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SUMMARY:Michał Wrochna ((Université de Cergy-Pontoise)
DTSTART:20210409T121500Z
DTEND:20210409T131500Z
DTSTAMP:20260404T110652Z
UID:EXACT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EXACT
 /1/">Spectral actions on asymptotically Minkowski spacetimes</a>\nby Micha
 ł Wrochna ((Université de Cergy-Pontoise) as part of EXACT - (KRAKOW - P
 OZNAN - WARSAW) Field Theory\n\n\nAbstract\nThe spectral theory of the Lap
 lace–Beltrami operator on Riemannian manifolds is known to be intimately
  related to geometric invariants such as the Einstein-Hilbert action. Thes
 e relationships have inspired many developments in physics including the C
 hamseddine–Connes action principle in the non-commutative geometry progr
 amme. However\, a priori they do only apply to the case of Euclidean signa
 ture. The physical setting of Lorentzian manifolds has in fact remained la
 rgely problematic: elliptic theory no longer applies and something differe
 nt is needed.\n\nIn this talk I will report on joint work on this problem 
 with Nguyen Viet Dang. We consider perturbations of Minkowski space and mo
 re general spacetimes on which the d’Alembertian P is essentially self-a
 djoint (thanks to recent results by Dereziński–Siemssen\, Vasy and Naka
 mura–Taira). It is then possible to define functions of P\, and we demon
 strate that their Schwartz kernels have geometric content largely analogou
 s to the Riemannian setting. In particular\, we define a Lorentzian spectr
 al zeta function and relate one of its poles to the Einstein–Hilbert act
 ion\, paralleling thus a result in Euclidian signature attributed to Conne
 s\, Kastler and Kalau–Walze.\n\nThe primary consequence is that gravity 
 can be obtained from a spectral action directly in Lorentzian signature. T
 he proofs involve mathematical ingredients from Quantum Field Theory on cu
 rved spacetime\, in particular the Feynman propagator.\n\nPlease contact t
 he organizers for the link to the meeting.\n
LOCATION:https://stable.researchseminars.org/talk/EXACT/1/
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BEGIN:VEVENT
SUMMARY:Vitaly Moroz (Swansea University)
DTSTART:20210416T121500Z
DTEND:20210416T131500Z
DTSTAMP:20260404T110652Z
UID:EXACT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EXACT
 /2/">Thomas-Fermi type models for graphene.</a>\nby Vitaly Moroz (Swansea 
 University) as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theory\n\n
 \nAbstract\nWe discuss density functional theories of Thomas-Fermi and Tho
 mas-Fermi-von Weizsacker type which describe the response of a single laye
 r of graphene to an external electric charge. Mathematically\, this amount
 s to the analysis of two nonlocal variational problems which involve Coulo
 mbic terms and a Hardy type potential. We develop the variational framewor
 k in which the proposed energy functionals admit minimizers and prove the 
 uniqueness and regularity of the ground states for the associated Euler-La
 grange equations which involve the fractional Laplacian. In addition\, we 
 discuss positivity and decay rate of the ground states and present several
  open problems. This is a joint work with Jianfeng Lu (Duke) and Cyrill Mu
 ratov (NJIT\, USA).\n\nPlease check for the zoom link 1 hour before the ta
 lk.\n
LOCATION:https://stable.researchseminars.org/talk/EXACT/2/
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BEGIN:VEVENT
SUMMARY:Katarzyna Rejzner
DTSTART:20210514T121500Z
DTEND:20210514T131500Z
DTSTAMP:20260404T110652Z
UID:EXACT/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EXACT
 /3/">Thermal states in Sine-Gordon model in Lorentzian signature</a>\nby K
 atarzyna Rejzner as part of EXACT - (KRAKOW - POZNAN - WARSAW) Field Theor
 y\n\n\nAbstract\n<p align="justify">This talk concerns massive Sine-Gordon
  model in the\nultraviolet finite regime in thermal states over the two-di
 mensional\nMinkowski spacetime. In the recent joint work with D. Bahns and
  N.\nPinamonti we have applied the methods of perturbative algebraic QFT i
 n\nLorentizan signature combined with some estimates inspired by older\nEu
 cildean QFT results to construct interacting observables in the\nmassive S
 ine-Gordon model in thermal states.</p>\n
LOCATION:https://stable.researchseminars.org/talk/EXACT/3/
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