We are thrilled to unveil the proposal for the upcoming Summer School titled “Direct and Inverse Problems with Applications, and Related Topics: A Comprehensive Summer School in Mathematical Analysis,”
We are happy to announce the receipt of the grant of 18,000€ from UGent Doctoral School for the organisation of this event.
This educational endeavor promises to dive deep into mathematical analysis, with a keen focus on direct and inverse problems, their applications, and related subjects, offering a profound interdisciplinary perspective both scientifically and societally.
Key Highlights:
🔍 Theme: The school aims to explore the comprehensive mathematical tools for solving direct and inverse problems across various fields, fostering new methods and techniques through lectures, exercises, and participant interactions. The lectures will also include broader related topics of mathematical analysis and partial differential equations.
📅 Dates: Scheduled from August 19 to 23, 2024, the program intends to provide approximately 29 contact hours, including lectures, discussions, problem-solving sessions, and an outreach event featuring a public lecture and poster presentations.
📚 Learning and Collaboration: With an environment conducive to learning and discussion, the school presents a unique opportunity for researchers and students to engage with the international mathematical community, enhancing academic careers and encouraging future studies.
📝 Program Structure: The curriculum includes 22.5 hours of lectures by ten esteemed lecturers, 6.5 hours dedicated to discussion and problem-solving sessions, and additional time for participants’ presentations and a public lecture, aiming to cover the latest problems and techniques in the field.
🏆 Participation Criteria: Recognition in the doctoral training programme requires at least 50% attendance in lectures, discussions, and problem sessions, along with participation in the poster session.
🎓 Lecturers: The list of speakers includes distinguished experts in the field of partial differential equations with applications.
- Michael Anoussis
University of the Aegean, Greece - Hajer Bahouri
Sorbonne Université, France - Jean Dolbeault
Université Paris-Dauphine, France - Alessia Kogoj
Università di Urbino Carlo Bo, Italy - Mansur I. Ismailov
Gebze Technical University, Turkey - Cristiana Sebu
University of Malta, Malta - Bianca Stroffolini
University of Naples, Italy - Luis Vega
University of the Basque Country UPV/EHU, Spain - Baoxiang Wang
Jimei University, China - Bauer Wolfram
Leibniz Universität Hannover, Germany - Semyon Yakubovich
University of Porto, Portugal
🔍 Justification: This summer school aligns seamlessly with the ongoing PhD research at Ghent University. By focusing on the mathematical analysis of PDEs, it enriches existing courses and offers advanced techniques vital for engineering applications. Students will delve deep into problem-solving sessions, fostering direct application to their research projects.
👥 Organising and Scientific Committee: The event is spearheaded by a distinguished committee, comprising experts from Ghent University and beyond.
🤝 Inter-University Partnership: The Ghent Analysis & PDE Center leads the initiative, with support from the Faculty of Engineering and Architecture. Additionally, collaboration with esteemed researchers from other Belgian and international universities strengthens our endeavor.
🎯 Targeted Audience: PhD candidates from Ghent University and partner universities are invited to participate, along with postdoctoral researchers and interested individuals from various scientific backgrounds.
🌐 Public Outreach Event: A captivating public lecture, poster session, and networking reception will complement the school, fostering engagement with a wider audience. Join us for an enlightening session!
🏛️ Location: Campus Sterre, Krijgslaan 281, 9000 Gent, gebouw S8!
📚 Summer School Program
📝 Registration:
Closed.
📌 The school will be free of charge for UGent PhD candidates. Other participants will be charged €10 per day to cover organizational expenses.
🌟 Summer School Workshop I 🌟
As a prelude to the upcoming Summer School “Direct and Inverse Problems with Applications, and Related Topics” scheduled from August 19-23, 2024, we are delighted to host a warming-up workshop.
Speakers and Topics:
- Erkinjon Karimov
(Fergana State University and Ghent University)
Topic: Inverse problems on finding unknown time-moment for time-fractional mixed partial differential equations - Rommel Real
(University of the Philippines Mindanao)
Topic: On a heuristic rule for Landweber iteration in Banach spaces - Armen Vagharshakyan
(Institute of Mathematics NAS, Armenia)
Topic: On the history of polynomial inequalities - Vahideh Vahidifar
(University of Sussex)
Topic: An Overview of My Work on PDEs, Geometric Analysis, and Machine Learning
📅 Dates & Times:
Thursday, July 18, 2024
2:00 PM – 4:00 PM 🕑
📍 Location:
Lecture Room 3.1, Building S8, Campus Sterre 🏫
This workshop is an excellent opportunity to delve into complex mathematical problems and methodologies ahead of our main Summer School event. 📖
🌟 Summer School Workshop II 🌟
As a prelude to the upcoming Summer School “Direct and Inverse Problems with Applications, and Related Topics” scheduled from August 19-23, 2024, we are delighted to host our second warming-up workshop.
Speakers and Topics:
- Ali Taheri
(University of Sussex, UK)
Topic: Geometric and Functional Inequalities in Sobolev and Related Spaces - Julio Delgado
(Universidad del Valle, Colombia)
Topic: Nuclearity, Schatten-von Neumann classes and tensors of Hilbert spaces - Nurgissa Yesirkegenov
(Institute of Mathematics and Mathematical Modeling, Kazakhstan)
Topic: Cylindrical and hypoelliptic functional inequalities - Mohammed Sebih
(Mustapha Stambouli University of Mascara, Algeria)
Topic: On the q-analogue of Duhamel’s principle - Sofwah Ahmad
(Khalifa University, United Arab Emirates)
Topic: On the blowing up solutions of a system of fractional differential equations
📅 Dates & Times:
Friday, August 9, 2024
2:00 PM – 5:00 PM 🕑
📍 Location:
Lecture Room 3.2, Building S8, Campus Sterre 🏫
This workshop offers a great opportunity to explore complex mathematical challenges and techniques before the main Summer School event. 📖
🌟 Summer School Workshop III 🌟
As a continuation of the recent Summer School “Direct and Inverse Problems with Applications, and Related Topics” held from August 19-23, 2024, we are delighted to host our follow-up workshop. This workshop will feature presentations by esteemed speakers from University College London.
Speakers:
- Ilia Kamotski
- Valery Smyshlyaev
Joint Lecture Topic
“Analysis of a Class of Degenerating Operators and Their Spectra: Multiscale-type Approximations”
Abstract
Homogenization theory establishes that uniformly elliptic operators with rapidly oscillating periodic coefficients have operators with constant coefficients as their appropriate limits. One approach is based on applying a (scaled) Floquet-Bloch-Gelfand transform to the resolvent problem in $\mathbb{R}^n$ and then constructing uniform approximations near a singular point of the quasi-periodicity parameter. This becomes much more subtle if the coefficients are asymptotically degenerating, and the limit operator appears to be a “two-scale” one with a band-gap limit spectrum. There are diverse examples of PDE and other models displaying similar features. In this minicourse, based on [1], we review the background and introduce an abstract scheme allowing to construct such approximations for a wide class of asymptotically degenerating operators and their spectra. This is accompanied by error bounds, and illustrated this by various examples. In particular, a key example of high-contrast PDE models displays surprising links to signal processing via a novel $L^2$-isometric two-scale interpolation operator of Whittaker-Shannon type.
[1] S. Cooper, I.V. Kamotski, V.P. Smyshlyaev, Uniform asymptotics for a family of degenerating variational problems and error estimates in homogenisation theory. arXiv:2307.13151 (2023)
📅 Dates & Times:
- Monday, November 4, 2024: 2:30 PM – 4:30 PM
- Tuesday, November 5, 2024: 2:30 PM – 4:30 PM
📍 Location: Lecture Room 3.2, Building S8, Campus Sterre
🌟 Summer School Workshop IV 🌟
Following the success of our recent Summer School “Direct and Inverse Problems with Applications, and Related Topics” (August 19-23, 2024), we are pleased to invite you to a two-day workshop featuring a series of mini-lectures by Professor Federica Dragoni (https://profiles.cardiff.ac.uk/staff/dragonif) from Cardiff University.
Speaker:
- Federica Dragoni
(Cardiff University)
📅 Dates & Times:
1. Thursday, November 14, 2024
14:30 – 16:30
- Part I: The Euclidean case – Euclidean distance semiconcavity and viscosity solutions
- Part II: Carnot groups – introduction, the homogeneous distance, and the CC distance
2. Friday, November 15, 2024
14:30 – 16:30
- Part III: Horizontal convexity/semiconcavity
- Part IV: Results and a sketch of the proof for ideal groups
📍 Location:
Lecture Room 3.2, Building S8, Campus Sterre 🏫
This workshop is an excellent opportunity to engage with advanced topics in geometric analysis, including recent developments in distance and convexity analysis within Euclidean and non-Euclidean frameworks. 📖
🌟 Summer School Workshop V 🌟
As a follow-up to the Summer School “Direct and Inverse Problems with Applications, and Related Topics” (August 19-23, 2024), we are organising a two-day workshop featuring mini-lectures by Professor Yulia Kuznetsova from the Université de Franche-Comté.
Speaker:
- Yulia Kuznetsova
(Université de Franche-Comté)
The topic of the lectures: “An overview of dualities in noncommutative harmonic analysis”
📅 Dates & Times:
- Tuesday, November 19, 2024: 2:00 PM – 4:00 PM
- Wednesday, November 20, 2024: 2:00 PM – 4:00 PM
📍 Location:
Lecture Room 3.2, Building S8, Campus Sterre 🏫
This workshop provides an excellent opportunity to delve into the intricate world of noncommutative analysis, exploring advanced concepts and techniques in a rapidly evolving field. 📖
🌟 Summer School Workshop VI 🌟
We are thrilled to invite you to a two-day mini-course by Professor Dimitris Scarpalezos from the Paris Diderot University. This workshop will be the VI Summer School workshop and follows up on our recent Summer School, “Direct and Inverse Problems with Applications, and Related Topics” (August 19-23, 2024).
Speaker:
- Dimitris Scarpalezos
(Paris Diderot University)
📅 Dates & Times
Thursday, November 21, 2024
🕒 14:30 – 16:30
Part I: Asymptotic scales and parametric generalized functions and their topologies
Friday, November 22, 2024
🕒 14:00 – 16:00
Part II: Roumieu generalized functions, comparison of regularities, and conditions for equalities
📍 Location:
Lecture Room 3.2, Building S8, Campus Sterre 🏫🏫
This workshop offers a unique opportunity to delve into the specialized world of asymptotic and generalized function theory, focusing on parametric scales and regularity comparisons. Join us for an in-depth exploration of advanced topics in generalized functions and asymptotic analysis. 📖
This summer school promises to be a cornerstone event for advancing research and collaboration in the field of mathematical analysis. Keep an eye on our website and university communications for updates and registration details. Join us for a journey of discovery and innovation in mathematical analysis!🌟
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Ghent Analysis & PDE Center 