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Seminarium KMMF "Teoria Dwoistości"

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

K. Grabowska (KMMF)

Routh reduction - prequel

A few weeks ago, we attended a seminar by Eduardo Gracia Torano on Routh reduction in field theory. I am interested in revisiting the concept of Routh reduction, which originates from mechanics, and exploring the geometric structures that arise from it. In Hamiltonian mechanics with symmetry, it is customary to reduce the phase space without altering the Hamiltonian itself. However, Routh reduction, which is associated with the Lagrangian description of mechanics, involves reducing the entire Lagrangian bundle. This entails working with the space of infinitesimal configurations and the corresponding values of the Lagrangian, which often necessitates mathematical tools from the geometry of affine values.

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

C . Gass (KMMF)

Graviton couplings on Hilbert space

It is at the heart of gauge theory that one cannot find potentials forthe massless Wigner +/-h field strength tensors which are (i) local,(ii) covariant, (iii) have 2 degrees of freedom and (iv) live on theWigner-Fock Hilbert space of their field strength. Typically, one keepslocality, introduces unphysical degrees of freedom and works on anindefinite Krein space in intermediate steps. However, one can alsointroduce non-local potentials which satisfy (ii)-(iv), for example"string-localized" potentials.I present recent results on the self- and matter-interaction ofstring-localized graviton potentials. The structure of theseinteractions is determined by the requirements that the physicalquantities, in this case the S-matrix, are local and string independent.Although only derived at tree level, the results are "purely quantum" inthe sense that they do not refer to the gauge invariance of anunderlying classical theory.

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

N. Benedikter (University of Milan)

Bogoliubov Theory for Fermions and Bosons, and Fermi-Bose Transmutation

In the first part I will review Bogoliubov theory for many-body quantum systems, in particular its relation to quadratic Hamiltonians and Hartree-Fock theory of the electron gas. Moreover I will discuss the approximate transmutation of fermions into bosons (in dimension d > 1 !) through introduction of collective modes and present post-Hartree-Fock energy corrections obtained by this approach.In the second part I will discuss in more detail the specific implementation of a Fermi-Bose transmutation used to proof the mentioned energy corrections and comment on more recent results, in particular concerning the time evolution of a Fermi gas.

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

Michael Dutsch (Universitat Gottingen)

Perturbative QFT: off-shell fields, deformation quantization and causal perturbation theory

This talk is an introduction to an unconventional approach to pert.~QFT: - Fields are functionals on the configuration space, which are not restricted by any field equation (``off-shell'' fields). - Quantization of the free theory is done by deformation of the classical product (i.e., the pointwise product of functionals). - The interacting quantum theory is treated as a perturbative expansion around the free quantum theory, which is defined by axioms, the most important one being causality. All solutions of the axioms are constructed. The set of solutions is the orbit of the Stückelberg--Petermann renormalization group when acting on a particular solution.The interaction is adiabatically switched off. Hence, the IR-problem is separated from the UV-problem. The adiabatic limit (i.e., the limit removing this unphysical switching) is performed only at the end of the construction; typically it exists only for observable quantities. However, local, algebraic properties of the observables can be obtained without performing the adiabatic limit.

Zapraszamy na spotkanie o godzinie 10:15

E. García-Toraño (Universidad Nacional del Sur, Argentina)

Routh reduction in field theory

I will discuss an extension of the so-called ``Routh reduction'' in mechanics to first-order field theories. Roughly speaking, this is a classical technique to reduce the number of unknowns in a Lagrangian system in the presence of symmetry.In the first part of the talk, aimed at a general audience, I will give an outline of what reduction is in mechanics. I will also make an introduction to polysympectic geometry and the polysymplectic formalism of field theory. In the second part of the talk I will review some of the geometric mechanics literature on Routh reduction, and build on some of these ideas to extend Routh reduction to first-order field theories. We will describe two possible ways of doing this: one based on the polysymplectic reduction theorem, and (time permitting) another one based on variational calculus. 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 11:15

K. Myśliwy (IFT, UW)

Rigorous derivation of the Fröhlich Hamiltonian for the long-ranged Bose polaron

Since the advent of new techniques in low temperature physics, the polaron problem — “quantum impurity and a large quantum medium” — has received renewed attention from experimentalists, theorists, and mathematicians alike. In contrast to widely studied models with contact interactions, the case when the impurity interacts with the medium via long-ranged potentials is still largely unexplored and only recently attacked in experiments with ions in cold gases. Here, we are going to present the first rigorous derivation of the well-known Fröhlich Hamiltonian as an effective theory for the polaron problem consisting of an impurity immersed in a Bose gas, in a suitable mean-field limit corresponding to the long-ranged case. If time permits, we shall (heuristically) discuss surprising connections to the fermionic counterpart of the problem. UWAGA - Z POWODU PROBLEMU PRELEGENTA, SEMINARIUM ZACZNIE SIĘ O 11:15 I SKOŃCZY SIĘ O 12.

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

C. Brennecke (University of Bonn)

On the Replica Symmetric Phase of the SK Model

In this talk I will review basic predictions for the high temperature regime, the so called replica symmetric regime, of the Sherrington-Kirkpatrick spin glass model. I will discuss the TAP equations, their derivation and their validity in connection with the decay of the two point correlation functions. For the simplified case of vanishing external field, I will present recent results that characterize the susceptibility of the model as a resolvent of the interaction matrix, which suggests in a simple way the (well-known) RS-RSB transition temperature. The talk is based on joint work with A. Adhikari, A. Schertzer, P. von Soosten, C. Xu and H.-T. Yau.

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

J. Zahn (University of Lepizig)

Anomalies in Quantum Gauge Theories (a Proof of the Adler-Bardeen Theorem)

It is shown that the presence or absence of perturbative gauge anomalies in renormalizable Yang-Mills theories, such as the Standard Model, can be determined at the one-loop level, a statement usually called “Adler-Bardeen theorem”. The proof proceeds by relating gauge anomalies to background independence, which can be formalized by the concept of perturbative agreement. Before sketching the proof, I will provide an introduction to framework of locally covariant quantum field theory and the definition and cohomological classification of gauge anomalies in that context.

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

Michal Wojciechowski (IMPAN)

Microlocal approach to the Hausdorff dimension of measures

We investigate the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. We prove our results by adapting the method of Brummelhuis to the non-analytic case. As an application we obtain a general form of the Uncertainty Principle for measures on the complex sphere. In particular we construct the spectral decomposition of spherical harmonics (on a three dimensional sphere it is even a spectral basis) which allows us to generalize the celebrated theorem of Aleksandrov and Forelli concerning regularity of pluriharmonic measures. Joint work with Rami Ayoush.

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

Michał Parniak (CeNT UW)

Light-matter interfaces operating in the quantum regime

Mapping quantum information from light to matter (such as atoms) is a challenging task if we wish for high efficiency and low noise, that enable operation in the so-called quantum regime - at the level of single photons or excitations. This crucial task can allow us to combine the properties of photons (which are best for long-distance transmission) and matter (which is best to facilitate interactions), in order to both process and transmit quantum information. I would like to present my efforts at constructing such light-matter interfaces, toward the goal of constructing a quantum network, with many side quests and other applications arising along the path. I will give a general introduction to the principles of operation of such interfaces, followed by examples of experimental implementations. I will also present our favorite experimental and theoretical tools enabling us to design new quantum protocols.

Zapraszamy na spotkanie o godzinie 10:15

M. Castrillon (Universidad Complutense de Madrid)

The geometry of the reduction by stages in Field Theories

Geometry has proven to be a powerful language in which the formulation of variational principles reveals their basic properties. From Mechanics to Field theories, variational problems described in the framework of manifolds, bundles and Lie group actions provide a convenient setting enjoying a long an active scientific production. In particular, one of the main cornerstones in this geometric formulation is the idea of reduction. When a Lagrangian is invariant with respect to certain group of symmetries, this idea consists of the simplification of the configuration space of the variational problem. However, there are many interesting situations where the gorup of symmetries is composed by different subgroups of different nature (for example, rigid bodies with internal rotors, fluids, ...). In this case, it is convenient to reduce first by a subgroup and then by the rest of the symmetries. This is known as Reduction by Stages. Unfortunately, once a single reduction is performed, the configuration space is not longer a tangent (or jet) space, and the standard variational calculus must be redesigned. In this talk we will gently review the reduction by stages scheme and introduce the so-called category of Lagrange-Poincaré configurations spaces, first Mechanics and then in Field Theories. Some examples and applications will be provided. 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

P. Nayar (MIMUW)

Inequalities in information theory

The notion of entropy was introduced in 1872 by Ludwig Boltzmann in the study of his famous equation describing distribution of positions and velocities of particles in the classical gas with particle collisions. In 1948 Claude Shannon, the father of information theory, used the same mathematical notion to quantify the amount of information contained in a given random variable. During the talk we will deal with entropy in the context of probabilistic inequalities, in particular discussing variance-entropy comparisons and bounds on entropy of sums of independent random variables. We shall also describe relations with convex geometry and isoperimetric inequalities.

Zapraszamy na spotkanie o godzinie 10:15

M. Zambon (KU Leuven)

Coisotropic Submanifolds in b-Symplectic Geometry

I will report on joint work with Stephane Geudens. A b-symplectic structure is a certain kind of Poisson structure which is symplectic outside of a hypersurface. We single out two classes of coisotropic submanifolds: those transverse to the hypersurface turn out to admit a normal form theorem, which extends Gotay's theorem in symplectic geometry. Those that satisfy a stronger transversality property admit a coisotropic quotient which locally is always smooth, and which inherits a reduced b-symplectic structure.In the first part of the talk, I will give review some of the background material, including symplectic geometry and the role of coisotropic submanifolds there, as well as the b-tangent bundle. To attend our online seminar please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15

Luca Vitagliano (University of Salermo)

Characteristics and Geometric Singularities of Solutions of PDEs

Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy data, there may exist characteristic Cauchy data. Characteristics of PDEs play an important role both in Mathematics and in Physics. In the first part of the talk, I will review the theory of characteristics of PDEs, with a special emphasis on intrinsic aspects, i.e., those aspects which are invariant under general changes of coordinates. In the second part of the talk, I will pass to a modern, geometric point of view, presenting characteristics within the jet space approach to PDEs. In particular, I will discuss the duality relation between characteristics and singularities of solutions and observe that: "wave-fronts are characteristic surfaces (and propagate along bicharacteristics)". This remark may be understood as a mathematical formulation of the wave/particle duality in optics and/or quantum mechanics. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09. There will be a meeting in room 1.02 to follow our online seminar too.

Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15

K. Merz (Osaka University)

The Scott conjectures for relativistic atoms

We consider large neutral atoms of atomic number Z. For such atoms the speed of electrons close to the nucleus is a substantial fraction of the speed of light. Thus, a relativistic description is mandatory. We show that the one particle ground state density on the (hydrogenic) Scott length scale, given by Z^{-1}, converges to the density of an infinite Bohr atom in the Chandrasekhar and Furry models. Eventually, we provide pointwise upper bounds for the latter.The talk is based on joint works with Rupert L. Frank, Heinz Siedentop, and Barry Simon.

Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15

David Mitrouskas (IST Austria)

The Fröhlich polaron at strong coupling

The Fröhlich polaron is a model for an electron in a polarizable crystal described by a continuous quantum field. Despite being introduced by Landau almost 90 years ago, there are still some basic aspects of the polaron that are not fully understood mathematically. In particular, the connection between Pekar's semi-classical analysis, in which the field is treated as a classical variable, and the quantum model at strong coupling has posed interesting mathematical problems. In this talk, we will review the definition of the polaron model and some classic results, and thenfocus on recent results concerning the spectrum of the Fröhlich Hamiltonian. These include an asymptotic formula for the ground state energy as a function of the conserved total momentum and the abundance of eigenvalues below the essential spectrum at fixed total momentum. If time permits, we will also discuss the dynamical properties of the polaron. For suitable initial conditions, the quantum dynamics can be approximated by the time-dependent Landau-Pekar equations, a set of coupled partial differential equations that describe the evolution of an electron in a slowly varying classical polarization field. The talk is based on results obtained together with J. Lampart, N. Leopold, K. Mysliwy, S. Rademacher, B. Schlein and R. Seiringer.

Zapraszamy do sali 1.02, ul. Pasteura 5 o godzinie 10:15

T. Strobl (Claude Bernard University Lyon 1)

Hyzio, Dyzio and Zyzio's ghosts and their forest of Christmas trees

Our three beloved children, the angular momenta L_x, L_y, andL_z, when implemented as constraints in a Hamiltonian system so as toturn rotations into gauge symmetries, need an infinite tower of ghosts. These ghosts show a beautiful structure of trees with decorated leaves. More of this story when you attend!Based on joint work in progress with Camille Laurent-Gengoux and Aliaksandr Hancharuk.

Zapraszamy na spotkanie o godzinie 10:15

Casey Blacker (Saint Petersburg State University)

Reduction of multisymplectic manifolds

A multisymplectic manifold is a smooth manifold equipped with a closed and nondegenerate differential form of arbitrary degree. We begin with an exposition of the basic theory of multisymplectic manifolds, by analogy with the corresponding notions from symplectic geometry. We then review the Marsden-Weinstein symplectic reduction theorem and show how this result extends to the multisymplectic setting. For a special class of actions, we characterize the dependence of the reduced space on the reduction parameter, in a manner based on the symplectic Duistemaat-Heckman theorem. Finally, we present a multisymplectic extension of the Duistermaat-Heckman theorem. Finally, based on joint work with Antonio Miti and Leonid Ryvkin, we exhibit a reduction theorem for the L_\infty-algebra of observables associated to a premultisymplectic manifold. To take part in our seminar please use the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

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

N. Reshetikhin (University of California, Berkeley and Yau Mathematical Sciences Center)

Classical and quantum superintegrable systems related to moduli spaces of flat connections over surfaces

In the first part of the talk I will recall the notion of superintegrability in Hamiltonian mechanics and will introduce a family of superintegrable systems on moduli spaces of flat connections over a surface. In the second part I will focus on the quantum version of this construction. To take part in our seminar, online, please use the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09 There will be a meeting in room 2.23 to follow the seminar.

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

H. Nicolai (Max Planck Institute for Gravitational Physics)

A new look at supersymmetric Yang-Mills theories

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

C. Lazaroiu (National Institute of Physics and Nuclear Engineering)

The hidden symmetries of multifield cosmological models and Hesse geometry

I give a characterization of multifield cosmological modelswhich admit Hidden Noether symmetries through the existence of nontrivial solutions to a certain Hessian equation defined by theirscalar field metric and describe the geometric properties of theirscalar manifolds. As an application, I classify all two fieldmodels which admit such symmetries using uniformization theory. To take part in the seminar, please use the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09. There will be a meeting in room 2.23 to see the online seminar together.

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

Stanisław Kurdziałek (IFT, UW)

Measurement noise susceptibility in quantum estimation

Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum measurement. It fails, however, to quantify the robustness of quantum estimation schemes against measurement imperfections, which are always present in any practical implementations. During the seminar, I will describe a newly introduced concept of Fisher Information Measurement Noise Susceptibility that quantifies the potential loss of Fisher Information due to small measurement disturbance. I'll derive an explicit formula for the quantity, and demonstrate its usefulness in analysis of paradigmatic quantum estimation schemes, including interferometry and super-resolution optical imaging.

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

Andreas Deuchert (University of Zurich)

Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell. This is joint work with Christian Hainzl and Marcel Maier (born Schaub).

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

N. Mokrzański (KMMF, UW)

Translation invariant version of Little Grothendieck's Theorem

Little Grothendieck's Theorem in one of its version states that any bounded linear operator between Hilbert spaces which admits factorization through L^1 space is a Hilbert-Schmidt operator. During the presentation we will consider a possible generalization of this theorem for translation invariant operators on torus which admit invariant factorization through anisotropic Sobolev space. We will show that such operators belong to some non-trivial Schatten class.

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

(UPHF, France)

New applications of the reflection equation algebras

The REA are treated to be q-analogs of the enveloping algebras U(gl(N)). In particular, each of them has a representation category similar tothat of U(gl(N)). I plan to exhibit new applications of these algebras: 1. q-analog of Schur-Weyl duality, 2. q-Capelli formula, 3. q-Frobenius formula. Although there will be a meeting to see the seminar in room 2.23, it is possible to take part in our seminar, online, by means of the following Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09

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