Name: Dr. Alvaro Anton-Sancho
Affiliations: ¹ Fray Luis de León University, Spain; ² Catholic University of Avila, Spain

We wish to congratulate Dr. Alvaro Anton-Sancho on winning the Axioms Outstanding Reviewer Award. We had the pleasure of inviting him for this interview, in which we learned more about his background, views, and interests.

1. Could you briefly introduce yourself and your current research interests? Are there any recent projects or results you would like to share with our readers?
Originally, my research focused on the geometry of Higgs bundle spaces. This has connections with representation theory, group geometry, topology, and mathematical physics. Specifically, in my early work, I was interested in the automorphisms of these spaces. Since then, I have published work mainly focused on algebraic geometry, differential geometry, and the topology of spaces of bundles over curves, and their applications in various areas of science and technology. Currently, my interests encompass the geometry of moduli spaces of principal bundles and Higgs bundles, and applications in Langlands duality, electromagnetism, and the topological classification of control systems in robotics. My projects include the study of the geometry of principal bundles over curves with singularities and the description of automorphisms and fixed points of bundles with exceptional structure groups, which have many applications in theoretical and particle physics.

2. What motivated you to serve as a reviewer for Axioms, and could you share your experience reviewing for the journal?
High-quality research requires scientists to review the work of our colleagues to ensure that their contributions are strong enough. As such, we researchers have a responsibility not only to publish our own work, but also to participate in the ongoing process of reviewing the work of others. I am aware that many other colleagues have devoted their time and given their best to ensure the robustness of my own work. One way to acknowledge that effort is to take personal responsibility for actively participating in the peer-review process. This is what primarily motivates my work as a reviewer. In this regard, Axioms is a journal of the highest scientific level whose scope fits my interests perfectly, whose high standards of scientific quality ensure that the peer-review process is carried out with particular care, and in which I feel particularly comfortable serving as a reviewer, given the great respect with which it treats its reviewers.

3. What is your typical approach to reviewing a manuscript? How do you ensure both rigor and efficiency in your review process?
When reviewing an article, it is very important to understand that it is the result of the creative intellectual work and efforts of researchers who have given their very best in the sincere hope of contributing to collective knowledge. Consequently, every paper I read deserves my utmost respect. From there, it is necessary to read the text carefully, understand the specific context to which the authors are seeking to contribute, and ensure that this context is well understood by the reviewer. Respect for others’ work, a thorough knowledge of the field, and careful examination of the text will enable one to assess the degree of novelty and originality of the contributions, their mathematical correctness, and their impact within the knowledge area.

4. In your opinion, what are the key elements of a high-quality manuscript? What aspects do you pay the most attention to when reviewing?
In mathematics and related fields, a top-tier research article must make novel and original contributions that are of interest within an active line of research. Thus, analyzing the impact of these contributions is crucial to ensuring a useful report. Naturally, the primary criterion for evaluation is mathematical correctness and the rigor of the statements and proofs. Furthermore, it is important to justify the significance of these contributions by developing appropriate applications, where possible. An effective structure of the manuscript is also essential to facilitate access to and reading of the main results.

5. How has your reviewing experience influenced your own research or academic writing? Do you have any advice for early career researchers on how to write a strong manuscript and respond effectively to reviewers’ comments?
I have learnt a great deal by studying the work of my distinguished colleagues. Above all, I have gained a more realistic understanding of the nature of the different active lines of research. Reviewing research articles has also helped me broaden my mindset regarding ways of reasoning and reflecting. Undoubtedly, reading other researchers’ lines of thought is enriching, as it refreshes one’s own ideas. This is particularly significant in mathematics.

6. Looking ahead, which research topics or emerging directions do you believe will attract increasing attention in the next few years?
Looking ahead, I expect growing attention on the geometry of moduli spaces of principal and Higgs bundles, especially beyond the classical setting, such as in irregular or higher-dimensional contexts. I also think their interaction with mathematical physics, through gauge theory, mirror symmetry, and the geometric Langlands program, will remain a major driving force. More broadly, I see the field moving toward a deeper synthesis between geometry, representation theory, and physics, with Higgs bundles continuing to play a central unifying role.