Current Work and Research Interests

Previous Work

Planar Elastica

I have studied variational problems for planar elastic rods under magnetic and gravitational loading. In joint work with C. Tropp, we developed a unified variational and integral-reduction framework for investigating these problems. This work combines variational methods with the analysis of the differential equations governing planar elastic curves.

My decision to write this paper also had a personal motivation. I wanted to study algebraic geometry and derived geometry more deeply, and I felt that completing a research project in analysis would give me both a concrete reason and the confidence to temporarily set aside further research and study in analysis before turning toward algebraic subjects. Writing the elastica paper was therefore part of a deliberate change in my mathematical focus: I wanted to complete this project in analysis so that I could concentrate more fully on these areas of geometry.

Real Algebraic Geometry

During an internship at TU Dresden, I explored real algebraic geometry through computational work on real algebraic surfaces. Using Julia, I combined theoretical descriptions with explicit computations to investigate the geometric properties of particular examples. This experience introduced me to an approach to research that begins with concrete geometric objects and uses computation to explore mathematical questions.

My research focus subsequently shifted to derived geometry and homotopical algebra, and I am no longer working in real algebraic geometry. Nevertheless, this experience broadened my mathematical perspective. Ideas from real algebraic geometry, particularly through positive geometry and its connections with scattering amplitudes, also showed me another mathematical route toward understanding quantum field theory. This encouraged me to learn more about how different areas of mathematics approach related problems through their own objects and methods.

Current Research Interests

My main interests currently lie in derived geometry, algebraic K-theory, and homotopical algebra, with a particular emphasis on derived smooth geometry and $C^\infty$-rings. I am interested in how algebraic and homotopical methods help us formulate and study geometric questions, especially in a smooth setting.

My current research concerns derived Azumaya algebras and Brauer theory on derived smooth manifolds. This work involves module categories, Morita equivalence, Picard-theoretic constructions, and the assembly of local data into global structures. Alongside this research, I am interested in algebraic K-theory, higher category theory, and their connections with geometry and homotopy theory, which I hope to explore further in future work.

These experiences have also shaped my understanding of mathematical research. Particularly in the age of artificial intelligence, I believe that mathematicians need to develop a broad and deep understanding of mathematics. Alongside studying a particular subject in depth, we also need to understand the basic ideas and methods of other fields and how they relate to our own work. This understanding helps us assess the significance of problems, choose suitable methods, and recognise possible connections between different theories.

I also tend to think that mathematical research will place increasing importance on communication and collaboration between researchers from different fields. The long-established practice of large-scale collaboration in experimental physics provides a point of reference for how I think about the organisation of mathematical research. Researchers with different areas of expertise can bring their knowledge and methods together around a shared problem. Working closely together also requires an understanding of one another’s questions, mathematical language, and ways of thinking.

For me, depth in research, breadth of mathematical understanding, and the ability to collaborate are all aspects worth developing continuously. I hope to pursue derived geometry and homotopical algebra in depth while remaining open to other areas of mathematics, and to explore connections between different methods through discussion and collaboration.