BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joscha Henheik (IST Austria) DTSTART:20250312T150000Z DTEND:20250312T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/1 DESCRIPTION:Title: Prethermalization for deformed Wigner matrices\nby Joscha Henheik (IST Austria) as part of SISSA Mathematical Physics seminar\n\n\nAbstract \nWe prove that a class of weakly perturbed Hamiltonians of the form $H_\\ lambda = H_0 + \\lambda W$\, with $W$ being a Wigner matrix\, exhibits pre thermalization. That is\, the time evolution generated by $H_\\lambda$ rel axes to its ultimate thermal state via an intermediate prethermal state wi th a lifetime of order $\\lambda^{-2}$. Moreover\, we obtain a general rel axation formula\, expressing the perturbed dynamics via the unperturbed dy namics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_\\lambda$. \nBased on a joint work with L. Erdös\, J. Reker\, and V. Riabov.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Giancarlo Benettin (University of Padova) DTSTART:20250205T150000Z DTEND:20250205T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/2 DESCRIPTION:Title: Thermalization vs. integrability in the Fermi-Pasta-Ulam(-Tsingou) pr oblem\nby Giancarlo Benettin (University of Padova) as part of SISSA M athematical Physics seminar\n\n\nAbstract\nThe talk is devoted to the cele brated FPU problem\, namely the interplay between dynamics and statistics in a chain of weakly interacting oscillators. The perspective we shall fol low\, after a wide introduction to the problem\, is that FPU should be reg arded as a perturbation of the (completely integrable) Toda model. Normal statistic behavior\, including thermalization\, requires rather long times \, scaling as inverse powers of the specific energy E/N. On substantially shorter times\, FPU is practically indistinguishable from Toda: neverthele ss\, its statistical behavior is not clear\, since Toda itself\, although integrable\, in the thermodynamic limit is not well understood. A crucial question for statistical mechanics turns out to be the relation between To da actions and standard normal modes\, which looks quite puzzling for larg e N.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Renzi (SISSA) DTSTART:20250305T150000Z DTEND:20250305T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/3 DESCRIPTION:Title: Universality in interacting dimers at the rough-frozen transition \nby Bruno Renzi (SISSA) as part of SISSA Mathematical Physics seminar\n\n \nAbstract\nA central issue in equilibrium statistical mechanics is the un iversality of critical phenomena. In this talk\, we explore the two-dimens ional dimer model\, a simple yet rich model for discrete random surfaces. Originally solved in the 1960s by Kasteleyn\, Temperley\, and Fisher for p lanar graphs\, its phase diagram was later fully characterized for doubly periodic graphs by Kenyon\, Okounkov\, and Sheffield (2006). They revealed a deep geometric structure and\, in the so-called rough phase\, a univers al Gaussian limit for surface fluctuations. Here\, we investigate universa lity specifically at the liquid-to-frozen transition\, where integrability -breaking perturbations are introduced. We show that for small perturbatio n strength λ\, the frozen boundary is shifted by O(λ) and at distance ϵ inside the liquid phase\, the Ronkin function R satisfies a so called Pok rovsky-Talapov scaling law universally in the interaction. This heuristica lly suggests a connection with the KPZ universality class\, offering insig hts into the fluctuations of the level lines of the associated height func tion. Based on a joint work with A. Giuliani\, V. Mastropietro\, F. L. Ton inelli.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Moll (Reed College) DTSTART:20250319T150000Z DTEND:20250319T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/4 DESCRIPTION:Title: On Dubrovin’s Characterization of Schur Polynomials\nby Alexand er Moll (Reed College) as part of SISSA Mathematical Physics seminar\n\n\n Abstract\nSchur polynomials have been studied for over two centuries since the works of Cauchy (1815)\, Jacobi (1841)\, and Schur (1901). In his wo rk on symplectic field theory\, Dubrovin (2016) gave a remarkable new char acterization of these multivariate polynomials from first principles of ge ometric quantization of classical Hamiltonian PDEs: they are the simultane ous eigenfunctions of Eliashberg’s explicit operator quantization of the classical hierarchy of Hopf Hamiltonians on the circle with respect to th e Gardner-Faddeev-Zakharov Poisson bracket. In this talk\, I will present work in progress with Robert Chang (Rhodes College) in which we combine D ubrovin’s spectral theorem with general analytic results in the semiclas sical approximation of quantum Gaussian wavepacket dynamics to derive old and new limit theorems for Okounkov’s Schur measures on partitions.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Guido Carlet (Institut de Mathématiques de Bourgogne) DTSTART:20250326T150000Z DTEND:20250326T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/5 DESCRIPTION:Title: Structure\, cohomology and deformations of local homogeneous Poisson brackets of arbitrary degree\nby Guido Carlet (Institut de Mathématiq ues de Bourgogne) as part of SISSA Mathematical Physics seminar\n\n\nAbstr act\nDubrovin and Novikov initiated the study of local homogeneous differe ntial-geometric Poisson brackets of arbitrary degree k in their seminal 19 84 paper. Despite many efforts\, and several results in low degree\, very little is known about their structure for arbitrary k. After an introducti on to the topic\, we first report on our recent results on the structure o f DN brackets of degree k. By applying homological algebra methods to the computation of their Poisson cohomology (or rather of an associated differ ential complex) we show that certain linear combinations of the coefficien ts of a degree k DN bracket define k flat connections. Moreover the Poisso n cohomology of such brackets is related with the Chevalley-Eilenberg coho mology of an associate finite-dimensional Lie algebra. In collaboration wi th M. Casati.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Gallone (SISSA) DTSTART:20250226T150000Z DTEND:20250226T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/6 DESCRIPTION:Title: Prethermalization and conservation laws in quasi-periodically driven lattice quantum systems\nby Matteo Gallone (SISSA) as part of SISSA Ma thematical Physics seminar\n\n\nAbstract\nUnderstanding the route to therm alization of a physical system is a fundamental problem in statistical mec hanics. When a system is initialized far from thermodynamical equilibrium\ , many interesting phenomena may arise. Among them\, a lot of interest is attained by systems subjected to periodic driving (Floquet systems)\, whic h under certain circumstances can undergo a two-stage long dynamics referr ed to as “prethermalization”\, showing nontrivial physical features. I will present some prethermalization results for a class of lattice system s with quasi-periodic external driving in time. When the quasi-periodic dr iving frequency is large enough or the strength of the driving is small en ough\, we show that the system exhibits a prethermal state for exponential ly long times in the perturbative parameter. Focusing on the case when the unperturbed Hamiltonian admits constants of motion\, under suitable non-r esonance condition we prove the quasi-conservation of a dressed version of them.\n\nJoint work with B. Langella (SISSA).\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Amol Aggarwal (Columbia University) DTSTART:20250401T140000Z DTEND:20250401T160000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/7 DESCRIPTION:Title: The Toda Lattice as a Soliton Gas\nby Amol Aggarwal (Columbia Uni versity) as part of SISSA Mathematical Physics seminar\n\n\nAbstract\nA ba sic tenet of integrable systems is that\, under sufficiently irregular ini tial data\, they can be thought of as dense collections of many solitons\, or “soliton gases.” In this talk we explain how the Toda lattice\, un der certain random initial data\, can be interpreted through solitons\, an d provide a framework for studying how these solitons asymptotically evolv e in time. The arguments use ideas from random matrix theory\, particularl y the analysis of Lyapunov exponents governing the decay rates of eigenvec tors of random tridiagonal matrices.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Piorkowski (KTH Stockholm) DTSTART:20251117T150000Z DTEND:20251117T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/8 DESCRIPTION:Title: Steepest descent analysis on Riemann surfaces and generalized discrim inants\nby Mateusz Piorkowski (KTH Stockholm) as part of SISSA Mathema tical Physics seminar\n\n\nAbstract\nDouble contour integral formulas appe ar surprisingly often in expressions for correlations in various models--- allowing for a swift asymptotic analysis via steepest descent analysis. R ecent results on random tiling models demonstrate that such double contour formulas can also include integration on compact Riemann surfaces. Motiva tion by these developments\, I will in this talk generalize the notion of a discriminant of a polynomial (corresponding to the Riemann sphere)\, to a discriminant of meromorphic sections on a general compact Riemann surfac es. As a corollary we obtain degree formulas for arctic curves that depend only on the topology of the frozen\, rough and smooth regions of the Azte c diamond\, extending thereby the famous arctic circle theorem of Jockusch \, Propp and Shor. This talk is based on the preprint arXiv:2410.17138\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Marcantoni (GSSI L'Aquila) DTSTART:20251201T150000Z DTEND:20251201T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/9 DESCRIPTION:Title: Dynamics of open quantum systems under strong coupling\nby Stefan o Marcantoni (GSSI L'Aquila) as part of SISSA Mathematical Physics seminar \n\n\nAbstract\nWe consider the prototypical example of an open quantum sy stem\, that is a finite-level quantum system linearly coupled to a bosonic reservoir\, and we study the dynamics of the finite system when the coupl ing constant tends to infinity. In particular\, under mild assumptions on the interaction\, we prove that the dynamics corresponds to a nonselective projective measurement followed by a unitary evolution generated by an ef fective (Zeno) Hamiltonian. The proof can be generalized to the case of a small system interacting with two reservoirs\, when one of the couplings i s finite and the other one tends to infinity. In this second scenario the reduced dynamics is richer and possibly non-Markovian. \nJoint work with M arco Merkli\, Quantum 9\, 1656 (2025).\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Mucciconi (National University of Singapore) DTSTART:20251218T100000Z DTEND:20251218T110000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/10 DESCRIPTION:Title: The Skew Column RSK dynamics and the Box and Ball System\nby Mat teo Mucciconi (National University of Singapore) as part of SISSA Mathemat ical Physics seminar\n\n\nAbstract\nWe introduce a two-dimensional discret e integrable system\, the \\emph{Skew Column RSK Dynamics}\, which is a tw o dimensional extension of the classical Box and Ball System (BBS) of Taka hashi and Satsuma. The evolution acts deterministically on particle config urations over a periodic planar lattice\, with local moves governed by the Fomin growth rules associated with the Robinson–Schensted–Knuth algor ithm under column insertion. We construct a linearization algorithm that g eneralizes the Kerov–Kirillov–Reshetikhin (KKR) bijection\, mapping th e nonlinear particle dynamics to a linear evolution. Such linearization is stated as a bijection between pairs of semi-standard Young tableaux of sk ew-shape $(P\,Q)$ and quadruples $(H_1\,H_2\;\\kappa\,\\nu)$\, where $H_1\ ,H_2$ are horizontally weak tableaux encoding conservation laws of the dyn amics\, $\\kappa$ is a list of non-negative integers and $\\nu$ is a parti tion. As a by-product\, we obtain bijective proofs of summation identities for modified Hall–Littlewood polynomials.\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Perletti (SISSA) DTSTART:20260126T150000Z DTEND:20260126T170000Z DTSTAMP:20260422T225702Z UID:SISSAmath-ph/11 DESCRIPTION:by Sara Perletti (SISSA) as part of SISSA Mathematical Physics seminar\n\nLecture held in Room 134.\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SISSAmath-ph/11/ END:VEVENT END:VCALENDAR