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Wydział Fizyki UW > Badania > Seminaria i konwersatoria > Seminarium KMMF "Teoria Dwoistości"

Seminarium KMMF "Teoria Dwoistości"

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Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

K. Grabowska oraz P. Urbański (KMMF)

"...ale o co chodzi? PU - 50 lat po doktoracie"

"...but what is it about? PU - 50 years after PhD"

Pierwsza opublikowana praca PU, której współautorką jest KG (jako KK), to "Double vector bundles and duality". Pierwsza wspólna działalność naukowa PU i KG dotyczyła geometrii wartości afinicznych. W pierwszej części seminarium KG przedstawi krótko obydwa zagadnienia. Drugą część seminarium stanowić będzie gawęda PU o rachunku wariacyjnym i opisie wariacyjnym układów fizycznych.

The first published paper of PU in which KG (at that time being KK) was a co-author was "Double vector bundles and duality". Their first common scientific activity was about the geometry of affine values. The first part of the seminar by KG will be about these two theories. In the second PU will tell us all that is to know about variational calculus and variational description of physical systems.

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

M. Wiatr (KMMF)

N-complexes as a language of classical field theory

In classical electrodynamics on simply connected space, equation dF=0 is equivalent to existence of electrodynamic potential (standard Poincare lemma). From a mathematical point of view, de Rham complex (algebra of total antisymmetric tensor fields with operator d fulfilling d^2=0) is the foundation of classical electrodynamics. In other tensor field theories we work with field T of more complicated symmetry and one of the field equations is DT=0, where "D" is some first order differential operator. In this talk I will define N-complex (algebra of tensor fields of given Young symmetry with operator D fulfilling D^N=0) and generalized Poincare lemma, which is the reason for existence of field potential in every integer-spin field theory.

Zapraszamy na spotkanie o godzinie 10:15

L. Schiavone (Università di Napoli Federico II-UC3M)

Poisson brackets on the space of solutions via coisotropic embeddings

The search for a solid classical analogue of the unequal time commutation relations of Quantum Field Theory has been a task that repeatedly received attention within theoretical and mathematical physical community in the last decades starting from the seminal paper of R. E. Peierls of 1952. From the mathematical point of view, following the ideas of Souriau, the problem can be formulated as the search for a Poisson structure on the space of solutions of a classical field theory. That the space of solutions of some non-singular first order field theories can be equipped with a symplectic (and, thus, a Poisson) structure is well known. On the other hand, it happens that within gauge theories such a structure turns out to be only pre-symplectic, in the sense that it presents a non-trivial kernel. In this talk we show how to induce, in some circumstances, a Poisson bracket on the space of solutions even in this pre-symplectic case, i.e, we show how to construct a Poisson bracket on the space of solutions of a class of gauge theories, by using a construction related with the so called coisotropic embedding theorem. Free Classical Electrodynamics will be our guiding example throughout all our constructions. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Jeremy Faupin (Universite de Lorraine)

Spectral decomposition of some non-self-adjoint operators

We will consider in this talk non-self-adjoint operators in Hilbert spaces given as relatively compact perturbations of a self-adjoint operator. Typical examples are Schrödinger operators with bounded, complex potentials vanishing at infinity. We will describe abstract conditions ensuring that the Hilbert space admits a direct sum decomposition into H-invariant subspaces, generalizing the well-known spectral decomposition of self-adjoint operators in terms of their spectral measures. A central role in the talk will be played by spectral singularities, an abstract notion corresponding to that of real resonances for Schrödinger operators. We will also present a useful regularized functional calculus for non-self-adjoint operators.This is joint work with Nicolas Frantz. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Edith Padron (Universidad of La Laguna)

Hamilton-Jacobi equations for Hamiltonian systems

In this talk, I will present, in a geometric framework, the Hamilton–Jacobi equations for a large variety of mechanical systems. In the first part of the talk, I will show the classical theory for Hamiltonian systems on a cotangent bundle and its relationship with the integrability of these systems. In the second part of the talk, we will see recent developments in the framework of general Poisson, almost-Poisson, contact manifolds and its relation with the integrability by quadrature. Several examples will illustrate the theory. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Piotr Kosiński (University of Lodz)

Relativistic Symmetries and Hamiltonian Formalism

The relativistic (Poincaré and conformal) symmetries of classical elementary systems are briefly discussed and reviewed. The main framework is provided by the Hamiltonian formalism for dynamical systems exhibiting symmetry described by a given Lie group. The construction of phase space and canonical variables is given using the tools from the coadjoint orbits method. It is indicated how the “exotic” Lorentz transformation properties for particle coordinates can be derived; they are shown to be the natural consequence of the formalism. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Laurent Bétermin (Université Claude Bernard Lyon 1)

Crystallization and optimal lattices

In order to explain the emergence of periodic patterns like atoms in solids or vortices in superconductors, mathematicians have been studying simplified models from a variational point of view. Finding energy minimizers and exploring the possible ground states of such systems is known as Mathematical Crystallization. The purpose of this talk is to review the main crystallization results that have been shown since the eighties. From the Heitmann-Radin Theorem to the recent result we obtained with De Luca and Petrache on the optimality of the square lattice for two-body potentials, I will briefly explain the main ingredients of the proofs as well as the important open problems arising in this field. Connections will be made with other related problems like the asymptotic expansion of the logarithmic energy on sphere, the Jellium energy as well as the question of Cohn-Kumar's Universal Optimality. Furthermore, I will also review some old and recent results about lattice energy minimization, i.e. minimization of pair energies among simple lattices, and associated open questions. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Łukasz Kaczmarczyk (University of Glasgow)

Mathematical modelling of crack propagation in nuclear graphite

Nuclear power provides ~17% of UK electricity. Seven out of the eight civil nuclear power stations in the UK are the Advanced Gas-cooled Reactor (AGR) design. Each reactor core is 10m high with a diameter of 10m contained within a concrete pressure vessel. A reactor comprises ~3,000 cylindrical graphite bricks that are connected and stacked vertically into 250 channels. Uranium fuel is inserted into these channels. The core provides structural integrity for housing the fuel and acts as the neutron moderator. The graphite undergoes neutron damage in the reactor’s aggressive environment, compromising reactor structural integrity. Assessment and prediction of integrity are critical to safety and planning reactor lifespan. The condition of the graphite reactor core is the major life-limiting factor for nuclear power stations. Routine inspections of the oldest AGR cores have shown significant cracks in the graphite bricks. Numerical models give EDF Energy the ability to predict if these cracks are life-limiting.Brittle crack propagation is an inherently unstable and highly nonlinear process that continues to be the subject of significant scientific attention despite decades of study. We established a new methodology and computational framework for simulating this phenomenon in the complex environment of a nuclear reactor. The research exploits Configurational Mechanics to describe crack propagation mathematically. This led to theoretical advances and new numerical methods integrated into MoFEM – an open-source finite element analysis software developed at the University of Glasgow, incorporating many of the latest advances in scientific computing.In the talk, after a brief introduction, I will focus on the Configurational (Eshelbian) Mechanics framework to model topology evolution due to crack propagation. From the first laws, I derive what is understood by the equilibrium of the crack front. Using Griffith criterion and the principle of maximal dissipation, I will derive kinematic constraints for crack area growth. The second part of the talk focus on the numerical aspect. I will conclude with some real-life examples. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Krzysztof Sacha (IFT, Jagiellonian University)

Time crystals

On one hand, the idea of time crystals seems very simple: everything we know about ordinary crystals in space, we should try to imagine, is happening in the time dimension. On the other hand, it requires a change in our view of systems that evolve periodically in time. During thelecture, I will try to explain what the time crystalline structures mean and how to observe the physics of condensed matter in the time dimension. In the second part of the lecture, I will show that time crystals can form spontaneously in periodically driven quantum multi-body systems. To attend our online seminar, please use the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Wouter Jangeleen (EPFL)

Topological obstructions to stability and stabilization

This talk aims to provide an overview of topological obstructions to stability and stabilization of dynamical systems defined on manifolds. We consider the interplay between the topology of an attractor, its domain of attraction and the underlying manifold that is supposed to contain these sets. We also highlight a few new results on multistability, the odd-number limitation and stabilization on bundles. This talk is based on joint work with Prof. Emmanuel Moulay.To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Jan Dereziński (KMMF, UW)

Bessel operators as toy models of renormalization group

In Quantum Field Theory one usually needs to perform the following steps:1. Cut off the formal Hamiltonian with a momentum cutoff.2. Add an appropriate counterterm times a running coupling constant. 3. Determine the differential equation for the coupling constant.4. Go with the cutoff to infinity.I will show that the same steps are needed in the much simpler context of Bessel Hamiltonians, that is, Schrodinger operators with the inverse square potential. The action of scaling on self-adjoint realizations of Bessel operators serves as a nice illustration of a "renormalization group flow".To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Bartłomiej Bąk (KMMF)

Krótka rozprawa o efekcie Penrose'a

A short deliberation about Penrose effect

W moim wystąpieniu wprowadzę niezbędne elementy geometrii czasoprzestrzeni Kerra takie jak: metryka, horyzonty, ergosfera, geodezyjne, wektory Killinga, stałe ruchu. Następnie zaprezentuję proces (zwany efektem lub procesem Penrose'a), w którym cząstka lecąca w stronę horyzontu rozpada się w taki sposób, że jeden z produktów rozpadu "wpada" za horyzont, a drugi ucieka do nieskończoności i niesie ze sobą energię większą, niż cząstka początkowa. Zaprezentuję również maksymalną sprawność takiego procesu oraz maksymalną energię jaką można wyekstrahować w sposób klasyczny. Okazuje się, że taki tok rozumowania pozwala stwierdzić, że powierzchnia czarnej dziury nie może maleć (tw. Hawkinga). Prowadzi to do opisu termodynamiki czarnej dziury Kerra, w którym zdefiniuję temperaturę i entropię. Na koniec zaprezentuję "analogony" efektu Penrose'a dla fal elektromagnetycznych (efekt Zeldowicza) oraz fal dzwiękowych. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

In my talk I will introduce some usefull elements of Kerr spacetime geometry e.g. metric, horizons, ergosphere, geodesics, Killing vectors, constans of motion. The next step will be the process description (so called "Penrose effect" or "Penrose process"), where the particle, which is coming to horizon, decays to two pieces in such a way that one of them is falling down into horizon and the second one escapes to infinity with energy greater than the initial particle had. Hence, I present the maximal energy conversion efficiency for such process and maximal energy which could be extracted in a classical way. Furthermore, this discussion will easily lead to the observation that the horizon of black hole cannot decrease (Hawking theorem) and hence, the thermodynamical description of Kerr black hole -- the definition of temperature and entropy will be brought in. Finally, I will briefly introduce the "analogues" of Penrose effect for electrodynamical waves (Zel'dovich effect) and sound waves. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Jean-Claude Cuenin (Loughborough University)

Random Schrödinger operators with complex decaying potentials

I will report on recent progress concerning eigenvalues of Schrödinger operators with complex potentials. In the first part of the talk I will explain how techniques from harmonic analysis (related to Fourier restriction theory) can be used in the context of spectral theory of Schrödinger operators. I will give some details on the recent counterexample to the Laptev-Safronov conjecture.In the second part of the talk I will try to convince you that the counterexample is non-generic. More precisely, I will show how the decay assumptions can be weakened under randomization. The tools used (multilinear expansion of the Born series, discretization and localization, entropy bounds, epsilon removal) may be of independent interest. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Wojciech Kamiński (IFT UW)

The ambient metric construction and some applications

First part of my talk will be an introduction to the ambient metric of Fefferman-Graham. This method provides a construction of important objects in conformal geometry like conformal powers of the Laplacians, obstruction tensor, Q-curvature. I will describe some surprising applications in general relativity. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Michel Rausch de Traubenberg (University of Strasbourg)

Generalisation of affine Lie algebras on compact real manifolds

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold $\mathcal{M}$ to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a Fourier expansion. The Peter--Weyl theorem for the case of manifolds related to compact Lie groups and coset spaces is discussed, and appropriate Hilbert bases for the space $L^{2}(\mathcal{M})$ of square-integrable functions are constructed. It is shown that such bases are characterised by the representation theory of the compact Lie group, from which a complete set of labelling operator is obtained. The existence of central extensions of generalised Kac-Moody algebras is analysed using a duality property of Hermitian operators on the manifold, and the corresponding root systems are constructed. Several examples are given. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Eva Miranda (UPC - CRM Barcelona)

From Euler equations to Turing machines via contact geometry

What physical systems can be non-computational? (Roger Penrose, 1989). Is hydrodynamics capable of calculations? (Cris Moore, 1991). Can a mechanical system (including the trajectory of a fluid) simulate a universal Turing machine? (Terence Tao, 2017).The movement of an incompressible fluid without viscosity is governed by Euler equations. Its viscid analogue is given by the Navier-Stokes equations whose regularity is one of the open problems in the list of problems for the Millenium bythe Clay Foundation. The trajectories of a fluid are complex. Can we measure its levels of complexity (computational, logical and dynamical)?In this talk, we will address these questions. In particular, we will show how to construct a 3-dimensional Euler flow which is Turing complete. Undecidability of fluid paths is then a consequence of the classical undecidability of the haltingproblem proved by Alan Turing back in 1936. This is another manifestation of complexity in hydrodynamics which is very different from the theory of chaos.Our solution of Euler equations corresponds to a stationary solution or Beltrami field. To address this problem, we will use a mirror [5] reflecting Beltrami fields as Reeb vector fields of a contactstructure. Thus, our solutions import techniques from geometry to solve a problem in fluid dynamics. But how general are Euler flows? Can we represent any dynamics as an Euler flow? We will address this universality problem using the Beltrami/Reeb mirror again and Gromov's h-principle. We will also consider the non-stationary case. These universality features illustrate the complexity of Euler flows. However, this construction is not "physical" in the sense that the associated metric is not the euclidean metric. We will announce an euclidean construction and its implications to complexity and undecidability. These constructions [1,2,3,4] are motivated by Tao's approach to the problem of Navier-Stokes [7,8,9] which we will also explain.[1] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Universality of Euler flows and flexibility of Reebembeddings. https://arxiv.org/abs/1911.01963.[2] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Constructing Turing complete Euler flows indimension 3. Proc. Natl. Acad. Sci. 118 (2021) e2026818118.[3] R. Cardona, E. Miranda, D. Peralta-Salas. Turing universality of the incompressible Euler equationsand a conjecture of Moore. Int. Math. Res. Notices, , 2021;, rnab233,https://doi.org/10.1093/imrn/rnab233[4] R. Cardona, E. Miranda, D. Peralta-Salas. Computability and Beltrami fields in Euclidean space.https://arxiv.org/abs/2111.03559 [5] J. Etnyre, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert conjecture.Nonlinearity 13 (2000) 441–458.[6] C. Moore. Generalized shifts: unpredictability and undecidability in dynamical systems. Nonlinearity4 (1991) 199–230.[7] T. Tao. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219–238.[8] T. Tao. On the universality of the incompressible Euler equation on compact manifolds. DiscreteCont. Dyn. Sys. A 38 (2018) 1553–1565.[9] T. Tao. Searching for singularities in the Navier-Stokes equations. Nature Rev. Phys. 1 (2019) 418–419. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Vedran Sohinger (University of Warwick)

Interacting loop ensembles and Bose gases

We study interacting quantum Bose gases in thermal equilibrium on a lattice. In this framework, we establish convergence of the grand-canonical Gibbs states to their mean-field (classical field) and large-mass (classical particle) limit.Our analysis is based on representations in terms of ensembles of interacting random loops, namely the Ginibre loop ensemble for quantum bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, we obtain corresponding results in the infinite volume limit by means of cluster expansions. This is joint work with Juerg Froehlich, Antti Knowles, and Benjamin Schlein. To attend, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Adam Sawicki (CFT PAN)

How to check universality of quantum gates?

I will discuss recent developments in the area of universality of quantum gates. In particular I will show that one can check if a gate-set in dimension d is universal by solving O(d^4) linear equations. The talk will be based on joint work with K. Karnas, L. Mattioli and Z. Zimboras. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy na spotkanie o godzinie 10:15

Xavier Rivas (Universitat Politecnica de Catalunya)

A geometric framework for field theories with dissipation based on contact geometry (ONLY ONLINE)

Many important theories in modern physics can be stated using the tools of differential geometry. It is well known that symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems and classical field theories, both regular and singular.In recent years there has been a growing interest in studying dissipative mechanical systems from a geometric perspective by using contact structures. In this talk we will review the main results on contact mechanics and work out some examples. We will also give a brief summary of how k-symplectic structures can be used to give a geometric formulation of classical field theories.Furthermore, field theories with damping will be described through a modification of the De Donder–Weyl Hamiltonian field theory. This is achieved by combining both contact geometry and k-symplectic structures, resulting in what we call the k-contact formalism.Finally we will study some interesting examples: the damped vibrating string, the Burgers’ equation and Maxwell’s equations of electromagnetism with dissipation. References • J. Gaset, X. Gracia, M. C. Munoz-Lecanda, X. Rivas and N. Roman-Roy. “New contributions to the Hamiltonian and Lagrangian contact formalisms for dissi- pative mechanical systems and their symmetries”. Int. J. Geom. Methods Mod. Phys., 16(6):2050090, 2020. https://doi.org/10.1142/S0219887820500905. • J. Gaset, X. Gracia, M. C. Munoz-Lecanda, X. Rivas and N. Roman-Roy. “A contact geometry framework for field theories with dissipation”. Ann. Phys., 414:168092, 2020. https://doi.org/10.1016/j.aop.2020.168092. • J. Gaset, X. Gracia, M. C. Munoz-Lecanda, X. Rivas and N. Roman-Roy. “A k-contact Lagrangian formalism for nonconservative field theories”. Rep. Math. Phys., 87(3):347–368, 2021. https://doi.org/10.1016/S0034-4877(21)00041-0. • X. Gracia, X. Rivas and N. Roman-Roy. “Skinner–Rusk formalism for k-contact systems”, preprint, 2021. https://arxiv.org/abs/2109.07257. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Hermann Nicolai (Albert Einstein Institute)

Observations on supermembrane theory

The maximally supersymmetric supermembrane theory in space-time dimension D = 11 is a model ‘beyond’ string theory that incorporatesD = 11 supergravity as a `low energy limit', and is thus a candidate theory for a non-perturbative formulation of superstring theory. In thistalk I will review some basic features, in particular the reformulationof this theory as a one-dimensional gauge theory of area preserving diffeomorphisms, which naturally leads to the matrix model of M theory.I will also mention very recent work (arXiv:2109.00346) to argue thatthis framework allows for a systematic investigation of the small andlarge tension limits of this theory.

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Krzysztof Jachymski (IFT)

Strong interactions in ultracold atomic systems

Atomic samples cooled to quantum degeneracy offer exciting opportunities for quantum simulations and precision measurements. Since the first realization of the Bose-Einstein condensate in a weakly interacting gas, many new systems emerged with different types of interactions. In particular, creation of hybrid ion-atom systems enabled the studies of impurity physics in the strongly interacting regime. In this talk, I will describe the basic features of few- and man-body problems involving mixtures of ions and atoms and then discuss recent breakthrough experiments studying charge transport in a cold gas and demonstrating control over the ion-atom interaction strength by means of Feshbach resonances.

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Tomasz Smołka (KMMF)

Hamiltonian charges in spacetimes with positive cosmological constant

Linear theories (linearized gravity, electromagnetism and scalar field theory) on de Sitter background will be discussed. I mainly focus on asymptotic analysis of Hamiltonian charges in the radiating regime. The talk is based on arXiv:2103.05982.

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Alexander Stottmeister (University of Hannover)

Conformal field theory from lattice fermions and its quantum simulation

I will explain how conformal symmetries can be recovered via the Koo-Saleur formula in the scaling limit of lattice models based on free fermions. The main tool for the construction of the scaling limit is given by operator algebraic renormalization. In addition, I will illustrate how these results pertain to the quantum simulation of conformal field theories.

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Erik Skibsted (Aarhus University)

Stationary scattering theory, the n-body long range case

Within the class of Dereziński pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known [De], we show that all entries of the N -body quantum scattering matrix have a well-defined meaning at any given non-threshold energy. As a function of the energy parameter the scattering matrix is weakly continuous. This result generalizes a similar one obtained previously by Yafaev for systems of particles interacting by short-range potentials [Ya1]. As for Yafaev’s paper we do not make any assumption on the decay of channel eigenstates. The main part of the proof consists in establishing a number of Kato-smoothness bounds needed for justifying a new formula for the scattering matrix. Similarly we construct and show strong continuity of channel wave matrices for all non-threshold energies. Away from a set of measure zero we show that the scattering and channel wave matrices constitute a well-defined ‘scattering theory’, in particular at such energies the scattering matrix is unitary and strongly continuous. To attend this ONLINE seminar you can meet us in room 2.23 or to use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 10:15

Andrzej Krasiński (N. Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw)

Relativistic cosmology from F to Sz (F = Friedmann, Sz = Szekeres)

1. The Friedmann-Lemaitre (FL) cosmological models and their basicimplications. In this part of the talk will I show how the FL models follow from symmetry assumptions imposed on the Einstein equations, and will briefly explain their relation to observational cosmology. Emphasis will be put on dubious claims based on these models, such as the cosmological principle and the hypothesis of accelerated expansion of the Universe. 2. The Lemaitre-Tolman (LT) models and their relation to some of thecosmological observations. These models are the simplest known generalisation of the FL models. In spite of being spherically symmetric, they allow for several interesting insights, within the exact theory, into the consequences of existence of matter condensations and voids in the Universe. In this part of the talk I will show how spatial variations in the expansion pattern can mimic the accelerated expansion of the Universe without the need to introduce "dark energy". 3. The Szekeres (Sz) models and their observational implicationsThese models are fully nonsymmetric generalisations of the LT models. They arise by making the spheres, invariantly defined in the LT geometry, non-concentric. This allows for describing still more observable phenomena. One of them is the direction drift of light rays propagating through mass inhomogeneities (this effect is also present for nonradial rays in LT models). This will signal inhomogeneity in large-scale matter distribution when the observations become sufficiently precise. 4. If time permits: In the LT and Sz models some of the light rays emitted soon after the Big Bang get blue-shifted rather than redshifted, i. e. their observed frequency is higher than at the emission point. Possible observational signatures of such rays will be discussed.