New Approaches in Computational Commutative Algebra

Congratulations to Barbara Betti on successfully completing her PhD! Her research brings a fresh perspective to solving polynomial systems, blending classical Gröbner bases with the concept of Khovanskii bases to address problems in algebraic geometry and beyond.

Solving systems of polynomial equations is a cornerstone of both pure and applied mathematics — with applications ranging from geometry and physics to engineering and the life sciences. In her doctoral thesis “Khovanskii and Gröbner degenerations in Computational Commutative Algebra” Barbara explores algebraic and numerical methods that offer new approaches to this classical problem. Her PhD dissertation was supervised at our institute by Simon Telen.

Barbara’s work lies at the intersection of commutative algebra and numerical algebraic geometry. Her research aims to build and refine algebraic tools that help tackle concrete questions in algebraic geometry, often motivated by challenges arising in broader scientific fields.

At the heart of her dissertation is a fresh perspective on zero-dimensional polynomial systems. “Solving such systems is a central task in mathematics,” she explains. “Gröbner bases are a powerful classical tool in computational commutative algebra, but their counterpart for finitely generated algebras — the Khovanskii bases — has not yet been used to solve polynomial systems. In this work, we develop new theory and algorithms based on Khovanskii and Gröbner bases.” Her results lay the groundwork for further exploration of these techniques and open promising avenues for future applications.

Since October 2025, Barbara has been a PostDoc at Otto von Guericke University Magdeburg, working in the research group Algebra, led by Thomas Kahle. Alongside her research, she has also begun teaching — a role she embraces with great enthusiasm. Her long-term goal is to continue her academic career while maintaining a healthy balance between professional and personal life.

Barbara Betti completed her Bachelor’s and Master’s degrees at the University of Genova — her hometown in Italy — in 2020 and 2022. In 2022 she moved to Leipzig, drawn by the vibrant research environment at MPI, where she enjoyed meeting colleagues from around the world and traveling to conferences across Europe and beyond.

We wish Barbara all the best for the future and much success in her academic and personal endeavors.