Research Group

Interdisciplinary Frontiers of Algebraic Geometry

Our goal is to explore and broaden the scope of algebraic geometry and its connections with different branches of mathematics and sciences. We are driven by the belief that this field transcends traditional boundaries, promoting collaboration and practical applications.


The Spohn variety of the game Bach or Stravinsky is a reducible curve of degree four in three dimensional complex projective space.

This journey in algebraic geometry takes inspiration from historic breakthroughs, including John Nash's contributions to game theory, which awarded him the Nobel Prize. Nash's work, based on the application of the Kakutani fixed-point theorem, not only advanced game theory but also expanded the horizons of economics, computer science, evolutionary biology, quantum mechanics, and social sciences. These breakthroughs serve as a catalyst for our multidisciplinary approach, aiming to enrich the landscape of algebraic geometry and build bridges not only to other sciences but also within the vast realm of mathematics.

The Spohn variety of a generic 2x3 game is a del Pezzo surface of degree two. The figure shows its projection under the payoff function in the probability simplex.

If you're interested in delving further into our research, we invite you to explore the talk titled What will happen in Algebraic Economics? presented at IMSI (University of Chicago). This presentation stands as an exemplary illustration of the type of work we are engaged in within our group. This talk, designed for a general audience during the Algebraic Statistics semester, offers insights into the potential directions of our interdisciplinary approach to game theory questions.