SSDNM

wykłady

rok 2015

Uniwersytet Warszawski
Liczba wykładów: 2
Prelegent Piotr Zgliczyński (Instytut Informatyki Uniwersytetu Jagiellońskiego)
Tytuł Exact numerical metods
Termin 7 maja 2015
Wymiar godzin 5 godz.
Materiały skrypt 1, skrypt 2, skrypt 3
Prelegent Prof. Arieh Iserles (University of Cambridge)
Tytuł Lie-group methods in computational mathematics
Termin 9-10.III.2015
Wymiar godzin 3 godz.
Rozkład godzin poniedziałek: 14:15-15:45 sala 2180 wtorek: 14:15-15:45 sala 2180
Opis Experts in theoretical differential equations investigate their qualitative features, experts in computational differential equations flesh out numbers and approximate solutions. The new discipline of Geometric Numerical Integration attempts to bring these two traditions together, to develop and analyse discretisation methods which, by design, respect qualitative and structural features of the underlying differential equation. In this short course I will review the theory and practice of Lie-group methods: discretisation algorithms that respect a homogeneous manifold structure. I will present discretisation methods that preserve Lie-group actions: examples include differential equations evolving on spheres, tori, Stiefel and Grassmann manifolds, affine and symplectic groups. All such methods are based on lifting the underlying Lie group to its Lie algebra and discretising the equation there. I will commence from the very basics, defining Lie groups, Lie algebras and homogeneous manifolds. Next we will move to the linear (Magnus expansions and canonical coordinates of the second kind) and nonlinear (Runge.Kutta.Munthe-Kaas methods) worlds and to the approximation of the exponential from a Lie group to a Lie algebra using generalised polar decomposition. Time allowing, I will review briefly two recent applications of Lie-group methods, to the computation of spectra of compact Sturm.Liouville operators and to the discretisation of the Schrödinger equation in a semiclassical regime.
Materiały skrypt wykładu

Uniwersytet A. Mickiewicza w Poznaniu
Liczba wykładów: 3

Przydatne informacje na temat zakwaterowania w trakcie wykładów: pdf.

Prelegent prof. Vitali A. Strusevich (University of Greenwich, Wielka Brytania)
Tytuł Mathematical Methods of Modern Scheduling Theory
Termin 23-25.05.2015
Wymiar godzin 5 godzin
Materiały skrypt wykładu
Prelegent prof. Natan Kruglyak (Linkoping University, Szwecja)
Tytuł Near-minimizers, Covering Theorems and Applications
Termin 12-19.03.2015
Wymiar godzin 20 godzin
Opis Abstract A uni.ed method of constructing near-minimizers for certain important functionals arising in approximation, harmonic analysis and inverse problems and most widely used in interpolation theory are suggested. The constructions based on far-reaching re.nements of the classical Calderón-Zygmund decomposition. These new Calderón-Zygmund decompositions in turn are produced with the help of new covering theorems that combine many remarkable features of classical results establishes by Besicovitch, Whitney and Wiener. The course is divided in two parts. While the new method is presented in the second part (Lectures 9-10), the .rst (Lectures 1-8) is mainly devoted to the well-known results which are needed for self-contained presentation of the main topic. Course is mainly based on the book: S. Kislyakov and N. Kruglyak, Extremal problems in interpolation theory, Whitney-Besicovitch coverings, and singular integrals, Springer, 2013, 316 pp. Materials will be distributed to students during the lectures.
Materiały plan wykładu, skrypt wykładu
Prelegent prof. Józef Przytycki (George Washington University, USA)
Tytuł Adventures of Knot Theorist: From Fox 3-colorings to Yang-Baxter homology with the Jones polynomial and the Khovanov homology in a background
Termin 25-29.05.2015
Wymiar godzin 20 godzin
Materiały plan wykładu, skrypt wykładu

Uniwersytet M. Kopernika w Toruniu
Liczba wykładów: 2
Prelegent Wojciech Jamroga (Instytut Podstaw Informatyki Polskiej Akademii Nauk)
Tytuł Specyfikacja i weryfikacja własności za pomocą logiki
Termin 13.05, 10-13 i 15-17, sala S5
Wymiar godzin 5 godz.
Opis Tematem wykładu są różne logiki modalne, pozwalające na wyrażanie własności typu "A wie, że własność F jest spełniona", "F na pewno stanie się prawdziwe kiedyś w przyszłości", "A wie, że F stanie się prawdziwe" itp. Opowiem, jak wyglądają modele tych logik, jak interpretruje się formuły i w jaki sposób mogą one posłużyć do specyfikacji ciekawych własności systemów. Zaprezentuję również algorytmy weryfikacji modelowej - inaczej mówiąc, automatycznego sprawdzania, czy własność F zachodzi w zadanym modelu M.
Materiały skrypt wykładu
Prelegent Jerzy Kaczorowski (Uniwersytet im. Adam Mickiewicza w Poznaniu)
Tytuł Funkcja Möbiusa w teorii liczb
Termin 5 i 12.03.2015
Wymiar godzin 10 godz.
Rozkład godzin 05.03, 14-18, sala S5 12.03, 10-12 i 14-18, sala S5
Opis Celem tej serii wykładów będzie wprowadzenie do teorii funkcji multyplikatywnych, za szczególnym uwzględnieniem własności funkcji Möbiusa i funkcji Liouville'a. W szczególności przestawione zostaną dowody równoważności twierdzenia o gęstości liczb pierwszych ze zbieżnością do zera średnich funkcji Möbiusa (Liouville'a), jak również dowód hipotezy Riemanna przy założeniu prędkości zbieżności do zera średnich funkcji Möbiusa.
Materiały skrypt wykładu

Uniwersytet Jagielloński
Liczba wykładów: 7
Prelegent Brian Harbourne (University of Nebrasca-Lincoln)
Tytuł Fat points in P^2 and their applications
Termin 25-29 maja 2015
Wymiar godzin 10 godzin
Rozkład godzin Wykłady (WMiI UJ, ul. Prof. Stanisława Łojasiewicza 6, jeżeli nie zaznaczono inaczej): poniedziałek: 25.05, 12:15-13:45, s. 0006 wtorek: 26.05, 10:15-11:45, s. 119 (Instytut Matematyki UP, ul. Podchorążych 2) środa: 27.05, 16:00-18:00, s. 1009 czwartek: 28.05, 16:00-18:00, s. 1009 piątek: 29.05, 14:00-16:00, s. 1009
Biogram wkładowcy Professor B. Harbourne works in the areas of algebraic geometry and commutative algebra. His best known achievements concern fat subschemes in projective spaces. He is one of the authors of the well-known Segre-Harbourne-Gimigliano-Hirschowitz Conjecture, which is one of the central problems in the theory of linear series on algebraic surfaces.
Opis Abstract: Many problems in algebraic geometry come down to computing dimensions of complete linear systems of divisors on an algebraic variety X; i.e., to computing dimensions of global sections of line bundles on an algebraic variety X. An interesting and informative special case of this is when there is a birational morphism from X to P^2. In this case computing dimensions of global sections of line bundles on X is equivalent to computing Hilbert functions of ideals of fat point subschemes of P^2. This dual perspective allows one to bring to bear both geometric and algebraic methods for many problems of current research interest. We will use both perspectives to develop tools to explore a number of such problems which grow out of one fundamental open problem: what is the least degree of a plane algebraic curve with given singular points of specified multiplicity. Tentative references: Lecture 1: S. Cooper, B. Harbourne, Z. Teitler, Combinatorial bounds on Hilbert functions of fat points in projective space, Journal Pure and Applied Algebra 215:9 (2011), 2165-2179. AV. Geramita, B. Harbourne, J. Migliore, Hilbert functions of fat point subschemes of the plane: the two-fold way, Progress in Commutative Algebra, Proceedings in Mathematics, C. Francisco, L. Klingler, S. Sather-Wagstaff, JC. Vassilev (ed.), de Gruyter 2012, pp. 55-74. Lecture 2: T. Bauer, S. Di Rocco, J. Huizenga, A. Lundman, P. Pokora, T. Szemberg, Bounded negativity and arrangements of lines, to appear in: International Math. Res. Notices, arXiv:1407.2966. T. Bauer, P. Pokora, D. Schmitz, On the boundedness of the denominators in the Zariski decomposition on surfaces. Preprint, arXiv:1411.2431. Lecture 3: M. Dumnicki, B. Harbourne, U. Nagel, A. Seceleanu, T. Szemberg, H. Tutaj-Gasińska, Resurgences for ideals of special point configurations in PN coming from hyperplane arrangements. Preprint, arXiv:1404.4957. M. Lampa-Baczyńska, G. Malara, On the containment hierarchy for simplicial ideals. Preprint, arXiv:1408.2472.
Materiały skrypt wykładu
Prelegent Adam Parusiński (Université de Nice Sophia Antipolis)
Tytuł Equisingularity theory of analytic and algebraic set germs (Teoria ekwisingularności kiełków zbiorów analitycznych i algebraicznych)
Termin 13-20 maja 2015
Wymiar godzin 8 godzin
Rozkład godzin Wykłady (WMiI UJ, ul. Prof. Stanisława Łojasiewicza 6, sala 0006): środa: 13.05: 10:30-12:45, s. 0006 czwartek: 14.05: 10:30-12:45, s. 0006 środa: 20.05: 10:30-12:00, s. 0006
Biogram wkładowcy Born in 1959 in Gdańsk, he studied mathematics and worked at the Gdańsk University (1982-1990). In 1990-1992 he was a Professor at the Georgia University in Athens (USA). In 1992-1995 he worked at the Sydney University. In 1995-2009 he was a Professor of University of Angers (France). Since 2009 until now he is a Professor of Nice University. He is an outstanding specialist in algebraic and analytic geometry and singularity theory. He has written 60 papers in these areas. Among his results there is Lipschitz equisingularity of subanalytic sets, generalizing an earlier result of T. Mostowski concerning complex analytic sets, and a solution of the gradient conjecture of René Thom (together with K. Kurdyka and T. Mostowski).
Opis These results can be proven by means of stratification theory, in some special cases by the resolution of singularities, or by Zariski equisingularity. The main purpose of this sequence of talks is to give an introduction to the latter method, that moreover provides an algorithmic and constructive approach. First we introduce such basic tools as Puiseux Theorem, Whitney Interpolation, and arc-analytic maps. Then we show how, for Zariski equisingular families, to construct trivializations satisfying strong additional properties, for instance being arc-analytic. Finally we compare Zariski equisingularity and various regularity conditions on stratifications. (Based on a recent joint paper with Laurentiu Paunescu.)
Materiały skrypt wykładu
Prelegent Krzysztof Kurdyka (Université de Savoie)
Tytuł Gradient trajectories - quantitative aspects
Termin 21-28 maja 2015
Wymiar godzin 7 godzin
Rozkład godzin Wykłady (WMiI UJ, ul. Prof. Stanisława Łojasiewicza 6, sala 0006): czwartek: 21.05: 10:30-12:00, s. 0006 środa: 27.05: 10:30-12:45, s. 0006 czwartek: 28.05: 10:30-12:00, s. 0006
Biogram wkładowcy Born in 1957 in Kraków, he studied mathematics at the Jagiellonian University. In 1984 he defended his PhD thesis "Regular points of subanalytic sets" prepared under the supervision of Stanisław Łojasiewicz. Since 1991 he works as Professor of mathematics at the Savoy University in Chambéry (France). His research interests include real analytic and algebraic geometry, singularity theory and o-minimal geometry. Together with T. Mostowski and A. Parusiński he solved in 2000 the famous gradient conjecture posed by René Thom. He introduced a notion of arc-analytic function which became an important and fruitful tool in singularity theory.
Opis Trajectories of gradient vector fields in the algebraic, analytic and o-minimal context will be discussed. A special interest will be in estimates for the length of trajectories between two levels of the potential function. A proof of the Łojasiewicz gradient inequality as generalized to o-minimal structures will be presented, followed -- as an application - by showing the main ingredients of the proof of Thom's gradient conjecture due to Kurdyka, Mostowski and Parusiński [2000]. Trajectories of horizontal gradients with respect to a nonholonomic distribution (contact or Engel structures) may also be discussed.
Materiały skrypt wykładu
Prelegent Michał Woźniak (Politechnika Wrocławska)
Tytuł Wybrane problemy projektowania systemów klasyfikacji
Termin 9-10 kwietnia, 14-15 maja 2015
Wymiar godzin 10 godzin
Rozkład godzin 9 kwietnia (czwartek), 11-13, sala 1094 10 kwietnia (piątek), 11-13, sala 0103 14 maja (czwartek), 11-13, sala 1094 15 maja (piątek), 11-13 i 15-17, sala 0103
Biogram wkładowcy Michał Woźniak jest profesorem Politechniki Wrocławskiej, gdzie pracuje w Katedrze Systemów i Sieci Komputerowych na Wydziale Elektroniki. Jego zainteresowania naukowe koncentrują się na problematyce projektowania złożonych systemów rozpoznawania, ze szczególnym uwzględnieniem podejścia kombinowanego i analizy dużych zbiorów danych oraz danych strumieniowych. Jest autorem ponad 250 publikacji naukowych, w tym ponad 40 artykułów w czasopismach indeksowanych przez ISI, 3 książek oraz redaktorem kilkunastu monografii, a także pełni funkcję redaktora w czasopismach m.in. w Pattern Analysis and Applications oraz Information Fusion. Był zapraszany kilkanaście razy do wygłoszenia referatów plenarnych na kongresach i konferencjach międzynarodowych. Jego race naukowe prof. Woźniaka są także szeroko wykorzystywane w gospodarce, jest on m.in. autorem kilkudziesięciu ekspertyz związanych z oceną stanu informatyzacji przedsiębiorstwa z sektora energetyki, bankowości oraz produkcji. W 2010 r. Michał Woźniak został mianowanych senior member IEEE.
Opis Celem kursu jest zapoznanie studentów z problemem projektowania systemów klasyfikacji, ze szczególnym uwzględnieniem pre-processingu (przygotowanie danych, uzupełnianie brakujących wartości, filtrowanie danych zaszumionych, redukcja i selekcja danych) oraz post-processingu (ewaluacja algorytmu klasyfikacji, przygotowane poprawnego eksperymentu komputerowego). Omówione zostanie zadanie uczenia indukcyjnego - w tym generowania drzew decyzyjnych, a także metody projektowania zespołów klasyfikatorów oraz ich zastosowanie w klasyfikacji danych strumieniowych. Literatura: 1. Garcia S. et al., Data Preprocessing in Data Mining, Springer, 2015. 2. Alpaydin E., Introduction to Machine Learning, 3rd edition, MIT Press, 2014. 3. Kuncheva L., Combining Pattern Classifiers: Methods and Algorithms, 2nd edition, Wiley 2014. 4. Gama J., Knowledge Discovery from Data Streams, Chapman & Hall/CRC Press, 2010.
Materiały skrypt wykładu
Prelegent Dániel Marx (Magyar Tudományos Akadémia - Węgierska Akademia Nauk)
Tytuł Minicourse on parameterized algorithms and complexity
Termin 21-23 kwietnia 2015
Wymiar godzin 15 godzin
Rozkład godzin Wykłady (sala 0174): Wtorek, 21 kwietnia, 10-16 Środa, 22 kwietnia, 10-14 Czwartek, 23 kwietnia, 10-15
Biogram wkładowcy Dániel Marx obtained his PhD from Budapest University of Technology and Economics in 2005. In the years 2005-2012 he was a postdoctoral researcher at Humboldt University of Berlin, Budapest University of Technology and Economics, and Tel Aviv University. Since 2012 he is a research fellow at Hungarian Academy of Sciences. His research interests lie in parameterized complexity, constraint satisfaction problems, graph theory, and combinatorial optimization.
Opis The theory of fixed-parameter tractability gives a finer understanding of the complexity of NP-hard problems. In recent years, research in this area emerged as one of the main trends in modern algorithmics. The goal of the course is to give an introduction to the basic algorithmic techniques and to the corresponding complexity results and lower bounds.
Materiały skrypt wykładu
Prelegent Thomas Ward (University of Durham)
Tytuł Topics in Numbers and Dynamics
Termin 31 marca - 3 kwietnia 2015
Wymiar godzin 10 godzin
Rozkład godzin Wykłady: wtorek, 31 marca, godz. 10-12, sala 0006 wtorek, 31 marca, godz. 16-18, sala 0004 środa, 1 kwietnia, godz. 10-12, sala 0094 środa, 1 kwietnia, godz. 16-18, sala 1016 czwartek, 2 kwietnia, godz. 10-12, sala 1016 Konsultacje: wtorek, 31 marca, godz. 15-16 środa, 1 kwietnia, godz. 15-16 czwartek, 2 kwietnia, godz. 12-14
Biogram wkładowcy Thomas Ward jest światowej sławy specjalistą z zakresu dynamiki algebraicznej, teorii ergodycznej i ich związków z arytmetyką. Jest autorem około 60 artykułów i 4 książek oraz promotorem jedenastu prac doktorskich. Jest także ceniony za swoje umiejętności dydaktyczne (jego książki stały się jednymi z najchętniej cytowanych monografii z dziedziny; w 2012 roku Amerykańskie Towarzystwo Matematyczne przyznało mu prestiżową nagrodę Lestera Ranforda Forda).
Opis Wykłady poświęcone będą interakcjom między teorią ergodyczną i teorią układów dynamicznych z jednej strony a algebrą i arytmetyką z drugiej. Kurs ten adresowany jest przede wszystkim do studentów drugiego stopnia, doktorantów i pracowników, ale może zainteresować także fizyków i przedstawicieli innych kierunków ścisłych.
Materiały skrypt wykładu
Prelegent Benjamin Weiss (Einstein Institute of Mathematics, Hebrew University of Jerusalem)
Tytuł Ergodic theory of actions of countable groups
Termin 20-28 stycznia 2015
Wymiar godzin 15 godzin
Rozkład godzin 20.01, 27.01, wt. 10-12, s. 0009 21.01, 28.01, śr. 16-18, s. 1016 22.01, czw. 12-14, s. 0094 23.01, pt. 10-12, s. 0106 26.01, pon. 14-16, s. 0106
Biogram wkładowcy Benjamin Weiss is an Israeli mathematician working in the areas of dynamical systems, probability theory, ergodic theory, and topological dynamics. Weiss earned his Ph.D. from Princeton University in 1965, under the supervision of William Feller. He is a professor emeritus of mathematics at the Hebrew University of Jerusalem, where Fields Medalist Elon Lindenstrauss was one of his students. Since 2000 Benjamin Weiss is an Honorary Foreign member of the American Academy of Arts and Sciences. In 2012 he became a fellow of the American Mathematical Society in recognition of his outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.
Opis After an introduction to the main classes of groups that will be discussed - amenable, residually finite and sofic - we will survey the ergodic theory of their actions as measure preserving transformations. The emphasis will be on the theory of entropy and Bernoulli shifts. 1-2. Amenable, residually finite and sofic groups. 3-4. Ergodic theorems and the "Rohlin lemma" for amenable groups. 5-6. Sofic groups and surjunctivity. 7-8. Entropy for amenable groups and Bernoulli shifts. 9-12. Entropy for sofic groups - "Kolmogorov's theorem". 13-15. A survey of some recent developments. References. 1. B. Weiss, Sofic groups and dynamical systems, Sankhya - Indian J. of Statistics, Series A 62 (2000), Special Issue on Ergodic Theory and Harmonic Analysis, 350-359. 2. B. Weiss, Actions of amenable groups, in Topics in Dynamics and Ergodic Theory, ed. by Sergey Bezuglyi and Sergiy Kolyada, London Math. Soc. Lecture Note Series 310 (2003), 226-262. 3. L. Bowen, Measure conjugacy invariants for actions of countable sofic groups. J. Amer. Math. Soc. 23 (2010), 217-245.
Materiały skrypt wykładu

Instytut Matematyczny PAN
Liczba wykładów: 5
Prelegent Prof. Francisco Gancedo (Universidad Sevilla)
Tytuł Lectures on Muskat problem
Termin 11-15 maja 2015
Wymiar godzin 10 godz.
Rozkład godzin Poniedziałek (11 V): 16:00-17:30, sala 106 Wtorek (12 V): 11:00-12:30, sala 106 Środa (13 V): 12:00-13:30, sala 403 Czwartek (14 V): 11:00-12:30, sala 403 Piątek (15 V): 11:00-12:30, sala 405
Opis The purpose of these lectures is to show recent mathematical results concerning the classical Muskat problem. The Muskat problem models the evolution of incompressible fluids of different nature in porous media. The starting point is to motivate the problem and to establish several basic properties from its modeling equations. The final goal is to show well-posed scenarios in order to prove formation of singularities in finite time and existence of solutions for all time.
Materiały skrypt wykładu
Prelegent Dr Yemon Choi (Lancaster University)
Tytuł Topics in the (non-)amenability of Banach algebras
Termin 13-16.IV.2015
Wymiar godzin 15 godz.
Rozkład godzin Poniedziałek (13 IV): 12:30 - 13:45, 14:15 - 15:30 sala 321 Wtorek (14 IV): 12:30 - 13:45, 14:15 - 15:30 sala 321 Środa (15 IV): 15:00- 16:15 sala 321 Czwartek (16 IV): 12:30-13:45, 14:15 - 15:30 sala 321 Piątek (17 IV): 11:00-12:15, 13:15-14:30 sala 321
Biogram wkładowcy Yemon Choi obtained his PhD from the University of Newcastle upon Tyne in 2006, working on the higher-degree Hochschild cohomology groups of various semigroup algebras. He subsequently held postdoctoral positions at the University of Manitoba and Universit\'e Laval. In 2010 he took up a tenure-track position at the University of Saskatchewan; in January 2014 he returned to the United Kingdom to take up a lectureship at Lancaster University, where he is presently employed. His main theme of research is the study of Banach algebras that arise in noncommutative harmonic analysis. His mathematical interests remain varied and haphazard but in recent years he has worked on: perturbation problems for Banach algebras; direct finiteness for algebras of convolution operators; the study and explicit description of derivations on semigroup algebras and Fourier algebras; and most recently, the investigation of amenable operator algebras.
Opis The lecture series will give an introduction to amenability for Banach algebras, attempting to show where it comes from, and how it can give a unifying context for various averaging or splitting arguments in algebraic functional analysis. In particular we will start not with derivations, as is done in many accounts, but with the fundamental notions of projective and injective Banach module as adapted by A. Ya. Helemskii from the classical theory of Cartan and Eilenberg. It has been necessary to make a very limited selection from the extensive body of work that has been done on amenability, which no doubt reflects the lecturer's own biases and interests. The eventual choice hopefully strikes a balance between basic background material, and particular results of interest or importance. Topics I hope to include, with varying levels of detail, are: examples of flat and injective modules for various function algebras; Sheinberg's theorem characterizing C(X); some discussion of Hochschild cohomology; amenability and unitarizability for $L^1$ group algebras (theorems of Johnson and Dixmier--Day); amenability of algebras of approximable operators on Banach spaces (Gronbaek, Johnson and Willis); amenability and strong amenability for some classes of $\Cst$-algebras (results of Bunce, Rosenberg and others); some applications of amenability to perturbation problems (Johnson, mainly). If time permits I will finish by discussing the recent construction of amenable subalgebras of B(H) that are not similar to self-adjoint subalgebras.
Materiały skrypt wykładu
Prelegent Dr Damian Osajda (Instytut Matematyczny PAN i Uniwersytet Wrocławski)
Tytuł Embedding infinite graphs into finitely generated groups
Termin 11-13 marca 2015
Wymiar godzin 5 godz.
Rozkład godzin Środa, 11.03, 15.00-16.30, sala 321 IMPAN Czwartek, 12.03, 15.00-16.30, sala 106 IMPAN Piątek, 13.03, 10.15-11.30, sala 106 IMPAN
Biogram wkładowcy Damian Osajda obtained his Ph.D. from the Institute of Mathematics of the Polish Academy of Sciences in 2004, under the supervision of Tadeusz Januszkiewicz. Since then he held positions in Wroc law, Paris, Berkeley, Strasbourg, Lille and Vienna. His main field of interest is Geometric Group Theory, and in particular, various notions of a combinatorial nonpositive curvature. Those include hyperbolic, systolic, CAT(0) cubical, and small cancellation complexes and groups, as well as various generalizations of those (weakly systolic, bucolic, weakly modular...).
Opis The aim of this course is to explain the recent construction [Osa14] of finitely generated groups whose Cayley graphs contain isometrically some infinite sequences of finite graphs. For expanding sequences the resulting groups are not coarsely embeddable into Hilbert spaces and are counterexamples to the Baum-Connes conjecture with coeficients. The only other groups with those features are Gromov monsters [Gro03] - groups into which expanders embed weakly. For other families of graphs the technique allows to construct first examples of finitely generated groups with some exotic properties, e.g. a-T-menable groups without Yu's property A. The course will cover (hopefully, roughly, and up to some shifts) the following subjects: Day 1. Formulation of the main goal, some motivations, and generalities on the approach. Basics of graphical small cancellation theory: definitions, examples, main properties (e.g. isometric embedding of relators). Some history, including a short discussion of Gromov's method [Gro03]. Day 2. A fairly detailed presentation of the proof of the main theorem from [Osa14] - embedding isometrically an infinite sequence of graphs into a finitely generated group. Applications to specific families of graphs. Finitely generated groups containing expanders. Further applications and remarks. Day 3. Yu's property A and coarse embeddability into a Hilbert space. The construction of groups without property A acting properly on CAT(0) cubical complexes: Small cancellation labellings of graphs with walls, and defining a proper lacunary walling for such groups. Final remarks. References [Gro03] M. Gromov, Random walk in random groups, Geom. Funct. Anal. 13 (2003), no. 1, 73-146. [Osa14] D. Osajda, Small cancellation labellings of some infinite graphs and applications (2014), preprint, available at arXiv:1406.5015.
Materiały skrypt wykładu
Prelegent Prof. David Gérard-Varet (Université Denis Diderot Paris 7, France)
Tytuł The Taylor model in magnetohydrodynamics
Termin 9 marca 2015
Wymiar godzin 2 godz.
Rozkład godzin 16.30-18.00, sala 106 IMPAN
Biogram wkładowcy Professor David Gerard-Varet received his doctorate from Ecole Normale Supérieure in Lyon in 2003. He was a CNRS junior researcher between October 2004 and September 2009, at the Mathematics department of Ecole Normale Supérieure in Paris. He spent one year at Courant Institute in 2006. Since September 2009, he has been Professor at University Paris Diderot. His research lies in the field of partial differential equations. Its main themes are the asymptotic analysis of fluid dynamics models, and homogenization theory.
Opis We shall discuss a model introduced by J.B. Taylor in 1963, that comes from a formal asymptotic limit of MHD equations with rotation. This asymptotic model, relevant to the Earth's dynamo problem, should in principle allow for easier numerics. However, its simulation has been unsuccessful so far, due to unclear stability properties. The aim of the talk is to present recent mathematical results on this stability issue (joint works with E. Dormy, I. Gallagher, L. Saint-Raymond).
Prelegent Prof. David Gérard-Varet (Université Denis Diderot Paris 7, France)
Tytuł Mathematical analysis of boundary layers in fluid mechanics
Termin 10-13 marca 2015
Wymiar godzin 8 godz.
Rozkład godzin Wtorek, 10.03, 16.30-18.00, sala 321 IMPAN Środa, 11.03, 10.00-11.30, sala 321 IMPAN Czwartek, 12.03, 10.00-11.30, sala 403 IMPAN Piątek, 13.03, 10.00-11.30, sala 321 IMPAN
Biogram wkładowcy Professor David Gerard-Varet received his doctorate from Ecole Normale Supérieure in Lyon in 2003. He was a CNRS junior researcher between October 2004 and September 2009, at the Mathematics department of Ecole Normale Supérieure in Paris. He spent one year at Courant Institute in 2006. Since September 2009, he has been Professor at University Paris Diderot. His research lies in the field of partial differential equations. Its main themes are the asymptotic analysis of fluid dynamics models, and homogenization theory.
Opis In a fluid flow of high velocity, or small viscosity, one can observe strong velocity gradients near the solid boundary surrounding the flow. The thin region near the boundary where this phenomenon takes place is called a boundary layer. Mathematically, it corresponds to a singular limit of the Navier-Stokes equation, in which a parameter called Reynolds number is sent to infinity. This generates various mathematical problems : derivation of a reduced system describing the boundary layer, well-posedness of this system, rigorous justification of the boundary layer asymptotics. The lectures will present some recent developments on these topics, and the underlying mathematical tools. Outline for the lectures Lecture 1: - D'Alembert's paradox. - Inviscid limit of the Navier-Stokes equation. - The boundary layer phenomenon : Kato's theorem. Lecture 2: - The Prandtl model for the boundary layer. - Positive results on the Prandtl model : Oleinik's result for monotonic data, Sammartino and Caflisch result for analytic data. - Grenier's instability theorem for the Prandtl boundary layer expansion. Lecture 3: Ill-posedness of the Prandtl equation in Sobolev spaces. Lecture 4: Boundary layers for rotating fluids.
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