[IM Webinar Series] Talks by Jryl Maralit and Rodolfo Maza on 04 May 2026, 10AM-12PM

You are all invited to the second set of talks in the 2026 IM Webinar Series on Monday, 04 May 2026, 10AM – 12PM, featuring research from our faculty members from the Matrix Analysis and Linear Algebra (MALA) and the Differential Equations (DE) research groups, Jryl Maralit (10AM-11AM) and Rodolfo Maza (11AM-12PM), respectively. Please feel free to forward this invitation to anyone who might be interested. We look forward to seeing you there.

JOIN THE MEETING HERE

• Meeting Link: bit.ly/IMWebinar2026
• Talk Abstracts: bit.ly/IMWAbstracts26

The details of the talks are as follows:

1. Title: Extending Leonard pairs to Leonard triples and Leonard quadruples
   Speaker: Jryl Maralit (University of the Philippines Diliman)
   Abstract: In 2001, Paul Terwilliger classified Leonard pairs. In 2004, during a series of lectures at Universidad Carlos III de Madrid, he presented several open problems related to this theory. In 2011, we studied one of these problems, namely, the extension of a specific Leonard pair to a Leonard triple. Since then, new techniques and perspectives have emerged, offering deeper insight into the subject.
       In this talk, we revisit the problem using these new tools. In particular, we extend a given Leonard pair to a Leonard quadruple.
   
2. Title: Energy Convergence and a corrector result for the Homogenization of a class of elliptic problems with imperfect interface and weak data
   Speaker: Rodolfo Maza (University of the Philippines Diliman)
   Abstract: In the homogenization of elliptic PDEs over a domain Ω, the solution u^ε of the heterogenuous problems at the scale ε converges weakly to a function in H¹(Ω) as ε goes to 0. Compactness argument shows strong convergence of the solutions in L²(Ω), however, the gradients only converge weakly in L²(Ω). It is the main goal of corrector results to establish a strong convergence for the gradients of the solutions.
       This talk will be grounded on the homogenization of quasi-linear elliptic problems with weak data over a fixed domain Ω with two components Ω^ε₁ and Ω^ε₂, and a jump on the interface Γ^ε depending on a parameter γ for -1 < γ < 1 and γ < -1. In addition to the framework of renormalized solutions used due to the weak data, we apply the periodic unfolding method in formulating an energy convergence result. Then we proceed in establishing the corrector results for the linear case.