BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michał Wrochna ((Université de Cergy-Pontoise) DTSTART;VALUE=DATE-TIME:20210409T121500Z DTEND;VALUE=DATE-TIME:20210409T131500Z DTSTAMP;VALUE=DATE-TIME:20240329T154624Z UID:EXACT/1 DESCRIPTION:Title: Sp ectral actions on asymptotically Minkowski spacetimes\nby Michał Wroc hna ((Université de Cergy-Pontoise) as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n\nAbstract\nThe spectral theory of the Laplace– Beltrami operator on Riemannian manifolds is known to be intimately relate d to geometric invariants such as the Einstein-Hilbert action. These relat ionships have inspired many developments in physics including the Chamsedd ine–Connes action principle in the non-commutative geometry programme. H owever\, a priori they do only apply to the case of Euclidean signature. T he physical setting of Lorentzian manifolds has in fact remained largely p roblematic: elliptic theory no longer applies and something different is n eeded.\n\nIn this talk I will report on joint work on this problem with Ng uyen Viet Dang. We consider perturbations of Minkowski space and more gene ral spacetimes on which the d’Alembertian P is essentially self-adjoint (thanks to recent results by Dereziński–Siemssen\, Vasy and Nakamura– Taira). It is then possible to define functions of P\, and we demonstrate that their Schwartz kernels have geometric content largely analogous to th e Riemannian setting. In particular\, we define a Lorentzian spectral zeta function and relate one of its poles to the Einstein–Hilbert action\, p aralleling thus a result in Euclidian signature attributed to Connes\, Kas tler and Kalau–Walze.\n\nThe primary consequence is that gravity can be obtained from a spectral action directly in Lorentzian signature. The proo fs involve mathematical ingredients from Quantum Field Theory on curved sp acetime\, in particular the Feynman propagator.\n\nPlease contact the orga nizers for the link to the meeting.\n LOCATION:https://researchseminars.org/talk/EXACT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Vitaly Moroz (Swansea University) DTSTART;VALUE=DATE-TIME:20210416T121500Z DTEND;VALUE=DATE-TIME:20210416T131500Z DTSTAMP;VALUE=DATE-TIME:20240329T154624Z UID:EXACT/2 DESCRIPTION:Title: Th omas-Fermi type models for graphene.\nby Vitaly Moroz (Swansea Univers ity) as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n\nAbstr act\nWe discuss density functional theories of Thomas-Fermi and Thomas-Fer mi-von Weizsacker type which describe the response of a single layer of gr aphene to an external electric charge. Mathematically\, this amounts to th e analysis of two nonlocal variational problems which involve Coulombic te rms and a Hardy type potential. We develop the variational framework in wh ich the proposed energy functionals admit minimizers and prove the uniquen ess and regularity of the ground states for the associated Euler-Lagrange equations which involve the fractional Laplacian. In addition\, we discuss positivity and decay rate of the ground states and present several open p roblems. This is a joint work with Jianfeng Lu (Duke) and Cyrill Muratov ( NJIT\, USA).\n\nPlease check for the zoom link 1 hour before the talk.\n LOCATION:https://researchseminars.org/talk/EXACT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Katarzyna Rejzner DTSTART;VALUE=DATE-TIME:20210514T121500Z DTEND;VALUE=DATE-TIME:20210514T131500Z DTSTAMP;VALUE=DATE-TIME:20240329T154624Z UID:EXACT/3 DESCRIPTION:Title: Th ermal states in Sine-Gordon model in Lorentzian signature\nby Katarzyn a Rejzner as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n\n Abstract\n
This talk concerns massive Sine-Gordon model in the\nultraviolet finite regime in thermal states over the two-dimension al\nMinkowski spacetime. In the recent joint work with D. Bahns and N.\nPi namonti we have applied the methods of perturbative algebraic QFT in\nLore ntizan signature combined with some estimates inspired by older\nEucildean QFT results to construct interacting observables in the\nmassive Sine-Gor don model in thermal states.
\n LOCATION:https://researchseminars.org/talk/EXACT/3/ END:VEVENT END:VCALENDAR