Dear colleagues, The year is coming to an end and we are excited to announce that our next and final speaker of the year will be Giulia Sebastiani (Universität Bonn) who will be speaking about From Parisi to Boltzmann: via GREM and TAP. on December 17, at 13:30 GMT / 14:30 CET / 15:30 EET, on Teams broadcast with the following link: Link to join teams<https://teams.microsoft.com/l/meetup-join/19%3ameeting_N2Q2NGY2NDEtYWVmNS00NzE3LWI0ZWMtMWFiZmE3NGM2MTc3%40thread.v2/0?context=%7b%22Tid%22%3a%22377e3d22-4ea1-422d-b0ad-8fcc89406b9e%22%2c%22Oid%22%3a%2243af9e94-a882-4d59-8a92-d00c8899065e%22%7d> The talk is scheduled for one hour, allowing time for questions. Additionally, we'll be remaining on the call for a chat afterwards if you'd like to join us. We are looking forward to seeing you. Speaker: Giulia Sebastiani Title: From Parisi to Boltzmann: via GREM and TAP Abstract: Introduced by Derrida in the 80s, the Generalized Random Energy Models (GREM) serve as simplified, abstract models that are completely solvable and have significantly contributed to our comprehension of specific facets within the Parisi theory for mean-field spin glasses. In this talk, after an overview of Parisi’s ultrametric principle for the free energy of the Sherrington-Kirkpatrick (SK) model, we will turn to the alternative approach due to Thouless, Anderson, and Palmer (TAP). The TAP approach provides a representation of the SK free energy as the maximum of a random functional over local magnetizations. A simple reformulation reveals that, when evaluated at its critical points, the TAP free energy becomes a nonlinear functional of empirical measures constructed from local fields. Motivated by this structure, we construct abstract GREM-like models whose Hamiltonians are nonlinear functionals of empirical measures associated with GREM-like variables. For the thermodynamic free energy of these abstract models, dual Parisi-like formulas hold and turn out to be finite-dimensional “collapsed” versions of the underlying infinite-dimensional Gibbs-Boltzmann principles. Crucially, the nonlinearity inherited from the TAP representation generates a correction term (absent in canonical GREM-like models) that substantially reduces the gap between the free energies of such abstract hierarchical models and Parisi’s solution for the SK. Based on joint work with Nicola Kistler and Marius Alexander Schmidt. You can find more information about the talk on our website Postgraduate Online Probability Seminars (pg-prob-sem.github.io)<https://pg-prob-sem.github.io/>. Warm regards, The POPS Team This talk will be broadcast on December 17, at 13:30 GMT / 14:30 CET / 15:30 EET on MS Teams only. Meeting ID: 393 527 089 878 Passcode: dsm7py