# Vishvesh Kumar at Virtual Math Fest

Vishvesh Kumar has just given a nice talk at the Virtual Math Fest 2020 (Symposium on Analysis and PDE)

on the joint work with Marianna Chatzakou from Imperial College London.

Well done, Vishvesh!

• Chatzakou M., Kumar V., Lp-Lq boundedness of Fourier multipliers associated with the anharmonic oscillator. arxiv
• Chatzakou M., Delgado J., Ruzhansky M., On a class of anharmonic oscillators. arxiv
• Cardona D., Kumar V., Ruzhansky M., Tokmagambetov N., LpLq boundedness of pseudo-differential operators on smooth manifolds and its applications to nonlinear equationsarxiv

# Linda Botchway starting her PhD

Congratulations to Linda Botchway, for receiving the grant of USD 15,500 from the Carnegie Corporation of New York (CCNY), for her PhD at the University of Ghana, Legon, under our supervision.

Well done, Linda!

We are looking forward to Linda’s visits to our Analysis & PDE Center at Ghent University, and to her enrolment to UGent PhD program for a joint PhD.

Research of Linda on pseudo-differential operators on ${\mathbb Z}^n$ started while she was a Master student at AIMS Ghana. This resulted in a substantial (41 pages) publication, a great achievement for a Master Student:

Botchway L., Kibiti G., Ruzhansky M., Difference equations and pseudo-differential operators on ZnJ. Funct. Anal.278 (2020), no. 11, 108473, 41pp. link (open access)arxiv

In the above paper one makes a consistent development of the calculus of pseudo-differential operators which can be called pseudo-difference operators in the context of the lattice ${\mathbb Z}^n$ Some interesting questions to answer:

• how to define Hörmander type or other symbol classes on ${\mathbb Z}^n$?
• what is the relation to the analysis on the torus ${\mathbb T}^n$?
• can it be used to derive new properties of operators on ${\mathbb Z}^n$?
• how to apply it to solving difference equations and to finding properties of their solutions?

# Webinar by AMS.org: Accessibility Best Practices for Moving Mathematics Online

Description: For many years there has been a push for moving teaching and research content online in a form that goes beyond just linking print versions of documents. The COVID pandemic has only accelerated this trend, forcing all faculty to focus on how to deliver courses online. However, hastily moving material online bears the risk that important accessibility considerations are neglected, threatening fair and inclusive education for all. This is especially true for mathematics and other STEM fields where complex structures such as equations and diagrams play an integral role. In this webinar we will advocate that in addition to moving content online quickly, instructors can use best practices developed for authors to ensure accessibility of math content from the start, thus avoiding additional and duplicate work.

Our presentation shall give an overview of different requirements on presentation and content for students and readers with special needs and how assistive technology support can be provided. We shall particularly concentrate on what this means for math content and how it is made accessible on the web. We argue that the web is the ideal platform for hosting and curating modern content regardless of their original sources like LaTeX, Word, or plain text. And we will demonstrate how accessibility can be practically a free byproduct of conversion from traditionally authored content. In conclusion we discuss ways of authoring, preparing, and teaching accessible web documents containing mathematics, highlighting some of the best practices.

Presented by Prof. Volker Sorge, University of Birmingham, UK & MathJax Consortium

Time:   July 13, 2020 02:00 PM in Eastern Time (US and Canada)

This information is presented here

# Dr Durvudkhan Suragan on Kazakh TV

Another of our former postdocs (still at Imperial College London), and an associated collaborator of our Ghent Analysis and PDE Centre, Dr Durvudkhan Suragan, featured on Kazakh TV, in a special program about him and his achievements.

Congratulations, Durvudkhan!

It is very rewarding to see current and former students and postdocs being recognised for their achievements!

Also, with the appearance of Dr Berikbol Torebek:

Recently: another of our associated member, Dr Erkinjon Karimov, on Uzbek State TV, read here.

Our books with Durvudkhan Suragan:

1. Ashyralyev A., Kalmenov T., Ruzhansky M., Sadybekov M., Suragan D. (Eds.) Functional Analysis in Interdisciplinary Applications II, Springer Proceedings in Mathematics & Statistics, Springer, 2020, to appear
2. Ruzhansky M., Suragan D., Hardy inequalities on homogeneous groups: 100 years of Hardy inequalities, Progress in Mathematics, Vol. 327, Birkhauser, 2019. xvi+588pp. link, free download (open access book), poster, the winner of  Ferran Sunyer I Balaguer Prize 2018
3. Ruzhansky M., Sadybekov M., Suragan D., Spectral geometry of partial differential operators, Monographs and Research Notes in Mathematics, Chapman and Hall/CRC Press, 2020. 378pp. link, free download (open access book), poster

Our papers with Durvudkhan Suragan:

1. Restrepo J., Ruzhansky M., Suragan D., Explicit representations of solutions for linear fractional differential equations with variable coefficients. arxiv
2. Kassymov A., Ruzhansky M., Suragan D., Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, arxiv
3. Kassymov A., Ruzhansky M., Suragan D., Reverse integral Hardy inequalities on metric measure spaces. arxiv
4. Ruzhansky M., Sabitbek B., Suragan D., Geometric Hardy inequalities on starshaped sets. arxiv
5. Ruzhansky M., Sabitbek B., Suragan D., Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups. Bull. Math. Sci., to appear. arxiv
6. Kassymov A., Ruzhansky M., Suragan D., Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems. arxiv
7. Ruzhansky M., Sabitbek B., Suragan D., Subelliptic geometric Hardy type inequalities on half-spaces and convex domainsAnn. Funct. Anal., to appear. arxiv
8. Ruzhansky M., Suragan D., Yessirkegenov N., Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups. Semigroup Forum, to appear. link (open access), arxiv
9. Ruzhansky M., Suragan D., Green’s identities, comparison principle and uniqueness of positive solutions for nonlinear p-sub-Laplacian equations on stratified Lie groups, Potential Analysis, to appear. arxiv, link
10. Ruzhansky M., Sabitbek B., Suragan D., Hardy and Rellich inequalities for anisotropic p-sub-Laplacians, Banach J. Math. Anal., 14 (2020), 380-398. linkarxiv
11. Kassymov A., Ruzhansky M., Suragan D., Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups. NoDEA Nonlinear Differential Equations Appl., 27 (2020), no. 1, Paper No. 7. link
13. Kassymov A., Ruzhansky M., Suragan D., Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. Integral Transforms and Special Functions, 30 (2019), 643-655. linkarxiv
14. Ruzhansky M., Sabitbek B., Suragan D., Weighted anisotropic Hardy and Rellich type inequalities for general vector fields, NoDEA Nonlinear Differential Equations Appl., 26 (2019), no. 2, 26:13. linkarxiv
15. Kalmenov T. Sh., Ruzhansky M., Suragan D., On spectral and boundary properties of the volume potential for the Helmholtz equation. Math. Model. Nat. Phenom., 14 (2019), no. 5, Art. 502, 11 pp. link
16. Ozawa T., Ruzhansky M., Suragan D., Lp-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, Quart. J. Math., 70 (2019), 305-318. arxiv, link, offprint (open access)
17. Ruzhansky M., Sabitbek B., Suragan D., Weighted Lp-Hardy and Lp-Rellich inequalities with boundary terms on stratified Lie groups, Rev. Mat. Complutense, 32 (2019), 19-35. enhanced pdf (open access)arxiv, link
18. Ruzhansky M., Suragan D., A note on stability of Hardy inequalitiesAnn. Funct. Anal., 9 (2018), 451-462. arxiv, link
19. Ruzhansky M., Suragan D., A comparison principle for nonlinear heat Rockland operators on graded groups, Bull. Lond. Math. Soc., 50 (2018), 753-758. enhanced pdf (open access)arxiv, link
20. Ruzhansky M., Suragan D., Elements of potential theory on Carnot groups, Funct. Anal. Appl., 52 (2018), 158-161. link(eng)link (rus)
21. Ruzhansky M., Suragan D., Yessirkegenov N., Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces, Fract. Calc. Appl. Anal., 21 (2018), 577-612. arxiv, link
22. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities, Trans. Amer. Math. Soc. Ser. B, 5 (2018), 32-62offprint (open access), link, arxiv
23. Ruzhansky M., Suragan D., Yessirkegenov N., Sobolev type inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groupsIntegral Equations Operator Theory, 90 (2018), no. 1, 90:10. enhanced pdf (open access)arxiv, link
24. Ruzhansky M., Suragan D., Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups, Adv. Math., 317 (2017), 799-822. offprint (open access), arxiv, link
25. Ruzhansky M., Suragan D., Anisotropic L2-weighted Hardy and L2-Caffarelli-Kohn-Nirenberg inequalities, Commun. Contemp. Math., 19 (2017), no. 6, 1750014, 12pp. offprint (open access), arxiv, link
26. Ruzhansky M., Suragan D., Yessirkegenov N., Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups, NoDEA Nonlinear Differential Equations Appl, 24 (2017), no. 5, 24:56. offprint (open access), arxiv, link
27. Ruzhansky M., Suragan D., Geometric maximizers of Schatten norms of some convolution type integral operators, J. Math. Anal. Appl., 456 (2017), 444-456. arXivlink
28. Ruzhansky M., Suragan D., Yessirkegenov N., Extended Caffarelli-Kohn-Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities, C. R. Acad. Sci. Paris, 355 (2017), 694-698. offprint (open access), link
29. Ruzhansky M., Suragan D., Uncertainty relations on nilpotent Lie groups, Proc. R. Soc. A, 473 (2017), no. 2201, 20170082, 12pp. offprint (open access), arxiv, link
30. Ruzhansky M., Suragan D., Isoperimetric inequalities for some integral operators arising in potential theory, in Functional Analysis in Interdisciplinary Applications. FAIA 2017, 320-329, Springer Proceedings in Mathematics & Statistics, vol 216, Springer, 2017. arxivlink
31. Ruzhansky M., Suragan D., Local Hardy and Rellich inequalities for sums of squares of vector fields, Adv. Diff. Equations, 22 (2017), 505-540. arxiv, link
32. Garofalo N., Ruzhansky M., Suragan D., On Green functions for Dirichlet sub-Laplacians on H-type groups, J. Math. Anal. Appl., 452 (2017), 896-905. offprint (open access), link, arxiv
33. Ruzhansky M., Suragan D., Layer potentials, Green formulae, Kac problem, and refined Hardy inequality on homogeneous Carnot groups, Adv. Math., 308 (2017), 483-528. offprint (open access), arxiv, link
34. Ruzhansky M., Suragan D., On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups, J. Differential Equations, 262 (2017), 1799-1821. offprint (open access), arxiv, link
35. Ruzhansky M., Suragan D., On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries, Bull. Math. Sci., 6 (2016), 325-334. offprint (open access), arxiv, link
36. Rozenblum G., Ruzhansky M., Suragan D., Isoperimetric inequalities for Schatten norms of Riesz potentials, J. Funct. Anal., 271 (2016), 224-239. offprint (open access), arxiv, link
37. Ruzhansky M., Suragan D., On Schatten norms of convolution-type integral operators, Russ. Math. Surv., 71 (2016),157-158link
38. Ruzhansky M., Suragan D., On Kac principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group, Proc. Amer. Math. Soc., 144 (2016), 709-721. arxiv, link
39. Ruzhansky M., Suragan D., Isoperimetric inequalities for the logarithmic potential operator, J. Math. Anal. Appl.,434 (2016), 1676-1689. offprint (open access), arxiv, link

# Dr Erkinjon Karimov on State TV

Dr Erkinjon Karimov, a long-term collaborator and an associated member of our Ghent Analysis & PDE Center was on the Uzbekistan State TV, celebrated for his scientific achievements. A special program was filmed about him.

Congratulations, Erkinjon!

Erkinjon has been our long-term visitor in 2019, and is planning to join us as a researcher from Autumn 2020, in the framework of our Odysseus project.

Erkinjon has just co-organised the Fractional Calculus Workshop with us.

Watch the YouTube Video (in Russian):

# Presentation of the GAP centre

Finally the presentation of our Ghent Analysis & PDE (GAP) Center is ready. Many thanks to Ljubica Oparnica for the design and for putting it together!

Click on it to explore:

The movie is coming up as well.

# New style of books of abstracts

During this times, when conferences and workshops are held online, it is a good chance to experiment with visual books of abstracts. See the book of abstracts movie for the workshop that we have just organised:

# Workshop: Fractional Calculus

### ZOOM instructions (updated)

For the convenience of participants, if you want to obtain the zoom address of the meeting (before or during the conference), please send an email to Berikbol Torebek at berikbol.torebek@ugent.be

You can send it any time before or during the workshop. Once we have your interest and email address, we will send you the updated zoom link.

## Description

The aim of the workshop is to exchange the recent progress and ideas in the field of fractional calculus and fractional differential equations (FDEs), and their applications to a variety of concrete problems. Our group took an initiative to organise this workshop for the continuity of research in the field despite the coronovirus times, therefore, the conference will take place on ZOOM.

There is also a forthcoming special issue on evolution equations with singularities.