Ran Tao sits outside of Wean Hall and smiles at the camera.

Ran Tao Awarded FRQNT Fellowship

By Kirsten Heuring Email Kirsten Heuring

Heidi Opdyke

Carnegie Mellon University graduate student Ran Tao is set on mathematical logic research.

Tao's work is primarily in a subfield of logic known as descriptive set theory. In mathematics, a set is a collection of objects, such as numbers, sequences, functions and lines. Descriptive set theory focuses on sets that mathematicians can describe in an infinitary-algorithmic way, which is a form of logic that allows infinitely long statements and proofs. From there, set theory connects sets' mathematical properties to how hard they are to define.

"In mathematics and, in particular, in descriptive set theory, we're trying to classify certain objects and prove how they're the same or different," Tao said. "To do that, you need to find a property of one object that another doesn't have."

Though Tao's work is mainly focused on descriptive set theory, it has connections to topology, combinatorics and discrete math. She focuses on an area known as orbit equivalence, which looks at potential trajectories an object, such as a point on a circle, can follow over time.

"We're asking: how complex are these orbits?" Tao said.

Because her research spans multiple areas of mathematical sciences, Tao works with Clinton Conley and Florian Frick, associate professors of mathematical sciences.

"Ran does a great job at breaking large, complicated arguments into more digestible pieces, which is a really important skill to develop in mathematics," Conley said. "In addition to being a valuable way of organizing your research, this way of thinking is essential in the effective communication and teaching of mathematics."

Outside of her academic work, Tao is drawn to building community, which was an important factor when she chose her field of study.

"I like the topic, but I fell in love with the community," Tao said. "Descriptive set theory has a really nice set of people who drive the research, and it's a super welcoming field."

Tao wants to ensure that mathematical sciences is welcoming for all. She organized a panel discussion in the Department of Mathematical Sciences featuring faculty members who discussed the realities of working in mathematics.

She was awarded a fellowship from Fonds de Recherche du Québec — Nature et Technologies (FRQNT) to support her work.

"Ran's research sits at the interface of several different mathematical disciplines," Conley said. "There is a lot of potential for these ingredients to be combined in exciting new ways, and I'm really looking forward to seeing how her research develops."