What happens when a surface changes shape, and can you “hear” it?

In the second season of “Keeping up with the Boost Fellows”, GSO’s Birte Seffert travels across Germany to visit the 15 fellows who started their Klaus Tschira Boost Fund projects in 2025. The series offers a closer look at their research, their working environments, and the realities of building a research career today.

This article combines both: a glimpse into Cipriana Anghel-Stan’s work in global analysis and what it reveals about how to succeed as a math postdoc. This time, the visit leads to Göttingen, a place with a long history in mathematics, associated with names like Carl Friedrich Gauss, Bernhard Riemann and Emmy Noether. Here we meet Cipriana Anghel-Stan, postdoc at the University of Göttingen, working within the Fourier Analysis and Spectral Theory Research Training Group.

From geometry to “music”: what Cipriana’s research is about

Cipriana works on hyperbolic geometry. In her Boost Fund project, she studies what happens to a surface as one of its loops, one that encircles a hole in the surface, is gradually tightened and its length shrinks toward zero: the surface „pinches“ and develops a kind of bottleneck. She traces how this pinching propagates into a covering of the surface — a kind of unwrapped, infinite version of the same space, where each pinch on the original echoes across infinitely many layers.

Her goal is to understand the „music“ of this process — the spectrum of frequencies that the geometry produces, and how each note shifts as the surface pinches. The idea recalls a classic question in mathematics: can one „hear“ the shape of a space? The instrument Cipriana listens to is an operator that also appears at the heart of quantum physics, and the music plays not only on the surface itself, but also on the infinite covering, where ordinary counting breaks down and one needs new ways of “listening”.

Asked what results would make her happy, her answer is simple: to establish clarity, continuity, and ultimately, to hear that music unfold in harmony.

“Mathematics is the language of nature”

What draws her to work on questions like these?  For Cipriana, the answer is fundamental: “Mathematics is the language of nature, and if we want to understand the world around us, we need to study mathematics.”

Cipriana describes her work as following “natural questions” that arise from within the field, but connect to a broader attempt to understand the world. Echoing an idea of her PhD advisor, she is sure that …

“…if mathematics were to disappear and all the other sciences too, if we had to start again from scratch, we would refine mathematics in the same way, and we would probably arrive at the same kind of questions that we are tackling right now. So, somehow, there is a unique language, natural language, in which one could describe the world, and that is mathematics.”

Her motivation is not only technical, it is about making sense of the world through a precise language.

Curiosity, tools, and how ideas develop

While Cipriana names curiosity as the most important tool in mathematics, another one becomes just as central in her work: the chalkboard.

Covered in equations and pictures, photographed, erased, and rewritten, this is where ideas come to life. It is where thoughts are collected, tested, adjusted, and made visible to others.

Progress here does not come from a single breakthrough, but from repeated cycles of writing, revising, and discussing. This is also how ideas become accessible to others, and how collaboration starts to take shape.

How to succeed as a math postdoc

Beyond curiosity and a deep understanding of one’s field, Cipriana points to several elements that shape progress in mathematics:

• Collaborations and conversations with others
• Staying close to the questions that drive the field, and to the people thinking about them
• Visibility through sharing work at conferences and presentations
• The energy to pursue and complete projects, often several at once

These are familiar ideas. But putting them into practice requires constant choices: where to direct one’s attention, who to think alongside, which problems to pursue for a while.

At the same time, Cipriana highlights something that is often harder to maintain in systems focused on output:

“You need the courage to address risky projects. If you aim high, you have a real chance of reaching something deep.”

Progress in mathematics is not only about productivity, it is also about the willingness to take intellectual risks.

How flexible funding supports Cipriana’s research and new roles

Taking risks is not only a personal decision. It depends on the conditions researchers work in.

“The Boost Funds gave me the courage to work on two risky projects. Maybe without it, I wouldn’t have tried. I would have settled for less.”

This shift is visible in how Cipriana approaches her work. The funding allows her to explore new directions and engage more actively in collaborations. She invites researchers to Göttingen for visits and exchanges, creating space for ongoing discussions and joint work.

She also steps into a new role by organizing an international conference in Göttingen, “Pseudodifferential Techniques in Singular Analysis” (August 31 – September 4, 2026). While collaborations grow through continuous exchange, the conference creates a more focused setting, bringing together different perspectives around a shared topic.

Through organizing a conference, Cipriana discovered a new set of skills and perspectives:

• Defining a clear focus matters. Choosing the right theme and direction shapes everything that follows.
• Building the right group of people is key. Inviting both established and early-career researchers creates the liveliest
• Organization is part of academic work. Planning, coordinating, and making decisions are essential and learnable.

What we can learn from this

A research career in mathematics does not unfold through results alone. It is shaped by which questions are pursued, how collaborations are built, and how one’s work finds its way to others.

Cipriana’s example makes this visible. Risk taking, exchange with others, and taking on responsibilities beyond one’s own project reinforce each other and influence both research direction and the roles a postdoc grows into.

These patterns are not always explicit, but they are reflected in the everyday decisions that shape research work and, over time, careers.

About the KT Boost Fund

The Boost Fund supports postdoctoral researchers and early group leaders in Germany with flexible funding for independent, often higher-risk and interdisciplinary projects, combined with career development opportunities and access to a strong peer network.

The program addresses a critical phase after the PhD, where researchers are expected to develop independence, but often lack the resources and flexibility to do so. It creates space to explore new directions, build collaborations, and take responsibility early on.