Speaker: Alexandre Kirilov
Affiliation: Universidade Federal do Paraná

Title:
Global Properties for Systems in Time‑Periodic Gelfand‑Shilov Spaces

Abstract:
Time‑periodic Gelfand‑Shilov spaces provide a natural framework for the analysis of evolution equations combining periodic behavior in time with strong regularity and decay properties in the spatial variables. Introduced by F. de Ávila Silva and M. Cappiello, these spaces make it possible to extend techniques from compact settings to a non‑compact framework, while also revealing new phenomena in the study of regularity and solvability.

In this talk, I will focus on global hypoellipticity and solvability for operators and systems of evolution equations in this setting. I will present recent joint results, including sharp characterizations for systems, and briefly comment on ongoing work. Perspectives for extending these results beyond the torus, in particular toward more general geometric settings, will also be discussed.

References:

1. F. de Ávila Silva and M. Cappiello, Time‑periodic Gelfand‑Shilov spaces and global hypoellipticity on $\mathbb{T}\times {\mathbb{R}}^n$, J. Funct. Anal. 282 (9) (2022), Article 109418.
2. F. de Ávila Silva and M. Cappiello, Globally solvable time‑periodic evolution equations in Gelfand‑Shilov classes, Math. Ann. 391(1) (2025), 399–430.
3. F. de Ávila Silva, M. Cappiello and A. Kirilov, Global hypoellipticity for systems in time‑periodic Gelfand‑Shilov spaces, J. Funct. Anal. 290 (6) (2026), Article 111300.
4. F. de Ávila Silva, M. Cappiello and A. Kirilov, Systems of differential operators in time‑periodic Gelfand‑Shilov spaces, Ann. Mat. Pur. Appl. 204 (2025), 643–665.

Date and Time: April, 24, 2026. at 14:00 (CET)
Location: Campus Sterre S8, Auditorium 3.1

This seminar is organized within the program “Global Minds in PDE and Control Theory.”
More information about the program is available here:
👉 https://analysis-pde.org/2025/07/11/global-minds-in-pde-and-control-theory/

We are delighted to celebrate the successful PhD defense of Zhipeng, who presented his dissertation on the topic:

Multipliers on Lie Groups of exponential growth

We wish Zhipeng every success in his future academic endeavors. May his mathematical journey be marked by impactful discoveries, fruitful collaborations, and continued contributions to the advancement of our field.

Supervisors: Prof. Yulia Kuznetsova and Prof. Micheal Ruzhansky

Examiners: Prof. Jean-Philippe Anker, Dr. Marianna Chatzakou, Prof. Olivier Fouquet, Prof. Angela Pasquale, Prof. Quanhua Xu.

We are delighted to celebrate the successful PhD defense of Santiago, who presented his dissertation on the topic:

Pseudo-differential operators and spectral multipliers on non-Euclidean settings

Academic Achievement

Throughout these years, Santiago has demonstrated an outstanding level of dedication to his research, characterized by profound scientific curiosity and notable perseverance. His work has been published in prestigious journals, including the Journal of the London Mathematical Society and the Comptes Rendus de l’Académie des Sciences (Paris), reflecting the high quality and impact of his contributions to the field.

Santiago has contributed to the Banach Space and Banach Algebra course over the past three years by leading exercise sessions and assisting students in developing a deeper understanding of the material through carefully prepared problems and practical applications.

We wish Santiago every success in his future academic endeavors. May his mathematical journey be marked by impactful discoveries, fruitful collaborations, and continued contributions to the advancement of our field.

After 18 wonderful months in our research group, we are saying farewell to Arshyn as he begins his next chapter.

Arshyn, thank you for the dedication, the ideas, and the steady, positive energy you brought into our research center.

In these 18 months you were remarkably productive: seven preprints took shape during your stay, and you also won a research grant in Kazakhstan. That kind of focus is rare—and it lifted the pace of the whole group. Your work, and the way you shared it, made a clear difference.

As you move on, we wish you good luck and continued success. We hope you keep this momentum, find new problems worth your attention, and keep building strong collaborations around you.

We are pleased to announce a workshop on Fractional Partial Differential Equations and Related Topics, jointly organized by the Ghent Analysis & PDE Center and the FracDiff Research Group at Sultan Qaboos University.

The workshop aims to bring together researchers and practitioners to discuss recent developments, theoretical advances, and applications in fractional PDEs and related areas.

Workshop Chair: Dr. Sebti Kerbal, Leader of the FracDiff Research Group, Department of Mathematics, Sultan Qaboos University

Date: February 10, 2026 

Venue: Department Resource Room 0135, Department of Mathematics, Sultan Qaboos University 

Speakers

• Professor Michael Ruzhansky (Ghent University, Belgium) 
• Professor Erkinjon Karimov (Ghent University, Belgium) 
• Dr. Nasir Hanifa (Sultan Qaboos University, Oman) 
• Dr. Mariam Al-Maskari (Sultan Qaboos University, Oman) 

Schedule

• 14:00 – 15:00 | Professor Michael Ruzhansky “Fujita exponent for heat equations for groups and sums of squares” 
• 15:00 – 15:30 | Professor Erkinjon Karimov “Green’s Function and Solution Representation for a Boundary Value Problem Involving the Prabhakar Fractional Derivative” 
• 15:30 – 16:00 | Coffee Break 
• 16:00 – 16:30 | Dr. Haniffa Mohamed Nasir. “A(0) and A(\pi/2) stabilities of fractional LMMs for fractional IVPs and applications“
• 16:30 – 17:00 | Dr. Mariam Al-Maskari.“Fractional Cahn-Hilliard equations: Analysis, Stochastic effects, and Numerical Perspectives“

We are delighted to congratulate Dr. Vishvesh Kumar on his new position at Department of Mathematical Sciences at IIT BHU Varanasi as an Assistant Professor. This is a wonderful milestone in his academic career, and a moment of pride for all of us at the Ghent Analysis & PDE Center.

Since joining our group as a postdoctoral researcher at Ghent University, Dr. Kumar has been an active and inspiring member of our community. Working within the Department of Mathematics: Analysis, Logic and Discrete Mathematics and the Ghent Analysis & PDE Center headed by Prof. Michael Ruzhansky, he has contributed significantly to our core areas of research.  

Research contributions in our group

Dr. Kumar’s research lies at the intersection of abstract harmonic analysis, pseudo-differential operators, geometric analysis, and partial differential equations on Lie groups.  

During his time in Ghent, he has:

• Co-authored numerous papers on nonlocal and subelliptic problems on stratified Lie groups, including work on Brezis–Nirenberg type problems, critical equations, and fractional Sobolev-type inequalities.  
• Made substantial contributions to the theory of damped and fractional wave equations on graded and stratified Lie groups, including results for higher order hypoelliptic equations with data in negative order Sobolev spaces.  
• Advanced functional inequalities and harmonic analysis on symmetric spaces and hypergroups, with applications to Fourier multipliers, Strichartz estimates, and related analytic inequalities.  

His work has appeared, or is forthcoming, in several respected international journals such as Journal of Evolution Equations, Mathematische Annalen, Journal of Geometric Analysis, Israel Journal of Mathematics, and others, reflecting both the depth and breadth of his contribution to our field.  

A valued colleague

On a personal level, Vishvesh has been a generous collaborator and a supportive colleague. His willingness to discuss ideas, share expertise, and encourage younger researchers and visitors has left a strong and positive impression in our group. Many of us have benefited from his clarity of thought, his calm problem-solving approach, and his enthusiasm for mathematics.

Looking ahead

While we will miss having him at the Ghent Analysis & PDE Center, we are equally excited to see him take this next step as an Assistant Professor at IIT BHU Varanasi. We are confident that he will continue to build a vibrant research program, inspire students, and develop new collaborations that will further strengthen the links between our institutions.