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Faculty of Physics University of Warsaw > Events > Seminars > "Theory of Duality" (KMMF) Seminar
2020-06-11 (Thursday)
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B. Zawora (KMMF)

The Energy-Momentum Method (CANCELLED)

IMPORTANT: Due to technical problems, this seminar has been cancelled. For general information, we enclose the abstract of the cancelled seminar. In my talk, I will present the energy-momentum method, intended for studying stability and bifurcation of Hamiltonian systems with symmetries. First, I shall introduce some fundamental notions from symplectic geometry such as Hamiltonian actions of Lie groups and momentum maps. In particular, I will briefly discuss the Marsden-Weinstein theorem, which allows for reducing Hamiltonian systems with a particular type of symmetries to Hamiltonian systems on certain quotient spaces. Then, I will explain the conditions on the stability of these reduced systems. Finally, I will present the energy-momentum method and briefly describe how it can be applied. To attend our online seminar, please use the identificator for Google Meet: meet.google.com/bhs-jvxy-kcw
2020-06-04 (Thursday)
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T. Smołka (KMMF)

Geometric Approach to Heat Kernel

Classical methods of studying parabolic equations, based on finding the integral kernel of the heat semi-group with the help of the Synge functions, will be discussed. Unlike in my last year's talk, I plan to focus on geometric aspects of objects that occur in the construction, rather than on a detailed presentation of the method itself. To join our online seminar, please use the identificator for Google Meet: meet.google.com/zgx-fdsa-nmd
2020-05-28 (Thursday)
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J. Lange (KMMF)

A Geometric Road to Twisted Poisson Structures

n this talk, I will present an introduction to twisted Poisson structures. First, I will briefly survey Lie and Courant algebroids. I will illustrate both structures via Dirac structures. In a nutshell, a Dirac structure is a Lagrangian subbundle of a generalised tangent bundle satisfying that the space of sections taking values in the aforementioned subbundle is involutive relative to the Dorfman bracket. Following Weinstein and Severa, I will modify the Dorfman bracket via a 3-form, and I will discuss conditions guaranteeing that our modified structure remains a Courant algebroid. In the end, I will define twisted Poisson structures on a manifold and introduce a related Dirac-like structure associated with a modified Dorfman bracket. To attend our online seminar, please use the meeting identificator for Google Meet meet.google.com/puj-xgzv-eiu
2020-05-21 (Thursday)
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M. Napiórkowski (KMMF)

Freeman J. Dyson, the Maker of Patterns

Freeman J. Dyson, arguably one of the greatest theoretical and mathematical physicists of the 20th century, sadly passed away three months ago. In my talk I will review some of the (many) achievements and contributions of Dyson to the field of mathematical physics, mostly from the perspective quantum theory and statistical mechanics. To join the seminar, please use the Hangouts Meet link: meet.google.com/puj-xgzv-eiu
2020-05-14 (Thursday)
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Bartłomiej Bąk (KMMF)

A contribution to the unification of gravity and electromagnetism

In this talk, I shall introduce the affine formulation of general relativity. First, I will present a toy-model illustrating the main features of the formulation. After that, I will define the geometrical objects appearing in the formalism. Then, I will briefly depict the fundamentals of electrodynamics in curved spacetimes. All these ideas will be the background for the unification of gravity and electromagnetism, which is the essence of this talk. To take part in our online seminar, please use the Hangouts Meet link: meet.google.com/qcy-swbt-sjy
2020-05-07 (Thursday)
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Piotr Kucharski (IFT)

Knots-quivers correspondence

In this talk I will introduce the relation between knots and quivers,which is proven for all arborescent knots and conjectured to hold ingeneral case. I will also discuss its geometric and physicalinterpretations in terms of holomorphic disks and BPS states. To take part in our online seminar, please use the Hangouts Meet link: meet.google.com/res-wbuu-ykj
2020-04-30 (Thursday)
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Daniel Wysocki (KMMF)

Introduction to Poisson-Lie groups and Lie bialgebras

The goal of this talk is to briefly introduce the basic theory ofPoisson--Lie groups and Lie bialgebras. Both notions (and otherfundamental concepts) will be discussed and relevant results, showing their interplay, will be proven. To attend our online seminar please use the Hangours meeting identificator meet.google.com/res-wbuu-ykj
2020-04-23 (Thursday)
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Piotr Waluk (KMMF)

Quasi-local mass of weak gravitational field

Assigning a "mass" or "energy" value to a gravitational field is asurprisingly difficult task. It is, in fact, still an open problem. Iwill discuss some of the difficulties that arise there and presentrecent results that Jacek Jezierski and I obtained in the linearizedtheory. We hope that insight gained from the approximated model canpoint us in the right direction in the search for a solution of thegeneral problem.Please join our online seminar at Hangouts using the link:meet.google.com/xdd-ejkz-vmw
2020-04-16 (Thursday)
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M. Wiatr (KMMF)

Funkcje Theta Jacobiego

Jacobi Theta Functions

Funkcje theta Jacobiego, to szczególne funkcje zespolone, posiadające ciekawe właściwości. Dzięki nim, pojawiają się one w zupełnie niezwiązanych ze sobą dziedzinach matematyki i fizyki. W sposób naturalny wyrastają one z funkcji eliptycznych, o których miałem przyjemność mówić rok temu na tym seminarium. Ten referat będzie kontynuacją owego wystąpienia. Przybliżę pokrótce definicje i podstawowe własności funkcji theta i wskażę ich związek z równaniami różniczkowymi fizyki oraz teorią funkcji modularnych. Link do spotkania zdalnego na Hangouts: https://meet.google.com/res-wbuu-ykj?hs=122&authuser=2

Jacobi theta functions form a class of complex functions showing remarkable features. Such properties make Jacobi theta functions to appear in different, completely unrelated, disciplines inmathematics and physics. In a natural manner, Jacobi theta functions appear as an extension of elliptic functions, which I discussed a year ago in this seminar. My present presentation will be a continuation of that seminar. In particular, I will briefly survey the definition and basic properties of the Jacobi theta function and I will show its relations to differential equations and the theory of modular functions. Link to the remote meeting in Hangouts: https://meet.google.com/res-wbuu-ykj?hs=122&authuser=2
2020-03-12 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Piotr Kucharski (IFT)

Knots-quivers correspondence (seminar cancelled)

In this talk I will introduce the relation between knots and quivers, which is proven for all two-bridge knots and conjectured to hold in general case. I will also discuss its geometric and physical interpretations in terms of holomorphic disks and BPS states.
2020-03-05 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
M. Nieszporski (KMMF)

Całkowalne układy równań różnicowych w dwóch zmiennych niezależnych zdefiniowanych na krawędziach grafu $\mathbb{Z}^2$

Integrable two-component systems of difference equations defined on the edges of the $\mathbb{Z}^2$ graph

In the first part of the talk I will give tendentious introduction todiscrete integrable systems. In the second part of the talkI will present two lists of two-component systems of integrable difference equations defined on the edges of the $\mathbb{Z}^2$ graph. The systems of difference equations give us in turn quadrirational Yang-Baxter maps. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatibility of these systems. Imposing constraints consistent with the systems of difference equations, I recover known integrable quad-equations including the discrete version of the Krichever-Novikov equation.
2020-02-27 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Anatol Odzijewicz (Uniwersytet w Białymstoku)

Struktury Poissonowski w modularnej teorii Tomity-Takesaki

Poisson geometrical aspects of the Tomita-Takesaki modular theory

Przedstawimy struktury geometryczne: grupoidy i algebroidy Banacha-Liego oraz grupoidy poissonowskie związane w sposób kanoniczny z dowolną $W^*$-algebrą $\mathfrak{M}$ (algebrą von Neumanna). Pokażemy również, że standardowa realizacja $(\mathfrak{M},\mathcal{H},J,\mathcal{P})$ $W^*$-algebry odpowiada naturalnej foliacji przestrzeni Hilberta $\mathcal{H}$ wyposażonej w bogatszą strukturę $\tilde{\mathcal{H}}$ rozmaitości Banacha. Opiszemy strukturę $(\tilde{\mathcal{H}}, \tilde{\omega})\rightrightarrows\mathfrak{M}^+_*$ grupoidu presymplektycznego nad przestrzenią stanów normalnych $\mathfrak{M}^+_*$ algebry von Neumanna $\mathfrak{M}$. Pokażemy, że grupoid Banacha-Liego $(\tilde{\mathcal{H}}, \tilde{\omega})\rightrightarrows\mathfrak{M}^+_*$ jest izomorficzny z grupoidem działania $\mathcal{U}(\mathfrak{M})*\mathfrak{M}_*^+\rightrightarrows\mathfrak{M}^+_*$, gdzie $\mathcal{U}(\mathfrak{M})\rightrightarrows \mathcal{L}(\mathfrak{M})$ jest grupoidem Banacha-Liego częściowych izometrii nad kratą projekcji ortogonalnych $\mathcal{L}(\mathfrak{M})$.

We investigate some genuine Poisson geometric objects in the modular theory of an arbitrary von Neumann algebra $\mathfrak{M}$. Specifically, for any standard form realization $(\mathfrak{M},\mathcal{H},J,\mathcal{P})$, we find a canonical foliation of the Hilbert space $\mathcal{H}$, whose leaves are Banach manifolds that are weakly immersed into~$\mathcal{H}$, thereby endowing $\mathcal{H}$ with a richer Banach manifold structure to be denoted by~$\widetilde{\mathcal{H}}$. We also find that $\widetilde{\mathcal{H}}$ has the structure of a Banach-Lie groupoid $\widetilde{\mathcal{H}}\rightrightarrows\mathfrak{M}_*^+$ which is isomorphic to the action groupoid $\mathcal{U}\mathfrak{M})\ast\mathfrak{M}_*^+\rightrightarrows\mathfrak{M}_*^+$ defined by the natural action of the Banach-Lie groupoid of partial isometries $\mathcal{U}(\mathfrak{M})\rightrightarrows\mathcal{L}(\mathfrak{M})$ on the positive cone in the predual $\mathfrak{M}_*^+$, where $\mathcal{L}(\mathfrak{M})$ is the projection lattice of $\mathfrak{M}$. There is also a presymplectic form $\widetilde{\omega}\in\Omega^2(\widetilde{\mathcal{H}})$ that comes fom the scalar product of $\mathcal{H}$ and is multiplicative in the usual sense of finite-dimensional Lie groupoid theory. We further show that the groupoid $(\widetilde{\mathcal{H}},\widetilde{\omega})\rightrightarrows \mathfrak{M}_*^+$ shares several other properties of finite-dimensional presymplectic groupoids and we investigate the Poisson manifold structures of its orbits as well as the leaf space the foliation defined by the degeneracy kernel of the presymplectic form $\widetilde{\omega}$.
2020-01-23 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
M. Kolanowski (IFT)

Scattering amplitudes from ambitwistors

The talk shall be gentle introduction into some advances in twistor theory from an outsider's point of view. After a short review of recent ideas and trends in the field, we will focus on a topic of scattering amplitudes and how to obtain them in a relatively straightforward manner from a higher dimensional generalization of twistors (so--called ambitiwistors) combined with a conformal field theory.
2020-01-16 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Miłosz Panfil (IFT)

Quantum Integrability in Condensed Matter

Quantum Integrable models play nowadays a prominent role in understanding strongly correlated low-dimensional quantum physics. The models that were once a mathematical curiosity, thanks to the advent in experimental methods, turned out to be actually useful. Their usefulness however goes beyond direct modelling of physical phenomena. They also help us with understanding problems of fundamental nature, concept of thermalization being one prominent, and recently explored, example. My talk will be roughly divided in two parts. In the first part I will try to present the (inevitably biased) state of art on the interplay between quantum integrability and condensed matter. In the second part, I will discuss our new contribution to this area, the Thermodynamic Bootstrap Program.
2019-12-12 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Katja Sagerschnig (CFT PAN)

Parabolic geometries and the exceptional group G_2

I will give an introduction to a class of geometric structures known as parabolic geometries: these are Cartan geometries modelled on homogeneous spaces of the from G/P, where G is a semisimple Lie group and P is a parabolic subgroup. The most prominent example of a parabolic geometry is conformal geometry in dimension >2; the symmetry group G of the flat homogeneous model in this case is the conformal group. A more exotic but still classical example is the geometry of (2,3,5) distributions, which is related to the exceptional simple Lie group G=G_2. In this talk I will review some history, explain how the Lie group G_2 appears in this context, and discuss recent developments in the field.
2019-12-05 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Henryk Żołądek (MIMUW)

Invariants of group actions, dimension/degree duality and normal forms of vector fields

We develop a constructive approach to the problem ofpolynomial first integrals for linear vector fields. As an applicationwe obtain a new proof of the theorem of Wietzenbock about finiteness ofthe number of generators of the ring of constants of a linearderivation in the polynomial ring. Moreover, we propose an alternativeapproach to the analyticity property of the normal form reduction of agerm of vector field with nilpotent linear part in a case considered byStolovich and Verstringe.
2019-11-28 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Jan Skowron (OAUW)

Trójwymiarowa mapa Drogi Mlecznej na podstawie cefeid klasycznych

A three-dimensional map of the Milky Way using classical Cepheid variable stars

Droga Mleczna jest galaktyką spiralną. Wiemy to z obserwacji radiowych gazu galaktycznego, ze zliczeń gwiazd, a także na podstawie podobieństwa do struktur obserwowanych w innych galaktykach. Jednakże są to metody pośrednie, a pomiary odległości do wspomnianych obiektów są oparte na rozmaitych założeniach. Dodatkową trudnością w stworzeniu mapy dysku naszej Galaktyki jest fakt, że obserwujemy go od wewnątrz poprzez obłoki gazu i pyłu. To wszystko sprawia, że dokładny obraz Drogi Mlecznej jest nadal tematem dyskusji.Istnieją jednak szczególne obiekty, których odległości mogą być zmierzone bezpośrednio oraz z dużą dokładnością. Są to młode gwiazdy pulsujące zwane cefeidami klasycznymi. W takcie wykładu pokażę jak wykorzystaliśmy próbkę tych gwiazd aby stworzyć nową, dokładną mapę Drogi Mlecznej w trzech wymiarach oraz opowiem o kształcie i historii dysku naszej Galaktyki.

The Milky Way is a spiral galaxy. This is inferred from various methods, suchas radio observations of Galactic gas, star counts, as well as from ourextrapolation of structures seen in other galaxies. However, these methodsare indirect and rely on many assumptions. Precise mapping of the Milky Wayis also difficult because we may only observe it from the inside throughclouds of gas and dust. In result, the exact picture of our Galaxy is stillunder debate.However, distances can be accurately measured to Classical Cepheids, whichare young pulsating variable stars. I will present a new comprehensive pictureof our Galaxy in three-dimensions based on the positions in the sky andprecisely measured distances of thousands of these objects.
2019-11-21 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Alexander Stottmeister (University of Munster)

Operator-algebraic renormalization and wavelets

I will discuss some on-going work with V. Morinelli, G. Morsella and Y. Tanimoto on an operator-algebraic approach to the Wilson-Kadanoffrenormalization group. I will explain how the theory of wavelets canbe utilized to implement this approach in the setting of scalar fieldtheories.
2019-11-14 (Thursday)
room 1.40, Pasteura 5 at 10:15  Calendar icon
Sabrina Pasterski (Princeton Center for Theoretical Science)

Implications of superrotations

The asymptotic symmetry algebra of asymptotically flat spacetimes implies an infinity of conserved charges for 4D scattering which can be neatly recast as 2D conformal Ward identities. We cover recent progress on the proposed 4D/2D dictionary starting from the conformally soft modes that appear as currents and extending our map to a basis for finite energy scattering states.
2019-11-07 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Latham Boyle (Perimeter Institute)

The standard model of particle physics, its Pati-Salam extension, and "Jordan geometry”

We argue that the ordinary commutative-and-associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in noncommutative geometry), but rather by a Jordan algebra of Hermitian operators (leading to a framework which we term "Jordan geometry"). We present the Jordan algebra (and representation) that most nearly describes the standard model of particle physics, and we explain that it actually describes a certain (phenomenologically viable) extension of the standard model: by three right-handed (sterile) neutrinos, a complex scalar field phi, and a U(1)_{B-L} gauge boson which is Higgsed by phi. We then note a natural extension of this construction, which describes the Pati-Salam model of unification. Finally, we discuss a simple and natural Jordan generalization of the exterior algebra of differential forms.
2019-10-31 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Piotr Stachura (SGGW)

Semiklasyczna granica kwantowej Grupy Poincarego

Semiclassical limit of the quantum Poincare group

Pokażę geometryczną konstrukcję struktury Poissona-Liego na GrupiePoincarego opisanej przez S. Zakzewskiego w 1994. Opowiem, dlaczego grupa kwantowa zdefiniowana przez pewien iloczyn bikrzyżowy może być uważana za deformację Grupy Poincarego.

I will portray a geometrical construction of a Poisson Lie structure on the Poincare Group described by S. Zakrzewski in 1994. I will explain why the quantum group described by a certain bi-cross product can be understood as a deformation of the Poincare Group.
2019-10-24 (Thursday)
room 2.23, Pasteura 5 at 10:30  Calendar icon
Richard Kerner (Sorbonne University)

The Z3-graded extension of the Poincaré algebra

A Z3 symmetric generalization of the Dirac equation was proposed in recent series of papers, where its properties and solutions discussed. The generalized Dirac operator acts on "coloured spinors" composed out of six Pauli spinors, describing three colours and particle-antiparticle degrees of freedom characterizing a single quark state, thus combining Z2 x Z2 x Z3 symmetries of 12-component generalized wave functions. Spinorial representation of the Z3-graded generalized Lorentz algebra was introduced, leading to the appearance of extra Z2 x Z2 x Z3 symmetries, probably englobing the symmetries of isospin, flavors and families. The present article proposes a construction of Z3-graded extension of the Poincaré algebra. It turns out that such a generalization requires introduction of extended 12-dimensional Minkowskian space-time containing the usual 4-dimensional space-time as a subspace, and two other mutually conjugate "replicas" with complex-valued vectors and metric tensors. Representation in terms of differential operators and generalized Casimir operators are introduced and their symmetry properties are briefly discussed.
2019-10-17 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Wojciech Dybalski (Technical University of Munich)

Bisognano-Wichmann property in algebraic QFT of massless particles

In algebraic QFT the Bisognano-Wichmann property allows tocompute the Lorentz boosts from algebras of observables with the help of the Tomita-Takesaki theory. Among other applications, this property enters as an assumption in modern CPT theorems. However, there are still many open questions concerning its status in the Haag-Kastler setting. In this talk, I will present aproof of the Bisognano-Wichmann property for asymptotically completeHaag-Kastler theories of massless particles. These particles shouldeither be scalar or appear as a direct sum of two opposite integer helicities.Thus, e.g., photons are covered. The argument uses results from the theory of induced representations of groups, such as the Mackey subgroup theorem, and Buchholz’ scattering theory of massless particles. (Joint work with V. Morinelli).
2019-10-10 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
P. Nurowski (CFT)

Parabolic geometries and a car

I will discus prime examples of parabolic geometries and show that they appear naturally in nonholonomic mechanics.
2019-10-03 (Thursday)
room 2.23, Pasteura 5 at 10:15  Calendar icon
Piotr Sołtan (KMMF)

Algebra grupowa grupy wolnej

Group algebra of the free group

Opowiem o C*-algebrze związanej z reprezentacją regularną grupy wolnej o dwóch generatorach. W szczególności udowodnię, że jest ona prosta i ma dokładnie jeden stan śladowy.

I will talk about the C*-algebra associated with the regular representation of the free group on two generators. In particular I will prove that it is simple and has a unique tracial state.
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