Future Proof - Pengfei Huang
Veröffentlicht am 19. August 2026
Unser Postdoktorand, Pengfei Huang, wurde zum Zhicheng-Nachwuchsprofessor/außerordentlichen Professor an der Fakultät für Mathematik der Nanjing University in China ernannt. Wir wünschen ihm alles Gute und viel Erfolg!
Pengfei Huang war Postdoktorand in der Forschungsgruppe „Geometrie, Gruppen und Dynamik“ unter der Leitung unserer Direktorin Anna Wienhard. Zuvor hatte er im Jahr 2020 seine Doktorarbeit unter der Betreuung von Prof. Carlos Simpson von der Université Côte d'Azur und Prof. Jiayu Li von der University of Science and Technology of China verteidigt.
Die Forschungsschwerpunkte von Pengfei Huang liegen in den Bereichen Algebraische Geometrie, Differentialgeometrie und Mathematische Physik. Im Einzelnen konzentriert sich seine Arbeit auf folgende Themen:
- Moduliräume von Higgs-Bündeln und lokale Systeme
- Geometrie der Moduliräume flacher Bündel
- Nicht-abelsche Hodge-Theorie (NAHT) über nichtkompakten Varietäten
- Anwendungen der NAHT auf die höhere Teichmüller-Theorie
- Quiver-Darstellungen und ihre Moduliräume
- Spiegelsymmetrie und geometrische Langlands-Theorie
Wissenschaftlicher Kontakt
Redaktioneller Kontakt
Jana Gregor
Interview
MPI MIS: How did you get into math and why did you choose this particular field of research?
Pengfei Huang: My path into mathematics was not completely direct. I studied engineering as an undergraduate, partly because engineering was always highlighted as the major of obtaining a good job with stable and high income. At that time, I had little sense of what a research career would involve. During my undergraduate years, however, I became increasingly interested in the mathematical structures behind the problems I encountered. I realized that I was attracted not only to applying methods to concrete problems, but also to understanding why those methods works, how different ideas fit together, and what remains true when a problem is placed in a more general setting. This curiosity eventually led me from engineering to doctoral studies in mathematics.
What fascinates me most about mathematics is that the same object can often be understood from several apparently different perspectives: algebraic, analytic, geometric, and topological; on the other hand, sometimes, objects from these different areas can be connected to each other. Moving between these viewpoints can reveal structures that are invisible from only one of them.
Nonabelian Hodge theory is a particularly beautiful example of this phenomenon. It connects objects such as Higgs bundles, flat connections, and local systems (equivalent to representations of the fundamental group). I chose this field because it brings together algebraic geometry, differential geometry, topology, representation theory, and mathematical physics, among others. On the other hand, organizing these objects into families leads to moduli spaces, they are geometric spaces that parameterize the objects up to an appropriate notion of equivalence. I find this combination of conceptual unity and difficult geometric problems especially compelling.
MPI MIS: How important was your time at the MiS for both your personal development and your scientific career?
Pengfei Huang: My time at MiS was extremely important to me, both scientifically and personally. Scientifically, it gave me the freedom to broaden my research beyond the questions I had already been pursuing for a long time and to place nonabelian Hodge theory in a wider geometric context.
Working with Prof. Dr. Anna Wienhard and being part of her research group “Geometry, Groups, and Dynamics” brought me into close contact with higher Teichmüller theory, representation varieties, and related areas. The institute’s seminars, visitors, and lively discussions made it possible to test ideas with people who approached similar questions from very different perspectives. A concrete outcome of these interactions was my joint work with Georgios Kydonakis, Eugen Rogozinnikov, and Anna Wienhard on symmetric spaces for groups over involutive algebras and their applications to Higgs bundles.
On a personal level, MiS helped me become a more independent and open-minded mathematician. I learned to explain my research to people outside my specialization, to initiate collaborations, and to think not only about individual projects but also about how to build a broader research program. I also formed friendships and professional relationships that I expect will continue long after my time in Leipzig.
MPI MIS: What advice would you give young researchers starting out at the institute?
Pengfei Huang: My first piece of advice would be to experience the institute as a community, not simply as a place to have an office. Attend some seminars outside your research area, speak with visitors and colleagues. Many valuable mathematical conversations begin with a simple question or an incomplete thought.
At the same time, it is important to keep more time for your own research, because difficult mathematical problems often require sustained thought. Try to keep one or two ambitious long-term questions in mind while also working on more concrete intermediate problems that allow steady progress.
The postdoctoral period is an important opportunity to develop a mathematical identity, and to build relationships with others based on curiosity and generosity. MiS provides considerable freedom, and the most important thing is to use that freedom deliberately.
Das ganze Interview als PDF (nur auf Englisch):
Research
MPI MiS: What are your current research interests, and how do you envision developing them at your new institution?
Pengfei Huang: In recent years, my research is centered on nonabelian Hodge theory, a modern mathematical field due to beautiful fundamental work of Donaldson, Corlette, Hitchin, and Simpson, among others. In its classical form, nonabelian Hodge theory provides different descriptions of the same underlying geometric information: one description comes from complex and algebraic geometry, another from differential equations, and another from topology and representation theory.
Much of my recent work concerns extending this picture to situations involving singularities and to objects with general reductive structure groups. I study parabolic and parahoric structures, meromorphic connections, filtered local systems, and together with the associated Stokes phenomena. A central goal is to construct the relevant moduli spaces carefully and to understand the relationships among their algebraic, differential-geometric, and topological descriptions. I am also interested in their connections with quiver representation theory, higher Teichmüller theory, mirror symmetry, and the geometric Langlands program.
At Nanjing University, I plan to develop these directions into a broader research program at the intersection of geometry, representation theory, and mathematical physics. In addition to pursuing foundational questions in tame and wild nonabelian Hodge theory, I would like to create an environment in which students and young researchers can enter the subject and move comfortably among algebraic, analytic, and topological methods. Through courses, seminars, workshops, and international collaborations, I hope to build a research community around these interactions and to establish lasting connections between researchers in China and colleagues abroad.
MPI MiS: What is your favorite Millennium problem and why?
Pengfei Huang: My favorite Millennium Prize Problem is the Hodge conjecture. More precisely, for a smooth complex projective variety, it asks whether every rational cohomology class of Hodge type (p,p) is a rational linear combination of cohomology classes of codimension-p algebraic cycles. Roughly speaking, it asks whether certain topological classes selected by the complex geometry of the variety have an algebraic origin. I find it fascinating because it lies at the meeting point of algebraic geometry, complex geometry, and topology.
Although the Hodge conjecture is not directly part of nonabelian Hodge theory, it strongly resonates with its philosophy. In both cases, one tries to understand a geometric object by translating among different mathematical languages. A structure that is difficult to recognize from an algebraic perspective may become more transparent analytically or topologically, and conversely.