Summer School in Total Positivity and Quantum Field Theory

Dates: June 2–4, 2025

Location: CMSA, 20 Garden Street, Cambridge MA

In the past decade, there has been a great deal of interest and progress in the study of algebro-combinatorial and geometric structures appearing across diverse areas of physics, from particle physics to cosmology. As these research programs expand, there is an ever-growing need for mathematicians and physicists to collaborate effectively and build a shared language. Join us at Harvard University’s Center of Mathematical Sciences and Applications for a week-long summer school dedicated to addressing these interdisciplinary connections. The school welcomes graduate students, postdocs, and early-career researchers drawn to the intersection of mathematics and physics. Whether you are an algebraic combinatorialist looking for a better grasp on the physics, a high energy theorist trying to figure out the math, or a newcomer to both fields, this summer school offers an ideal opportunity for you to learn.

Courses taught by both mathematicians and physicists will connect ideas from total positivity, matroid theory, discrete geometry, and real algebraic geometry with fundamental questions in quantum field theory. Topics will include amplituhedra, cluster algebras, and positive geometry as they relate to scattering amplitudes and cosmological correlators in high-energy physics. Our courses are designed to be accessible to a varied audience; speakers will be mindful of the diverse backgrounds of the participants from both fields.

Amid this exciting period of collaboration between mathematicians and physicists, we look forward to exploring these rich, cutting-edge topics with you.

Organizers:  Jonathan Boretsky (McGill University) |  Matteo Parisi (Harvard CMSA and IAS Princeton) | Lauren Williams (Harvard University)