## Algebraic Combinatorics and Mathematical Physics

An Online Workshop (January 13-14, 2022)

The links between combinatorics and statistical physics are of ancient origin (see, e.g., Rota's essay in "The mathematical sciences: A collection of essays", M.I.T. Press, Cambridge, Mass.-London, 1969, x+271 pp.). In the last few years, more and more connections have been found between the branch of combinatorics known as "algebraic combinatorics" (particularly enumeration, symmetric functions, cluster algebras, geometric combinatorics, and combinatorial representation theory) and various other areas in mathematical physics such as, for example, quantum field theory, tensor models, integrable Hamiltonian systems, conformal field theory, the KP-equation, the thermodynamic Bethe ansatz, super Yang-Mills scattering amplitudes, and the Toda lattice. These connections between combinatorics and mathematical physics are now so recognized that a name has been given to this area of interaction, and books have been written about it (see, e.g., A. Tanasa, "Combinatorial Physics", Oxford University Press, 2021, or "Physical combinatorics", Birkhäuser, Boston, MA, 2000, x+317 pp.). The aim of this online workshop is to explore some of these recent connections with the help of four of the leading experts in the area, and to encourage combinatorialists to look at mathematical physics as a rich source of interesting and challenging combinatorial problems, and mathematical physicists to look to combinatorics as a useful tool in their research.

#### Invited Speakers

- Petter Brändén (KTH, Stockholm)
- Thomas Lam (University of Michigan, Ann Arbor)
- Andrea Sportiello (CNRS and LIPN, Université Paris Nord)
- Lauren Williams (Harvard University, Cambridge)

The Workshop will take place online, from 4:00 pm until 6:30 pm (Rome time), in the afternoons of January 13-14, 2022, using the Microsoft Teams platform. Registration is free, but mandatory. To register please e-mail: brenti@mat.uniroma2.it, putting "ACAMP" in the Subject, and indicating your name, affiliation, and e-mail address.

#### Schedule

(All times are Rome time)Thursday, January 13

4:00 pm | Lauren Williams, Combinatorics of the amplituhedron
(Slides) |

5:30 pm | Thomas Lam, Positive geometries and scattering amplitudes
(Slides) |

4:00 pm | Petter Brändén, The Potts model and Lorentzian polynomials on cones
(Slides) |

5:30 pm | Andrea Sportiello, Many new conjectures on Fully-Packed Loop configurations
(Slides) |

Here are the links to attend the talks: Thursday, January 13 and Friday, January 14.

The Workshop is hosted and funded by the Department of Mathematics of the Università di Roma "Tor Vergata" as part of its activities for the Excellence Project 2018-2022, awarded to the Department by M.I.U.R., under contract number CUP E83C18000100006.