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Seminarium KMMF "Teoria Dwoistości"

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2024-10-10 (Czwartek)
Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15  Calendar icon
Serena Cenatiempo (Gran Sasso Science Institute)

Ground State Energy of Dilute Bose Gases: The Case of Hard Spheres

In recent years, there has been substantial progress in the mathematical understanding of the thermodynamic properties of dilute Bose gases. In particular, the validity of a celebrated formula for the second-order asymptotic of the ground state energy of dilute bosons — first predicted by Lee, Huang, and Yang in 1957 — has been fully established in the case of integrable (non-negative) interactions. In the first part of my talk, I will present the main ideas behind the recent results, the relevant length scales of the problem, and the open questions that lie ahead. I will then discuss how a simple trial state, introduced by Bijl-Dingle-Jastrow in the 1950s, can be used to derive an upper bound for the ground state energy of a dilute Bose gas of hard sphere, which captures the Lee-Huang-Yang expansion up to the order of the sub-leading correction. An upper bound that establishes the Lee-Huang-Yang formula for hard spheres is, in fact, still missing.
2024-10-03 (Czwartek)
Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15  Calendar icon
Pavlos Kassotakis (KMMF)

On quadrirational Yang-Baxter and pentagon maps

The Yang-Baxter and the pentagon equation serve as importantequations in mathematical physics. They appear in two equallysignificant versions, the operator and the set-theoretical one. In thistalk, we focus on the set-theoretic versions of both equations, wheretheir solutions are known as Yang-Baxter maps and pentagon maps,respectively. First, we recall rational Yang-Baxter maps of a specifictype (quadrirational maps) and show their connection to discreteintegrable systems. Then, we propose a classification scheme forquadrirational solutions of the pentagon equation. That is, we give afull list of representatives of quadrirational maps that satisfy thepentagon equation, modulo an equivalence relation that is defined onbirational functions on $\mathbb{CP}^1 \times \mathbb{CP}^1$. Finally,we demonstrate how Yang-Baxter maps can be derived from quadrirationalpentagon maps.