I am thrilled to apply for the Hong Kong Laureate Forum—a venue that perfectly aligns with my passion for interdisciplinary exploration and international collaboration. As a postdoctoral researcher at the Institute of Mathematics and Mathematical Modeling in Almaty, I have been fortunate to develop my expertise through diverse experiences. I earned my PhD at Kazakh National University in 2023 and further expanded my horizons during a postdoctoral stint at The Centre de Recerca Matemàtica in Barcelona.

My research encompasses two closely connected areas: PDEs and Analysis. In the realm of PDEs, I investigate degenerate hyperbolic equations with nonlocal boundary conditions and the modified Cauchy problem. Meanwhile, my work in Analysis focuses on understanding the growth properties of integral transforms and their relationship with moduli of smoothness.

I am equally passionate about inspiring the next generation of scientists. Dedicated to mentoring students and promoting science in my home country, I see the Forum as an unparalleled opportunity to amplify this impact. I am confident that engaging with esteemed Shaw Laureates and fellow emerging talents will enrich my perspective as a researcher, collaborator, and communicator in the scientific community.

Gebze Technical University

Centre de Recerca Matemàtica

NEW-Recommendation-letter-2_compressed.pdf

The focus of the current work is to establish a general inequality controlling the growth behavior of the Laguerre transform using the modulus of continuity defined by a generalized translation operator associated with the Laguerre translation. We first introduce the weighted Lebesgue measurable space $\mathcal{L}^p_{\alpha}$, then we prove the Riemann-Lebesgue lemma and the Hausdorff-Young inequality for the Laguerre transform. Furthermore, we introduce the Laguerre translation operator and define the modulus of continuity of a function with respect to this operator. Finally, study the growth property of the Laguerre transform and prove an analog of the Titchmarsh theorem for functions from $\text{Lip}(\beta, \mathcal{L}^p_{\alpha})$.