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Seminarium KMMF "Teoria Dwoistości"

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

Mikołaj Rotkiewicz (IM PAN)

Models for higher algebroids

The tangent bundle of a Lie group G bears a "symmetry". The reduced space, TG/G, is naturally identified with T_eG, the tangent space at the identity element of G, is not merely a vector space but has an algebraic (Lie algebra) structure inherited from the group multiplication in G. Similarly, the reduction of the tangent bundle of a Lie groupoid leads to a rich algebro-geometric structure called a Lie algebroid. Reductions of higher tangent bundles of Lie groupoids provide natural examples of structures which we would like to call higher algebroids. The basic problem is: what is the algebraic structure on the reduced bundle inherited from the groupoid multiplication? The key difficulty is that there is no bracket operation on the space of sections of a higher tangent bundle. The basic idea which allowed us to approach the problem is a reformulation of the definition of an algebroid in terms of a relation which can be obtained by a reduction of the canonical involution of TTG if the algebroid integrates to a Lie groupoid G. Thus a higher algebroid is, in principle, a graded bundle (a natural generalization of the notion of a vector bundle) equipped with a relation of a special kind. Such a point of view is natural in Geometric Mechanics as higher-order systems with internal symmetries can be reduced to systems defined on such higher algebroids. Based on a joint paper with Michał Jóźwikowski.

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

Paweł Duch (Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagielloński)

The construction of scattering states for massless particles in quantum field theory

Almost all experiments in the high energy physics involve collisions of particles. The description of such processes in quantum field theory models requires the identification of scattering states i.e. states which in the asymptotic past or future correspond to a specific configurations of particles. During the talk I will present the construction of scattering states of massless particles and prove that the Hilbert space formed by these states has Fock structure. Despite the long range correlation inevitable in the presence of massless particles the construction turns out to be simpler than the analogous construction for massive particles.

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

Daniel Siemssen (Riemann Fellow, Universität Hannover)

Construction of Hadamard states on asymptotically flat spacetimes

Hadamard states play a prominent role in quantum field theory in curved spacetimes. They generalize important properties of the Poincare invariant vacuum state from standard QFT. In particular, they permit the forumlation of a rigorous theory of renormalization. However, the construction of Hadamard states in generic globally hyperbolic spacetimes often presents a major obstacle. In this talk I will discuss a construction of Hadamard states in asymptotically spacetimes due to Moretti, Dappiagi and Pinamonti. At the basis of their construction is a correspondence between a quantum theory living in the interior of a lightcone and a theory intrinsically defined on its boundary. I will describe how this correspondence can be used to construct Hadamard states for the scalar field [Moretti, Dappiaggi, Pinamonti] and the electromagnetic potential [Dappiaggi, Siemssen] in asymptotically flat spacetimes.

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

Wojciech Kamiński (IFT WFUW)

Quantum energy inequalities

Many classical field theories satisfy various positive conditions for the stress-energy tensor. These conditions are crucial for example in singularity theorems of Penrose and Hawking. On the contrary, quantum stress energy tensors necessarily violate all such positivity conditions and admit negative expectation values. Surprisingly, there is still some reminiscence of the nice classical behavior: negative energy cannot last very long. This phenomenon is described by so-called averaged energy inequalities. I will talk about the work of Christopher Fewster on this subject.

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

Paweł Nurowski (Centrum Fizyki Teoretycznej)

On Penrose's Conformal Cyclic Cosmology

TBAL

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

Paweł Kasprzak (KMMF WFUW)

Groups, von Neumann algebras and Herz restriction theorem

Let G be a locally compact group and LG the group von Neumann algebra of G. In this talk I will discuss certain properties of G which are visible/invisible on the level of LG. In particular property (T), Haagerup property and amenability will be discussed. I will also explain the Tatsuuma duality for G. In the second part of the talk (which is based and the joint work with M. Daws, A. Skalski and P. Sołtan), the Herz restriction theorem in terms of group von Neumann algebras will be formulated and its relatively simple proof will be given.

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

Neil Lambert (King's College, London oraz Profesor wizytujący w WFUW)

M-branes

I will give an overview of the branes in M-theory and their associated quantum field theories. These include M2-branes, leading to 3D Chern-Simons Matter theories (BLG, ABJM), as well as M5-branes leading to 6D CFT's which remain very mysterious and challenging.

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

Katarzyna Rejzner (Department of Mathematics, University of York)

Renormalization without infinities and algebraic structures in quantum field theory

In this talk I will briefly review the approach to renormalization called causal perturbation theory that avoids dealing with ill-defined objects. This approach started with the seminal paper of Epstein and Glaser (1973) and recently got new interest because of applications to QFT on curved spacetimes. It also allows to uncover some interesting algebraic structures present in perturbative renormalization, like for example Hopf algebras and BV structures.

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

Krzysztof Turzyński (IFT WFUW)

Angels, demons and physics: in search of the dark matter particle

Answering the question about the nature and properties of dark matter has become a mandatory task for any theory extending the Standard Model of particle physics. I will present a personally biased review of some indirect evidence for the existence of dark matter, as well as the most important attempts to detect dark matter particles directly in the laboratory. My goal is to convey the state of confusion currently permeating the community of dark matter theorists and experimentalists.

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

Piotr J. Durka (ZFB WFUW)

Interfejsy mózg-komputer, technologie asystujące i analiza sygnałów

Wyjaśnimy pokrótce działanie interfejsów mózg-komputer opartych o odczyt EEG oraz naturalną konieczność badań interdyscyplinarnych w tej dziedzinie. Odkryjemy drugie znaczenie cytatu "przyszłość jest już dzisiaj, tylko nierówno rozłożona" i pokażemy, jak tworzony w projekcie http://PISAK.org system, podobny do używanego przez Stephena Hawkinga, daje szansę wyjścia z piekła zamknięcia tysiącom niepełnosprawnych. W drugiej części przedstawimy rozwijaną w Zakładzie Fizyki Biomedycznej metodę analizy sygnałów (matching pursuit) i jej implementację http://braintech.pl/svarog.

Literatura:

O technologiach asystujących -- esej http://braintech.pl/onas.html i strona projektu PISAK http://pisak.org
O analizie sygnałów: "Multivariate matching pursuit in optimal Gabor dictionaries: theory and software with interface for EEG/MEG via Svarog" http://www.biomedical-engineering-online.com/content/12/1/94

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

Jerzy Lewandowski (IFT WFUW)

Connections and parallel transports

The mathematical tools of Loop Quantum Gravity will be presented. The main one is the space of the parallel transports. It admits a natural compact topology, measures and geometric structures. They give rise to Hilbert spaces and operators. Generalized spin-networks are used for orthogonal decompositions. Operators represent quantum geometry. The diffeomorphism invariance plays important role. There are unsolved mathematical problems.

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

Paweł Jakubczyk (IFT WFUW)

Functional renormalization group: two applications

I will present two applications of the one-particle-irreducible variant of functional renormalization group to condensed-matter systems. These are:

classical O(N)-symmetric models;
effective models for classical and quantum interface unbinding transitions.

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

Jan Dereziński (KMMF WFUW)

Dlaczego kwantyzacja Weyla jest najlepsza?

Opiszę 5 najbardziej naturalnych kwantyzacji symplektycznej przestrzeni wektorowej: x-p, p-x, Wicka, anty-Wicka i Weyla(-Wignera), których relacje można wyrazić tzw. diagramem Bieriezina. Omówię centralną rolę graną przez kwantyzację Weyla. Ta rola ma dwa aspekty - większą grupę symetrii (niezmienniczość symplektyczną) i lepsze oszacowania błędów w przybliżeniu semiklasycznym.

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

Jacek Miękisz (IMSIM MIMUW)

Searching for formulas for moments of stationary states in stochastic models of self-repressing gene and ion channels

One of the main goals of statistical mechanics is to find equilibrium states of systems of many interacting particles and expected values of relevant random variables, for example magnetization in the Ising model. At low temperatures, equilibrium states may be constructed as small perturbations of ground states. Here we will discuss constructions of non-equilibrium stationary states in two simple models: gene self-regulation and Kawasaki dynamics in ion channels.

Mathematical cell: Stochastic model of gene expression
Intermission: Markov jump processes and detailed balance
Main actor: Self-repressing gene
Mean-field approximation
Expansions

around detailed balance
around adiabatic regime

Kawasaki dynamics in ion channels
Gibbs states versus non-equilibrium stationary states
Ground states versus stochastically stable states

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

Dariusz Baranowski (IGF WFUW)

Jak przeciwdziałać zmianom klimatu? Międzynarodowe negocjacje oczami fizyka z fizycznymi podstawami zmian klimatu w tle

W ramach Ramowej Konwencji Narodów Zjednoczonych w sprawie Zmian Klimatu (UNFCCC) w listopadzie 2013 r. odbyła się w Warszawie 19. Konferencja Stron (COP19). Kolejne spotkanie ministrów środowiska i międzynarodowych negocjatorów odbywa się w Limie w grudniu 2014 r. Coroczne spotkania mają doprowadzić do podpisania w Paryżu w 2015 r. międzynarodowego porozumienia dotyczącego skutecznego ograniczenia emisji gazów cieplarnianych, w szczególności dwutlenku węgla. Międzynarodowe negocjacje odbywają się w czasie, gdy publikowany jest najnowszy, 5. raport Międzyrządowego Panelu ds Zmian Klimatu (AR5), stanowiącego ogólnie akceptowalną podstawę naukową dla negocjacji. W czasie seminarium przedstawię dotychczasowe „osiągnięcia” Konwencji i wynikające z nich ramy dla nowego, negocjowanego porozumienia. Jako bezpośredni uczestnik konferencji w Warszawie i pośredni konferencji w Limie przedstawię wyniki rozmów starając się przybliżyć słuchaczom środowisko negocjacji oraz ich efekt.

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

Piotr Waluk (KMMF WFUW)

Various ways to positivity

ADM mass proves useful in analysis of asymptotically flat spacetimes, although the study of the notion itself was not devoid of difficulties. A good example here is the question of positive definiteness of this quantity, which had to wait over twenty years for a decisive answer. The talk will consist of a short historical review of main methods used to approach the problem, followed by a presentation of an alternative proof of positive-energy theorem, based on elementary tools of differential geometry only.

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

Maciej Karczmarczyk (KMMF WFUW)

Twierdzenie Calderóna–Vaillancourta o ograniczoności operatorów pseudoróżniczkowych

Kwantyzacja rozumiana jako przejście od funkcji do odpowiadającego jej operatora może być realizowana na wiele sposobów. Jedną z tych realizacji jest tzw. kwantyzacja Kohna–Nirenberga. W 1972 r. A. Calderón i R. Vaillancourt pokazali, że kwantyzacja ta prowadzi do operatora ograniczonego na L^2(|R^d) jeśli tylko funkcja ma ograniczone pochodne do pewnego stopnia. Stopień pochodnych w ich dowodzie nie jest optymalny. W trakcie seminarium przedstawię (pochodzący od H.O. Cordesa) dowód z optymalnie niskim stopniem pochodnych oraz powiem kilka słów o dowodzie tego twierdzenia dla bardziej naturalnej kwantyzacji Weyla–Wignera.

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

Nils Carqueville (Fakultät für Mathematik, Universität Wien oraz ESI, Wien)

Equivariant completion of defect bicategories

Two-dimensional topological field theories have three layers of structure: bulk theories living on two-dimensional worldsheet patches, one-dimensional defect lines between such patches, and zero-dimensional field insertions. We review how these layers naturally combine into the structure of a bicategory, and sketch how sigma models or Landau–Ginzburg models provide relevant examples. Next we explain how to encode orbifolds in entirely algebraic language in this general setting. In fact, this leads to a generalisation of orbifolds (and in this sense of "symmetry"), and to a construction of new equivalences of field theories. Much of this is based on joint work with Ingo Runkel.

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

Jacek Jezierski (KMMF WFUW)

Hidden symmetries in General Relativity

TBA

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

Javier de Lucas Araujo (KMMF WFUW)

Lie–Hamilton systems on the plane: theory and applications

The main aim of this talk is to study Lie–Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian vector fields with respect to a Poisson structure. First, we review the local classification of finite-dimensional real Lie algebras of vector fields on the plane. By determining which of these real Lie algebras consist of Hamiltonian vector fields with respect to a Poisson structure, we provide the complete local classification of Lie–Hamilton systems on the plane. As an application of our results, we investigate new and known Lie–Hamilton systems appearing in physical and mathematical problems: the Milne–Pinney, second-order Kummer–Schwarz, Cayley–Klein Riccati and Buchdahl equations as well as some Lotka–Volterra and other nonlinear biomathematical models.

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

Stanisław L. Woronowicz (KMMF WFUW)

Kwantowa grupa SUq(2) z zespolonym parametrem deformacji

Quantum SUq(2)-group with complex q

Pokażę, że relacje komutacyjne definiujące algebrę A funkcji na kwantowej grupie SUq(2) mają sens także dla nierzeczywistych wartości parametru deformacji q. Wszakże w tym przypadku nie ma komnożenia Δ odwzorowującego A w A⊗A. Żeby uratować istnienie Δ, musimy zmodyfikować iloczyn tensorowy w sposób znany w teorii superalgebr. Tym sposobem dochodzimy do pojęcia braidowanej grupy kwantowej. Na koniec mam nadzieję powiedzieć kilka słów o teorii reprezentacji braidowanych grup kwantowych.

Jest to wspólna praca Pawła Kasprzaka, Ralfa Meyera, Sutanu Roy'a i moja.

We shall show that the commutation relations defining the algebra A of functions on the quantum SUq(2)-group make sense also for non-real values of the deformation parameter q. However, in this case there is no comultiplication Δ acting from A into A⊗A. To regain the existence of Δ, we have to replace the tensor product by a sort of super tensor product. This way we arrive at a concept of a braided quantum group. The representation theory of the braided quantum SU(2) will be discussed.

This is a joint work of Paweł Kasprzak, Ralf Meyer, Sutanu Roy and myself.

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

Lyonell Boulton (Department of Mathematics, Heriot-Watt University, Edinburgh)

Bounds for the eigenvalues of the angular Kerr—Newman Dirac operator

In this talk I will describe how to compute sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients. My main concern will be the angular Kerr—Newman Dirac operator with the possible addition of a smooth perturbation. For the unperturbed model I will show how to validate existing benchmarks as well as how to sharpen them by several orders of magnitude. As a main tool I will employ a pollution-free Galerkin-type method known as the quadratic method. The research is based on recent joint work with Monika Winklmeier.

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

Michał Wrochna (CNRS, Institut Fourier, Grenoble)

Construction of pure states from characteristic Cauchy data

For the Klein–Gordon equation one formulates a characteristic Cauchy problem by specifying as initial datum the restriction to a lightcone. I will demonstrate how such characteristic Cauchy problem (also called Goursat problem) can be solved in the inside of a cone in a globally hyperbolic spacetime for data in adapted Sobolev spaces. I will then review applications in Quantum Field Theory, where one is interested in constructing solutions with a specific wave front set. (This is joint work with Christian Gérard.)

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

Szymon Charzyński (KMMF WFUW)

Równania Weia–Normana dla grup klasycznych

The Wei–Norman equations for classical groups

Równania Weia–Normana są równoważne równaniu ewolucji na grupie Liego i w niektórych przypadkach pozwalają znaleźć rozwiązanie. Okazuje się, że w przypadku równań na prostej klasycznej grupie Liego, równania Weia–Normana mogą być zredukowane do hierarchii macierzowych równań Riccatiego. Redukcję tę można uzyskać wybierając odpowiednio generatory algebry Liego i kolejność ich eksponentów w podstawieniu Weia–Normana. Przypadek grupy unitarnej jest szczególnie istotny z punktu widzenia mechaniki kwantowej. Dla tego przypadku rozpatruje się kompleksyfikację grupy unitarnej i jej algebrę Liego sl(|N;|C). Wyniki te nie uogólniają się na wszystkie proste algebry Liego, w szczególności na algebrę wyjątkową g₂.

The non-linear autonomous Wei–Norman equations are equivalent to a linear system of non-autonomous equations on a Lie group and in some cases provide a method to find the solution. In case of all classical simple Lie groups, they can be reduced to a hierarchy of matrix Riccati equations. This is achieved by an appropriate choice of generators of the Lie algebra and of the order of their exponentials in the solution provided by the Wei–Norman method. The unitary case, of particular significance for quantum optimal-control problems, fits into this scheme by considering the complexification of the unitary group and its Lie algebra sl(|N;|C). The result cannot be extended to all simple Lie algebras, in particular to the exceptional algebra g₂.

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

Karol K. Kozłowski (CNRS, IMB, UB Dijon)

Asymptotic behaviour of multi-point correlation functions in massless one-dimensional models

We discuss a microscopic model-based setting that allows one to readily access the large-distance asymptotic behaviour of multi-point correlation functions. This setting relies on a limited number of hypotheses about the model's spectrum and form-factor expectation values of local operators between eigenvectors of the model'sHamiltonian. In particular, it holds for several one-dimensional quantum integrable models. However, in principle, it is much more general and thus applicable as well to non-integrable models. This is joint work with N. Kitanine, J.-M. Maillet and V. Terras.

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