Faculty of Physics University of Warsaw > Events > Seminars > "Theory of Duality" (KMMF) Seminar

"Theory of Duality" (KMMF) Seminar

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room 2.23, Pasteura 5 at 10:15

Jarosław Wiśniewski (IM MIMUW)

Algebraic models of phylogenetic trees

Using the language of algebraic statistics one can describe Markov processes on tree-like graphs in terms of geometric objects, algebraic models of phylogenetic trees. I will consider phylogenetic trees arising from the binary isotropic model of evolution and their puzzling relations to objects emerging from other branches of mathematics.

room 2.23, Pasteura 5 at 10:15

Andrzej Weber (MIMUW)

Uniwersalna charakterystyka Eulera i twierdzenie o lokalizacji dla działania torusa

Universal Euler characteristics and localization theorem for torus action

I will discuss "motivic" invariants of complex algebraic manifolds. Such invariants satisfy the so-called scissor relation, just like the usual topological Euler characteristic. Motivic invariants are well defined on the Grothendieck ring of complex varieties and can be generalized to the singular spaces. Among motivic invariants which are expressed by Chern classes there exists a universal one. This is the Hirzebruch χy-genus. In a situation when the multiplicative group |C* acts on an algebraic variety, we apply localization theory. We express the global χy-genus in terms of local contributions coming from the fixed-point set. The resulting decomposition of the χy-genus specializes to the decomposition arising from the Białynicki-Birula plus-decomposition.

room 2.23, Pasteura 5 at 10:15

dr hab. Katarzyna Grabowska (KMMF)

Introduction to graded bundles

We shall review the concept of a graded bundle as a natural generalisation of a vector bundle. One of the reasons we are interested in such geometry is that there are many examples of graded bundles that appear in the existing literature, but their graded structure is not always taken inot account. We start with a discussion of graded spaces, passing through graded bundles and their linearisation, to end with weighted (graded) Lie groupoids/algebroids.

room 2.23, Pasteura 5 at 10:15

prof Bronisław Jakubczyk (IM PAN)

Pontryagin Maximum Principle, optimal control and geodesics on sub-Riemannian manifolds

We will state the Pontryagin Maximum Principle (PMP) and show some of itsconsequences. As a first order necessary condition for optimalityit allows finding extremals in optimal control problems. It is also a basic tool for analyzing their properties. In the second part of the seminar we intend to describe some fundamentalnotions and facts in sub-Riemannian geometry. Applying PMP we will brieflydescribe the structure of geodesics, especially of abnormal ones which do not appearin Riemannian geometry.

room 2.23, Pasteura 5 at 10:15

Jacek Wojtkiewicz (KMMF)

O Ansatzu Bethego słów kilka

Introduction to Bethe Ansatz

Weź wyrazu BABA pół.BA stoi tam jak wół.Czyli PÓŁBABEK = BA,zatem więź Dusiołka z Bethe Ansatzem została ustanowiona,gdyż półbabka, z łoża się gramolącego,Leśmian porównał do Dusiołka z rowu wyłażącego;Zatem bliskość Leśmiana oraz Bethego została udowodniona.Nie mam złudzeń, że Cię, Czytelniku, ta argumentacja przekona.Ale jedynie dla jaj ten piętrowy absurd został zapodany,Bo na seminarium temat Bethe Ansatzu zostanie dość techniczne potraktowany,więc, jako antidotum na ilość wzorków i przynudzanie,gwoli rozrywki (?) takie wstępne podsuwam danie.

Some introductory informations concerning Bethe Ansatz technique will be given.An example how it works will be given using XXZ Heisenbergone-half spin chain as an illustration.

room 2.23, Pasteura 5 at 10:15

Krzysztof Wohlfeld (IFT, WF UW)

Orbitons in solids: from experimental observation to theoretical understanding

In contrast to many "ordinary" metals or band insulators, in the case of transition metal oxides the Coulomb interaction between electrons cannot be easily neglected. As a consequence understanding such systems constitutes a challenge for theorists. At the same time, however, this many-body physics leads to a number of interesting phenomena that can be found in these compounds -- such as e.g. high temperature superconductivity, magnetic or orbital ordering, or the existence of more or less exotic quasiparticles (spinons, triplons, magnons, etc.).In this talk I will give a pedagogical introduction to the physics of one of such quasiparticles -- an "orbiton", i.e. a collective excitation in a solid carrying an orbital quantum number. While orbitons had been predicted by theory decades ago, their first unambiguous experimental observation took place only four years ago. Moreover, it has occurred that understanding the properties of the orbiton lead to the introduction of the concept of a separation of electron's spin and orbital quantum numbers.

room 2.23, Pasteura 5 at 10:15

Ivona Grzegorczyk (CSUCI, Camarillo, USA)

Stable holomorphic vector bundles on Riemann surfaces

We study moduli spaces of stable (in the sense of geometric invariant theory) vector bundles on Riemann surfaces. We report on the current state of the Brill—Noether problem that classifies bundles with global sections (i.e. non-trivial vector fields). We show various examples (including Higgs bundles), calculations of numerical invariants and specific bundle constructions

room 2.23, Pasteura 5 at 10:15

prof. Bohdan Grządkowski (IFT, WF UW)

Puzzles of the Standard Model

The Standard Model for electroweak interactions is challenged by experimental evidence andtheoretical prejudice. I am going to present the current status and review simplest solutions.

room 2.23, Pasteura 5 at 10:15

Maciej LASEK (MEiI PW)

Metody odtwarzania przebiegu wypadków lotniczych

Jednym z kluczowych elementów w badaniu wypadków lotniczychjest odtworzenie krytycznej fazy lotu, a w szczególnościtrajektorii lotu samolotu i jej powiązanie z pracą systemówsamolotu oraz działaniem załogi. Dopiero na tej podstawiemożna ocenić pracę załogi w sytuacji kryzysowej i jej reakcjena błędy w wykonaniu lotu lub niesprawność systemów samolotu,a wynik takich analiz stanowi podstawę do zaproponowaniazaleceń w celu poprawy bezpieczeństwa wykonywania operacjilotniczych.Z uwagi na różnorodność statków powietrznych ulegającychwypadkom, specjaliści zajmujący się badaniem wypadków niezawsze mają do dyspozycji zapisy parametrów lotu lub głosóww kabinie tak jak w przypadku dużych samolotów komunikacyjnych.W takich sytuacjach niekiedy jedynym dowodem wskazującymna przebieg wypadku są oględziny statku powietrznegolub subiektywne źródła informacji takie jak zeznania świadków.Nawet jeżeli samolot jest wyposażony w urządzenia rejestrująceto, pomimo minimalnych wymagań stawianych takim urządzeniom,odtworzenie trajektorii lotu na podstawie zapisów nie zawszemożliwe jest z dużą dokładnością i bardzo często wymagaweryfikacji i uzupełnienia o informacje z innych źródeł, np.śladów zderzenia samolotu z przeszkodami, zeznań świadkówlub zapisu z urządzeń radarowych służb kontroli ruchu lotniczego.W bardzo wielu przypadkach prawidłowe przedstawienie ciągu zdarzeń,który doprowadził do wypadku, silnie zależy też od doświadczeniaosób badających taki przypadek.W wystąpieniu przedstawione zostaną przykłady odtwarzania ciąguzdarzeń w zależności od rodzaju statku powietrznego i ilościdostępnych danych.

room 2.23, Pasteura 5 at 10:15

Piotr Sułkowski (WF UW)

Dwa plus cztery równa się sześć

Two plus four is equal to six

I will summarize properties of a number of exactly solvablequantum field theories in various dimensions – in particulartwo-dimensional conformal field theories, and four-dimensionalsupersymmetric gauge theories – and discuss dualities between thesetheories, originating from various compactifications of the theory ofM5-branes.

room 2.23, Pasteura 5 at 10:15

Paweł Jakubczyk (IFT, WF UW)

The imperfect Bose gas in d dimensions: criticality and Casimir forces

I will present the imperfect Bose gas as an exactly soluble model displaying Bose-Einstein condensation in dimensionality d>2. After discussing its bulk phase diagram, I will review finite-size effects and the related Casimir-type interactions between the system boundaries.

room 2.23, Pasteura 5 at 10:15

prof. Stanisław L. Woronowicz (KMMF)

Passive states of quantum systems

In the algebraic quantum theory we know a few properties characterising equilibrium states. These are KMS-condition, stability and passivity. Passivity is the property suggested by second law of thermodynamics. By definition a quantum system is in a passive state if it is unable to perform a work in any cyclic adiabatic process. I shall give mathematical formulation of this property and discuss its implications. In particular the relation between passivity and KMS-condition will be discussed. As an application the famous Carnot formula for the efficiency of heat engines will be derived. (Based on joint paper with W. Pusz)

room 2.23, Pasteura 5 at 10:15

prof. Stefan Pokorski (IFT WFUW)

Particle physics after the discovery of the Higgs boson

I shall review the impact of the Higgs discovery on the present state of particle physics and on the directions of the future research.

room 2.23, Pasteura 5 at 10:15

Paweł Kasprzak (KMMF WF UW)

Induced representations of locally compact groups

Induction is a technique yielding a large class of unitary representations of a given locally compact group G. It was used by Harish-Chandra in his theory of unitary representations of semisimple Lie groups. In my talk I will present the construction of representation of G which is induced from a representation of a closed subgroup H of G and discuss the main properties of the induction procedure. The example of the principal series of representations ofSL(2,C) will be presented. Then I will formulate the imprimitivity theorem characterising the class of induced representations of a given locally compact group and sketch its proof. The imprimitivity result will be linked with the Stone - von Neumann theorem and if time permits I will express the imprimitivity in terms of the Morita context assigned to a closed subgroup H of G. I will not say anything about the quantum version of the induction procedure which we are elaborating on with Kalantar, Skalski and Sołtan.

room 2.23, Pasteura 5 at 10:15

Piotr Waluk (KMMF)

The Ricci flow

The Ricci flow is a technique for analyzing Riemannian manifolds by evolving their metric with respect to a certain differential equation. The method was first introduced by Hamilton in his paper form 1982, as a means to solve a problem concerning classification of 3-dimensional compact manifolds. My talk will be a short introduction to the topic of the Ricci flow, explaining its basic ideas and illustrating them with some application examples.

room 2.23, Pasteura 5 at 10:15

prof. Krzysztof A. Meissner (IFT, WFUW)

Structure of the Standard Model

I will present main building blocks of the Standard Model discussing in particular the generation structure (Cabibbo-Kobayashi-Maskawa matrix) and the uniqueness of charge assignments stemming from chirality and vanishing of gauge anomalies.

room 2.23, Pasteura 5 at 10:15

Wojciech Pacuski (IFD, WF UW)

Pojedyncze domieszki magnetyczne

Single magnetic impurities

Opiszę metody technologiczne i spektroskopowe pozwalające na badanie pojedynczych domieszek magnetycznych w półprzewodnikach: wzrost kryształów przy pomocy epitaksji z wiązek molekularnych, spektroskopię optyczną pojedynczych kropek kwantowych, obserwację oddziaływania pojedynczego jonu magnetycznego z nośnikami w kropce kwantowej. Pokażę najnowsze wytworzone przez nas systemy i zaobserwowane dzięki nim zjawiska takie jak zmiana własności magnetycznych pod wpływem naprężenia kryształu, optyczna orientacja spinu jonu magnetycznego, koherentna precesja Larmora pojedynczego jonu magnetycznego.

room 2.23, Pasteura 5 at 10:15

Piotr M. Sołtan (KMMF)

Przestrzenie Operatorowe i Transpozycja

Operator Spaces and Transposition

Opiszę podstawy teorii przestrzeni operatorowych zwanej także "nieprzemienną analizą funkcjonalną". Pokażę też jak wprowadzony w ramach tej teorii język pozwala przeprowadzić analizę odwzorowania transpozycji macierzy.

I will describe theory of operator spaces, called also the 'non-commutative functional analysis'. I will also show how the language introduced within the framework of this theory allows to perform the analysis of the matrix transposition map.

room 2.23, Pasteura 5 at 10:15

Krzysztof Gawędzki (CNRS, ENS LYON)

Topological Invariants of Periodically Forced Crystals

I shall review a recent construction of invariantscharacterizing topological phases of crystals undergoinga time-periodic perturbation.

room 2.23, Pasteura 5 at 10:15

Daniel Siemssen (KMMF)

Classical Electrodynamics in Linear Media

In most generality, Maxwell's field equations are given as dH=J and dF=0, where H (field excitation) and F (field strength) are 2-forms and J (charge) is a 3-form, together with a constitutive law H=#(F) relating H and F. I will motivate these equations, following roughly the axiomatic approach of Hehl and Obukhov (among others). Setting #=* (Hodge star operator) one obtains Maxwell's equations in vacuum, but more general choices describing inhomogeneities, anisotropies, dispersion, non-linearities and non-local effects are possible (e.g. birefringent media, Born–Infeld theory, Bopp–Podolsky theory, ...). In my talk I will consider only local, linear, non-dispersive constitutive laws; this includes in particular birefringent media. Under these assumptions, I will study solutions of the field equations by deriving propagators for the equation d#dA=J.

room 2.23, Pasteura 5 at 10:15

Jacek Pawełczyk (IFT, WFUW)

Supersymetria vs. cząstki elementarne

Supersymmetry vs. elementary particles

I shall describe various attempts of use of supersymmety in ParticlePhysics. They range from the standard extensions of the existingStandard Model to some exotic Supergravity proposals.

room 2.23, Pasteura 5 at 10:15

Adrian Langer (IM PAN)

Mirror Symmetry (without physics) and Geometric Langlands (without theorems)

The talk will be a general account of Mirror Symmetry (from a purely mathematical point of view) and its relations to the geometric Langlands conjecture. I will concentrate on some simple cases related to a particularly simple class of hyper-Kähler varieties, namely moduli spaces of flat bundles on curves. In this case, Mirror Symmetry predicts various conjectures, e.g., on invariants of the moduli spaces of flat bundles. I will talk about some partial results, using various approaches ranging from non-abelian Hodge theory to calculations involving counting of points of varieties defined over finite fields.

room 2.23, Pasteura 5 at 10:15

Piotr Waluk (KMMF)

A curious property of near-horizon geometry

For every extremal black hole (in any dimension) there exists a well-defined notion of its near-horizon geometry. I will present the derivation and discuss some incentives that motivate investigation of this concept. I will also show that every near-horizon geometry allows a foliation consisting entirely of Killing horizons, a property that seems to have passed unnoticed until now.

room 2.23, Pasteura 5 at 10:15

Jacek Wojtkiewicz (KMMF)

Wersja twierdzenia Mermina-Wagnera dla temperatury zerowej

Mermin-Wagner theorem for zero temperature

Gdy d=1 i 2 układy sieciowe ciągłą symetrię wykazują,To się w dodatniej temperaturze nie porządkują.Pokazuje to twierdzenie Mermina - Wagnera znane,Doceniane, > 2 x 10^3 razy cytowane,oraz w różnych kierunkach uogólniane.Gdy układy ponadto przerwę energetyczną mają,To i w stanie podstawowym uporządkowania nie przejawiają.Treścią seminarium uczynić chcę tego przedstawienie,oraz wzmiankę, że ma to znikome praktyczne znaczenie.

The celebrated Mermin - Wagner theorem tells that lattice systems in one and two dimension, and with continuous symmetry group, does not exhibit the Long Range Order at positive temperatures. Such systems can or can not order in the ground state. In my talk, I will show one of extensions of the M-W theorem (after Auerbach et al.), i.e. that the existence of the energy gap over the ground-state implies lack of ordering also in the ground state.

room 2.23, Pasteura 5 at 10:15

Jurij Tomiłow

Wokół indeksu Wittena

Indeks Wittena operatora liniowego został wprowadzony w latach 80-ch przez Gesztesy'ego, Simona, Grosse'go i innych jako pewna regularyzacja indeksu Fredholma, służąca do badania pewnych operatorów nie będących operatorami Fredholma. Wciąż pytania, w jakim stopniu indeks Wittena jest podobny do indeksu Fredholma i czy (i kiedy) jest niezmiennikiem przy naturalnych założeniach, pozostają bez odpowiedzi. Wykład będzie poświęcony opisowi postępów w tym kierunku związanych z użyciem funkcji przesunięcia spektralnego Kreina—Lifshitza.

room 2.23, Pasteura 5 at 10:15

Adam Latosiński (MPI für Gravitationsphysik, Potsdam, Deutschland)

Gauge covariant propagators: derivation and properties

The most commonly used metod of derivation of quantities in quantum field theory uses Feynman diagrams and Feynman propagators. Unfortunately, when applied to gauge theories, it mostly ignores the gauge symmetry, which becomes obscured at intermediate steps, and even in the final result it's not always visible. However, there exists a manifestly covariant way to make calculations within a quantum field theory, with the use of gauge field-dependent propagators instead of the free-field Feynman propagators.

I'm going to present a way to derive gauge field-dependent propagators in the form that can be used in perturbative calculations made with Feynman diagrams and to show how this form can make the derivation of the chiral anomaly quick and transparent, as well as the way it shows how certain regularizations break Ward identites.

room 2.23, Pasteura 5 at 10:15

Artur Sergyeyev (SU Opava)

New integrable systems in 3+1 dimensions from contact geometry

We introduce a new kind of nonisospectral Lax representation, contact Lax pair, related to contact geometry. The compatibility conditions for the contact Lax pairs yield a broad new class of (3+1)-dimensional integrable systems, thus demonstrating that such systems are considerably less exceptional than it was generally believed.

To illustrate our results, we present, inter alia, a new (3+1)-dimensional integrable system with an arbitrarily large finite number of components. In the simplest special case, this system yields a (3+1)-dimensional integrable generalization of the dispersionless Kadomtsev—Petviashvili equation.