Name: Dr. Joseph Lakey
Affiliation: New Mexico State University, Las Cruces, United States
Research interests: harmonic analysis; signal processing; spectral graph theory
Brief introduction: I am an Associate Dean in the College of Arts and Sciences at New Mexico State University in Las Cruces, New Mexico, USA. I have worked at NMSU for over 25 years.

The following is a short interview with Dr. Joseph Lakey:

1. Could you give a brief introduction of yourself to the readers?  Could you introduce your current research direction and provide an update on your progress?
The past five years I have been studying primarily spectral graph theory for certain special types of graphs in which there should be results analogous to known results from classical harmonic analysis. I have also been working on higher dimensional versions of so-called prolate functions and prolate wavelets using techniques from Clifford analysis.

2. Could you share with us your emotions upon winning this award?
I am very pleased to be recognized as an exceptional reviewer for Mathematics.  The peer review process can be quirky but is critical for maintaining scientific standards. The vast majority of work I have reviewed for Mathematics is scientifically sound but can make a much more significant impact by providing clear motivation and context to explain where the results fall into the scope of other work, and how they advance the field of study.

3. Could you share some insights into your approach to reviewing manuscripts? How do you balance thoroughness with efficiency?
MDPI puts an emphasis on a fast publication cycle. I try to give manuscripts a quick initial read to orient myself, to allow myself to ask if the approach makes sense and if any change in approach will assist the interested reader. If proofs at the beginning and end are solid, then what is in the middle should be okay.

4. In your opinion, what are some key qualities that make a review outstanding?
An excellent review should add insight for the authors: not just check if the results are correct but also provide the author with the opportunity to make modifications that will help the reader to understand their work and its significance.

5. Based on your experience, which research topics do you think will be of particular interest to the research community in the coming years?
Obviously there has been emphasis on large language models and deep learning. I believe that spectral graph theory can be of use in understanding fundamental aspects of these models that are not well understood yet. Graphs provide models for so many things ranging from behavior of materials at the molecular level to providing insights for large scale networks. Understanding these structures benefits both from clever mathematical insight and careful combinatorial analysis to numerical simulation.