On the Frontiers of Geometric Topology

The Institute of Science and Technology Austria (ISTA) welcomes Xujia Chen to its faculty. Establishing her group in January 2026, the new assistant professor will explore intriguing landscapes in geometric topology. Chen’s work on manifolds and general topological spaces has the potential to deepen our understanding of both abstract and physical spaces. With experience from renowned institutions on three continents, she brings a wealth of knowledge and ambition to ISTA.

Manifolds are a key concept in geometry and topology, essential for understanding the models that describe the fabric of space-time. This concept goes beyond theoretical mathematics and finds practical applications, such as interpreting data clouds through the geometric shapes they create.

Xujia Chen (she/they) has focused her research on exploring the structures of manifolds, providing insights that connect theoretical mathematics with physical sciences. Her approach embraces both the theoretical and applied dimensions of mathematics. “The data cloud in an experiment can form the shape of a manifold. By studying the properties of this manifold, we will be able to better understand the nature of the data,” she explains.

Through Harvard and Max Planck to ISTA

Before embarking on her journey with the Institute of Science and Technology Austria (ISTA), Chen honed her skills at several renowned institutions. After completing her undergraduate degree at the University of Science and Technology of China, she earned her PhD in mathematics from Stony Brook University, USA, in 2021. During her doctoral studies, she was awarded the John Marburger III Fellowship and the President’s Award to Distinguished Doctoral Students. Her postdoctoral work took her to Harvard University as a Junior Fellow and later to the Max Planck Institute for Mathematics in Bonn, Germany.

At ISTA, Chen aims to pursue ambitious research goals. “There are some natural questions to be asked as follow-ups of some of my current work with collaborators, and I would like to investigate them,” she says. Her most recent research topic involves the construction of manifold operads—mathematical structures that combine manifold properties with algebraic systems. Looking ahead, she aims to create more manifold operads featuring additional structures.

Fostering scientific collaboration

Moreover, Chen is committed to expanding academic exploration in and around her fields of research. “I am very interested in broadening the scope of my research, especially to some topics that I am not yet quite familiar with but are related to my current research,” she notes, mentioning the homotopy type of configuration spaces as an area of interest. She envisions hiring postdoctoral scholars and collaborating with scientists in related fields to foster a dynamic exchange of ideas in mathematics.

Outside of their professional life, the 31-year-old Chinese mathematician enjoys reading, watching movies, and hiking. As they adapt to life in Austria, they hope to adopt a dog, which could accompany them on their outdoor adventures.

With the establishment of their research group, titled “Geometric Topology of Manifolds,” at ISTA in January, Chen will become the first female mathematician to join the Institute’s faculty. Their presence marks an important development for ISTA, as they contribute their expertise and perspectives to the Institute’s highly interdisciplinary academic community.