supported by ERCOFTAC and used its logo. The summer schools are organized as purely non-profit events. All the money gained from the registration fees and various grants are exclusively (and completely) spent to organization costs (including also refreshment, lunches, social programme, etc.), reimbursement of the travel and living costs for invited speakers and young researchers.

During the years, the summer school gained quite a good reputation and excellent feedback from the participants. Based on the outstanding quality of the speakers and courses, five books were already published by Birkhäuser – Springer (two more books, based on Fluids Under Control from 2021, are under preparation). The already published books are:

1. Fluid-Structure Interaction and Biomedical Applications (based on the summer school from 2011) - https://link.springer.com/book/10.1007/978-3-0348-0822-4
2. Particles in Flows (based on the summer school from 2014) - https://www.springer.com/gp/book/9783319602813
3. Fluids Under Pressure (based on the summer school from 2016) - https://link.springer.com/book/10.1007/978-3-030-39639-8
4. Waves in Flows (based on the summer school from 2018) - https://link.springer.com/book/10.1007/978-3-030-67845-6
5. Waves in Flows - The 2018 Prague-Sum Workshop Lectures - https://link.springer.com/book/10.1007/978-3-030-68144-9