Combinatorial Aspects of Scattering Amplitudes

Matteo Parisi is a joint postdoctoral fellow in physics at IAS and in math at Harvard CMSA. He is also a Lecturer in Physics at Princeton University. He obtained his DPhil (PhD) in Mathematics at the University of Oxford. He has been recipient of several honors and awards, among which the Daniel Sachs and Della Riccia scholarships during his DPhil at Oxford, the DAAD scholarship during his Master in Germany, and two Certificates of Merit by the Rector of his alma mater University of Bologna.
His research lies at the intersection of high energy physics and algebraic combinatorics. He has been working on a new program in which quantum mechanical observables in particle physics and cosmology arise from underlying novel mathematical objects. Physical properties purely emerge from their combinatorics and geometry. In particular, his research focuses on scattering amplitudes in quantum field theories, in relationto the (positive) Grassmannian, Amplituhedra, tropical geometry and cluster algebras. Being one of the leading contributors in this program, he produced over ten publications in major peerreviewed journals. These ranged from theoretical physics (Journal of High Energy Physics) to mathematical physics (Communications of Mathematical Physics) and pure mathematics (Communications of American Mathematical Society), with more than 250 total citations.
Teaching, outreach and advocating for inclusivity and diversity, within and beyond academia, are a key part of his identity. His teaching experiences ranged from holding Lectureships at two Oxford colleges (St. Peter's and Keble), to volunteering to organize and teach teenagers at the first ever Math Camp in Cameroon. He has worked with equality and diversity units of the university; he is a trained LGBT+ Role Model and organized conferences and interacted with charities on LGBTQ+ issues. In his free time, he loves playing the piano, playing volleyball, experiencing the beauty of art (concerts,

1.  Introduction.- 2. The Amplituhedron.- 3. The Hypersimplex.- 4. T-duality: the Hypersimplex VS the Amplituhedron.- 5. Positroid Triangulations.- 6. The Momentum Amplituhedron.- 7. Cluster Algebras and Amplituhedra.- 8. Conclusions