Geometry to Global Impact: How One LAS Mathematician Is Shaping the Future of STEM

How did you become interested in your field of Mathematics?

I’ve been fascinated by mathematics since I was a child, growing up in a household where both my parents worked in STEM fields—my father was a theoretical physicist, and my mother was a nuclear physicist. One of the earliest sparks for me was seeing how abstract concepts could be used to describe and solve real-world problems, whether in nature or mathematics. Moving between different countries at a young age following my academic parents also exposed me to various educational systems and languages. This broad perspective helped me see mathematics as a universal language that could remain constant. Later on, during my undergraduate studies in the National University of La Plata, Argentina, I discovered the elegance of geometry, and slowly started focusing in that field. That foundation set me on a path to pursuing graduate work at the University of Oxford, and ultimately dedicating my career to exploring the rich interplay between geometry, algebra, and mathematical physics.

Tell us a little bit about your work at LAS. What is a favorite accomplishmentfrom your nearly 10 years at the college?

One of the most rewarding aspects of my time at the College of Liberal Arts and Sciences (LAS) has been the opportunity to collaborate with colleagues across disciplines, from mathematics to physics and even computer science. I find that interdisciplinary connections often spark the most interesting research questions, and UIC has been extremely supportive in this respect. Over the years I’ve been growing my research scope, as well as my group, taking a lot of young students on interdisciplinary topics, as well as older students for more abstract geometric goals. We’ve tackled a range of questions involving moduli spaces, Higgs bundles, and their links to theoretical physics and integrable systems. Watching students transform into independent researchers at the top universities in the country, co-authoring papers, and presenting at international conferences has been incredibly fulfilling. I believe our collective accomplishments—especially forging strong mentorship frameworks—are some of my favorite achievements during my time at LAS.

What aspect does research play in your role as a faculty member at LAS?

Research is central to my work as a faculty member. I spend a significant portion of my time working closely with students and collaborators worldwide, investigating problems across geometry but also real world questions arising from our society. As a professor, I also integrate fresh research insights into the classroom—my teaching often benefits from the latest findings or new methods I’ve encountered in my work – for instance I thoroughly enjoyed teaching my class “Math and Society” this last semester, showing my undergraduate and graduate students different mathematical models that can be used to understand our everyday life. Of course, beyond the personal satisfaction, research plays a broader role: it helps raise the profile of our department, attracts external funding, and fosters an environment where students can experience cutting-edge mathematics firsthand. This, in turn, elevates the academic experience for everyone at LAS.

Is there anything in your research that has surprised you?

Absolutely. One of the joys of exploring mathematics is that it frequently takes you in unexpected directions. For instance, my early work was rooted in algebraic geometry, but I soon uncovered connections with string theory, an area I hadn’t imagined I’d ever contribute to. More recently, curiosity has taken me through all sorts of more applied projects, from behavioural science and the relation of colors and emotions, to the structural classification of viruses or understanding correlations between dengue and COVID-19. Each time we try to answer one question, new ones emerge—often leading to surprising collaborations with physicists or other scientists. Nowadays, I find the most fulfilling research topics are those that lead to new ways for pure math to resonate in more tangible fields.

You were recently selected for a Presidential Early Career Award for Scientists and Engineers (PECASE). Can you talk about this accomplishment and what this recognition means to you?

Receiving the PECASE award is both an incredible honor and a tremendous motivator. This award is one of the most prestigious acknowledgments for early-career researchers in the United States, recognizing not only past achievements but also potential for future impact in science and engineering.

For me, it reaffirms the importance research in geometry, and its connections to other fields. It also highlights the value of collaboration and mentorship, as these have been constant components of my research in the last decade. I hope the recognition will mean new opportunities to expand projects, attract additional funding, and deepen our international partnerships—all of which benefits our students, the department, and the broader mathematical community.

You have been working with students in a mentorship role and recently focused on forming a research group. Can you discuss this process and your experiences working with students in this capacity?

Mentorship is at the heart of why I like about academia. From high school students just starting to explore research, to graduate students pursuing advanced projects, working with students is incredibly rewarding. We’ve built a welcoming environment where students can share ideas freely, support each other, and develop as independent thinkers. I love introducing my students to my collaborators, and help the younger generations start building a network of scientists that can serve as role models.

Forming a research group is both exciting and challenging—it requires establishing a clear vision for the projects, securing funding, and fostering a culture of mutual respect and curiosity. The best part is seeing students grow in confidence: they begin by asking hesitant questions, and eventually they’re the ones presenting cutting-edge results at international conferences. Knowing I can help shape their academic journey and spark a passion for mathematics is truly a privilege.

Can you elaborate on the impact that collaborations with various departments and faculty members have had on you, particularly in relation to creating new connections between disciplines?

Since joining UIC, collaboration has been central to my academic journey. One of my closest collaborators is Prof. James Unwin from the Department of Physics, with whom I have worked extensively on projects spanning outreach, behavioral science, and mathematical physics. These collaborations have not only led to exciting publications but also enriched my research perspective by bridging disciplines in meaningful ways.

Globally, I have been fortunate to work with collaborators from many countries, connecting ideas across areas that might otherwise remain isolated. For example, my work with high school students and researchers has applied mathematical tools to diverse topics such as virus structures, crystal growth, the dynamics of diseases like COVID-19 and dengue, and even behavioral models of influencers and ant colonies. These interdisciplinary collaborations demonstrate the universal power of mathematics to solve real-world problems and uncover patterns in unexpected places.

At UIC, I particularly enjoy mentoring students to explore the practical applications of mathematics. Training high school and undergraduate students to use mathematical concepts to answer everyday questions has been one of the most rewarding parts of my work, showcasing how mathematics serves as a bridge across disciplines and a tool for innovation. Last summer, I was part of UIC’s SROP program, and for the previous few years, I’ve also been an Honors College Fellow, mentoring undergraduates in LAS. Moreover, only a few months ago, with Prof. Unwin and other colleagues in Physics and Philosophy, we organized a workshop on quantum theory at the extremes, bringing together the three departments (Physics, Mathematics, and Philosophy) – it was exciting and inspiring. We’re looking forward to seeing where these lines of thinking could take us.

Throughout your time as a researcher, you have organized various initiatives that benefit the LAS community and the larger Math community. Can you talk more about this work?

Outreach has been a cornerstone of my career, and I’m incredibly proud of the initiatives I’ve led to bring mathematics to a broader audience. One example is the Sonia Kovalevsky Days, which we began organizing at UIC a decade ago with Prof. James Unwin. These events encourage young girls to pursue careers in math and science by introducing them to engaging, hands-on activities and inspiring role models. Watching these days’ impact on participants and hearing about their continued interest in STEM has been incredibly rewarding.

I’ve also had the privilege of mentoring students through UIC’s Summer Research Opportunities Program and as an Honors College Fellow, providing guidance in mathematics and broader academic and professional development. Beyond UIC, my outreach extends to the Chicago Public Schools and the Chicago Lincoln Park Zoo, where I participate in career days and conduct interactive readings to foster a love for science and learning.

In addition, I organize yearly meetings on geometry and physics at UIC, funded by the NSF and my startup funds. These gatherings bring together researchers from diverse fields, highlighting the value of collaboration and creating a space for innovative ideas to thrive. Each initiative reflects my deep commitment to making mathematics accessible and inspiring to people of all ages and backgrounds.

What drives the motivation to give back to your community in this way?

Growing up in Argentina, where education is both free and a valued right, I witnessed firsthand the transformative power of teaching and mentorship. From my parents (who were also academics) to many of my professors and TAs, people in the university often worked “ad honorem”—without salaries—out of a profound belief in the value of education. This experience shaped my perspective on the privilege and responsibility of being an educator.

For me, giving back to the community is about creating opportunities for others to see the beauty and utility of mathematics, just as my teachers did for me. Whether it’s through outreach programs, mentoring, or career days, I aim to empower students with the tools to understand and question the world around them.

I also believe that educators have a vital role in fostering an informed community. By sharing knowledge, we contribute to a society that values critical thinking, curiosity, and innovation. Teaching is as much an act of learning as it is of giving, and it remains one of the most fulfilling aspects of my career.

Do you have any advice for students pursuing an LAS degree?

I’d say: Stay curious, and be open to new perspectives. In LAS, you’ll encounter a diversity of fields and ideas—try to embrace that breadth. I find that most often very innovative results happen when you draw on insights from multiple disciplines. Seek mentors or professors who inspire you, and don’t be afraid to ask for guidance or research opportunities. Finally, remember that perseverance is key in any academic pursuit; you’ll face challenges and unexpected setbacks, but they’re all part of the learning process.