Congratulations to Markos Fisseha Yimer on being awarded the IMU-Simons Research Fellowship, a prestigious grant for researchers from developing countries. This fellowship, up to 7,500 USD, will cover his travel, accommodation, and daily expenses for a research visit to our Ghent Analysis & PDE Centre from July 1, 2025, to September 30, 2025.
During his stay, Markos will work on a project titled Levin-Cochran-Lee inequalities on metric measure spaces, under the guidance of Prof. Dr. Michael Ruzhansky. This project aims to make new discoveries in mathematics and is a great opportunity for Markos to build his research skills and experience.
This visit is also about more than just research. It’s a chance for both Addis Ababa University and Ghent University to connect, exchange ideas, and build a stronger relationship that could lead to more collaboration in the future.
Once again, congratulations to Markos on this fantastic achievement!
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
As we conclude our comprehensive summer school on “Direct and Inverse Problems with Applications, and Related Topics” we want to extend our deepest gratitude to all the participants, lecturers, and organizers who made this event a great success. Over the past week, we’ve had an incredible journey through the intricate landscapes of mathematical analysis, with a particular focus on partial differential equations and their applications.
📅 Program Overview:
Dates: August 19 – 23, 2024
Distinguished Lecturers: We had the privilege of learning from leading experts like Luis Vega, Jean Dolbeault, Hajer Bahouri, and others who shared insights into the latest challenges in direct and inverse problems.
📝 Key Highlights:
Engaging Lectures and Discussions: Participants delved into advanced techniques in PDEs and inverse problems, with ample opportunities for discussions.
Active Participant Involvement: Our participants actively contributed to discussions, and we were impressed by the quality of the poster presentations during our public outreach event.
Public Outreach: The public lecture and poster session offered a platform for broader engagement, sparking insightful conversations and new ideas.
🎓 Looking Ahead:
This summer school not only provided advanced knowledge but also fostered connections that will undoubtedly lead to future collaborations and research opportunities. For those pursuing their PhDs, this event has added significant value to their academic journeys, particularly in the application of PDEs to engineering and other scientific fields.
We also appreciate the contributions of our scientific committee, whose guidance ensured the high quality of the program.
Thank you to all who participated. We look forward to seeing how you’ll apply these learnings to advance mathematical analysis.
Until we meet again, keep pushing the boundaries of knowledge and innovation! 📖
This workshop offers a great opportunity to explore complex mathematical challenges and techniques before the main Summer School event. Seize this chance to deepen your knowledge and connect with leading experts in the field.
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
This workshop is an excellent opportunity to delve into complex mathematical problems and methodologies ahead of our main Summer School event. Don’t miss out on this chance to enhance your understanding and network with experts in the field.
We are thrilled to announce the outstanding achievement of Abhilash Tushir, with his successful defense of his PhD thesis, “Semi-classical Analysis of Partial Differential Equations in Lattices”! 🌟📚
It is a testament to Abhilash’s dedication, perseverance, and intellectual excellence that he has been awarded the PhD title. Under the supervision of Prof. Aparajita Dasgupta from IIT Delhi and Prof. Michael Ruzhansky from the Ghent Analysis & PDE Center, Abhilash navigated the complexities of semi-classical analysis and its applications to partial differential equations, demonstrating exceptional scholarly ability. 🌐🔍
His research delved into:
The classical wave equation;
The fractional Klein-Gordon equation;
The heat equation with fractional Laplacian operator;
The wave equation with Schrödinger operator;
The general time-fractional diffusion equation associated with the Schrödinger operator.
This achievement not only marks the culmination of years of intense research but also represents the beginning of new opportunities and potential contributions to the scientific community. 📚🎓
Congratulations, Abhilash! We are excited to see all the great things you will accomplish in your future endeavors and wish you all the best in your continued journey of academic and professional excellence. 🥳🎉🎊
Since 2017, the Federal Government allocates funds, through the office of VLIR-UOS, to the Global Minds Fund (GMF) of Ghent University. GMF operates as driver of change for sustainable development, by producing and valorising relevant knowledge and expertise through mutually beneficial partnerships.
The idea is to collaborate with several outstanding Colombian mathematicians on a project leading to educational advancement in Colombia. This project will be valuable to pass to younger generations a significant perspective in the field of pseudo-differential operators through the leading Colombian partners of the project. This scientific plan is part of the initiatives of the Ghent Analysis and PDE Center to support mathematical research in developing countries, particularly, from Latin America. The project is promoted by Prof. Dr. Michael Ruzhansky (PI) and co-promoted by our FWO Postdoctoral Researchers (Co-PIs) Dr. Duvan Cardona and Dr. Marianna Chatzakou. As part of our strategic alliances we will cooperate with ICMAM Latin America (International Community of Mathematicians from Latin America) in the organisation of several virtual conferences related to this project.
About the Project
Project Title:Global Minds in Pseudo-Differential Analysis
Value of the grant: €7,500
Description: This transformative project focuses on enhancing educational opportunities in Colombia by partnering with prominent Colombian mathematicians. The aim of this project is to impart significant knowledge in the field of pseudo-differential operators to the younger generation. This initiative is part of the Ghent Analysis and PDE Center’s commitment to supporting mathematical research in developing countries, particularly in Latin America.
Promotor: Prof. Dr. Michael Ruzhansky (PI), Ghent University. Co-promotors: Dr. Duvan Cardona (Co-PI), Ghent University Dr. Marianna Chatzakou (Co-PI), Ghent University
Global South partners:
Prof. Dr. Jairo Hernández (Universidad del Norte, Colombia) Prof. Dr. Bienvenido Barraza (Universidad del Norte, Colombia) Prof. Dr. Carolina Neira Jiménez (National University of Colombia) Prof. Dr. Liliana Posada (Universidad del Valle, Colombia) ICMAM Latin America(International Community of Mathematicians from Latin America)
Locations:
Belgium: From April 14th to 18th 2025 (tentative), the workshop: Global Minds in Pseudo-differential Operators will take place in person at Ghent University. A minicourse on pseudo-differential operators on compact Lie groups will be given by the co-promotor Dr. Duván Cardona, and a minicourse about geometric operators on stratified groups will be given by the co-promotor Dr. Marianna Chatzakou. A day forum aboutWomen in Pseudo-differential Operators led by Dr. Marianna Chatzakou will be part of the program to exchange ideas about the mathematical contributions of the junior and senior women mathematicians participating in the workshop.
Colombia: The workshop will be preceded and succeeded by several virtual conferences and virtual seminars involving Colombian and also other Latin American researchers in the research program about pseudo-differential operators in the Ghent Analysis and PDE Center. To allow our scientific experiences to also involve young mathematicians from Latin America, our virtual conferences, seminars, lectures, forums, and mini-courses will be organised by ICMAM Latin America (International Community of Mathematicians from Latin America). We will cooperate with this research organisation to spread all these videos among young mathematicians from Latin America.
Project Goals
🌱 Sustainable Development: Enhance mathematical expertise in regions with limited access to advanced training.
🌐 Knowledge Exchange and Capacity Building: Facilitate learning and collaboration by providing a platform for researchers and students from the Global South.
🔍 Integration of Advanced Techniques: Empower participants to tackle complex problems using advanced mathematical techniques.
Activities Overview
📅 Workshop: From April 14th to 18th, 2025, an in-person workshop will be hosted at Ghent University. Local researchers will present their work on pseudo-differential operators, and invited Colombian researchers will share their advancements. Each day will end with a discussion forum to explore open problems and develop research collaboration plans.
🎓 Minicourses:
Pseudo-Differential Operators on Compact Lie Groups: Led by Dr. Duván Cardona.
Geometric Operators on Stratified Groups: Led by Dr. Marianna Chatzakou.
👩🔬 Special Forum: A forum on “Women in Pseudo-Differential Operators,” led by Dr. Marianna Chatzakou, will highlight the contributions by women mathematicians in the theory of pseudo-differential operators.
💻 Virtual Engagements: The workshop will include virtual conferences and seminars, recorded and made available on YouTube to reach young mathematicians in Latin America. We will collaborate with the International Community of Mathematicians from Latin America (ICMAM) to disseminate these videos.
Research Forum about Women in Mathematics From April 15h to 30th, two leading women mathematicians from Colombia, namely, Dr. Liliana Posada from Universidad del Valle, and Dr. Carolina Neira from National University of Colombia will deliver several presentations leading to discussions about research of women mathematicians, particularly, in pseudo-differential operators.
Expected Outcomes
📈 Enhanced research capacity and new collaborations.
🌍 Empowered researchers addressing local challenges.
🔗 Ongoing collaboration through an online platform and joint projects.
Join us in making an impact through the Global Minds Fund – Explore and Valorise 2024. Together, we can drive positive change and foster a brighter future for global education and sustainable development. 🌟🌐
Let’s collaborate to explore and valorise knowledge in pseudo-differential operators and make a lasting impact on mathematical education and research in developing countries. 🌟🎓📚
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
📝 Note that the summer school will take place from August 19 to August 24, 2024. We look forward to your participation in this enlightening event. Stay tuned for further details on the schedule and registration process.
We’re thrilled to have Prof. Maria Gordina from Connecticut University giving a mini-course on Infinite-dimensional Heisenberg groups! Yesterday, we delved into the first part, and today we were eager to explore the final session.
📅 Dates & Times:
Wednesday, April 24: 3:00 PM – 5:00 PM
Thursday, April 25: 11:30 AM – 12:30 PM
📍 Location: Leslokaal 3.1, Campus Sterre, 28, Ghent University
📝 Outline of the Mini-Course: These informative sessions cover various aspects of analysis on infinite-dimensional Heisenberg-like groups:
Abstract Wiener Spaces and Gaussian Measures
Finite-dimensional Heisenberg Groups: As Lie groups and as sub-Riemannian manifolds
Review of Analysis on Heisenberg Groups: Gradient estimates and log Sobolev inequalities
Analysis on Infinite-dimensional Heisenberg Groups
This mini-course provided an invaluable opportunity for our group members, especially for our PhD students, to deepen their understanding of this complex subject. It offers a unique opportunity for participants to actively engage in cutting-edge research within the field.
A special thank you to Prof. Maria Gordina for sharing her expertise with us. Let’s make today’s session as enlightening as yesterday’s!
Ghent Analysis and PDE Center is glad to have hosted Gihyun Lee as a postdoctoral researcher for 2 years, and now we are happy to announce that Gihyun has succeeded in obtaining a further 2+1 years postdoctoral position at the Institute for Mathematics, University of Potsdam! 👏👏👏
It is always good to see our postdocs moving on to further positions and endeavours.
🎓 Gihyun Lee’s accomplishment reflects not only his talent but also his dedication and hard work in the field of mathematics. His innovative research and intellectual contributions have undoubtedly impressed the selection committee, earning him this well-deserved opportunity. 📖✏️
🎉 As he prepares to embark on this exciting journey at the University of Potsdam, we extend our warmest congratulations and best wishes for continued success in his academic pursuits. 🥂🎊🎉
📚🌟We have no doubt that his expertise and dedication will contribute to the mathematical community at the University of Potsdam, fostering collaboration, discovery, and intellectual growth. 📚🌟
Ghent Analysis & PDE Center 