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13:20 Joe Leys, Étienne Ghys, Aurélien Alvarez English 2012

Chaos | Chapter 1 : Motion and determinism - Panta Rhei

  • Published: 2012
  • Publisher: Joe Leys, Étienne Ghys, Aurélien Alvarez
  • Language: English
13:30 Joe Leys, Étienne Ghys, Aurélien Alvarez English 2012

Chaos | Chapter 9 : Chaotic or not - Research today

  • Published: 2012
  • Publisher: Joe Leys, Étienne Ghys, Aurélien Alvarez
  • Language: English
13:51 Joe Leys, Étienne Ghys, Aurélien Alvarez English 2008

Dimensions | Chapter 7

  • Published: 2008
  • Publisher: Joe Leys, Étienne Ghys, Aurélien Alvarez
  • Language: English
41:47 Open Science Training Initiative (OSTI) English 2013

3. Data, Code & Content Licensing

The following video is an original recording from the OSTI pilot initiative. Entitled "Data, Code & Content Licensing", the seminar introduces the theme of licensing, outlines the advantages of this approach, and takes students through the main steps of implementation.
  • Published: 2013
  • Publisher: Open Science Training Initiative (OSTI)
  • Language: English
41:32 droidcon Berlin English 2015

Android reactive programming with Rxjava

In a world where there is a smartphone in every pocket, designing and building applications that can run smoothly and provide the User Experience that users will like it’s the only way to go. Reactive Programming style with RxJava will help you to beat Android Platform limitations to create astonishing Android Apps. This talk will be a practical journey from basic Reactive Programming and Observer Pattern concepts to the main feature of RxJava, with practical code examples and a real-world app. I'll show the audience how to create an Observable "from scratch", from a list or from a function we already have in our code base. Our listeners will learn how to filter an Observable sequence to create a new sequence containing only the values we want; they will learn how to apply a function to an Observable, how to concatenate, merge or zip Observables. I'll show how to enjoy RxAndroid Schedulers to overcome the threading and concurrency hell in Android. I will close the talk with a practical example about RxJava + Retrofit, to easily communicate with a REST API.
  • Published: 2015
  • Publisher: droidcon Berlin
  • Language: English
1:02:05 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/4 Automorphic forms in higher rank

  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:15:07 Institut des Hautes Études Scientifiques (IHÉS) English 2015

Quantum Geometry and Strings

  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
49:58 Institut des Hautes Études Scientifiques (IHÉS) English 2013

Counterterms in gravity and N = 8 Supergravity

I will discuss counterterms in gravity using the light-cone frame formulation and show that also in this fully gauge fixed formulation we do need a local symmetry to find the correct counter terms.
  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:05:36 Institut des Hautes Études Scientifiques (IHÉS) English 2015

Approaches to quantum gravity

At this time, we do not have a theory of quantum gravity. In this talk I will first reiterate the reasons why such a theory is absolutely needed, and then review some of the proposals towards it, with special emphasis on `non-string' approaches. The presentation will be kept mostly at a general and introductory level.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:17:54 Institut des Hautes Études Scientifiques (IHÉS) English 2015

Quantum Field Theory and Gravitation

The incorporation of gravity into quantum physics is still an essentially open problem. Quantum field theory under the influence of an external gravitational field, on the other side, is by now well understood. I is remarkable that, nevertheless, its consistent treatment required a careful revision of traditional quantum field theory in the spirit of algebraic quantum field theory. Moreover, it allows a background independent perturbative construction of quantum gravity as an effective theory.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
56:40 Institut des Hautes Études Scientifiques (IHÉS) English 2013

The correlation numbers in Minimal Liouville gravity

The correlation numbers in Minimal Liouville gravity from Douglas string equation We continue the study of (q, p) Minimal Liouville Gravity with the help of Douglas string equation. Generalizing the earlier results we demonstrate that there exist such coordinates
  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:25:34 Institut des Hautes Études Scientifiques (IHÉS) English 2015

3/3 Supersymmetric Vacua and Integrability

"I review the relationship between supersymmetric gauge theories and quantum integrable systems. From the quantum integrability side this relation includes various spin chains, as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalisations. From the gauge theory side one has supersymmetric gauge theories with four (and eight) supercharges in various space-time dimensions (compactified to two-dimensions, or in Omega-background). Gauge theory perspective provides the exact energy spectrum of corresponding quantum integrable system. Key elements, usually appearing in the topic of quantum integrability, such as Baxter equation, Yang-Yang function, Bethe equation, spectral curve, Yangian, quantum affine algebra, quantum elliptic algebra - all acquire meaning in the supersymmetric gauge theory." 29 avril 2015
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:03:38 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge number of relations represented in the form of partial differential equations for their generating function. This includes equations of the KP hierarchy, Virasoro-type constraints, Chekhov-Eynard-Orantin-type recursion and others. Only a few of these relations can be derived from elementary combinatorics of permutations. All other relations follow from a deep relationship of Hurwitz numbers with moduli spaces of curves, Gromov-Witten invariants, matrix models, integrable systems and other domains of mathematics which are often referred to as `mathematical physics'. When discussing Hurwitz numbers in the talks, we consider them, thereby, as a sufficiently elementary but highly nontrivial model of all mentioned theories where all computations can be fulfilled completely, and all formulated relations can be checked explicitly in computer experiments.
  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:01:45 Institut des Hautes Études Scientifiques (IHÉS) English 2014

4/4 Analytic number theory around torsion homology

  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
45:19 Institut des Hautes Études Scientifiques (IHÉS) English 2013

Equations for stability­

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:54:58 Institut des Hautes Études Scientifiques (IHÉS) English 2013

3/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:50:24 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/4 Singular support of coherent sheaves

Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference between "coherent" and "perfect" is responsible for the appearance of Arthur parameters in the context of geometric Langlands correspondence.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:06:56 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/4 Motivic periods and the cosmic Galois group

In the 1990's Broadhurst and Kreimer observed that many Feynman amplitudes in quantum field theory are expressible in terms of multiple zeta values. Out of this has grown a body of research seeking to apply methods from algebraic geometry and number theory to problems in high energy physics. This talk will be an introduction to this nascent area and survey some recent highlights. Most strikingly, ideas due to Grothendieck (developed by Y. André) suggest that there should be a Galois theory of certain transcendental numbers defined by the periods of algebraic varieties. Many Feynman amplitudes in quantum field theories are of this type. P. Cartier suggested several years ago applying these ideas to amplitudes in perturbative physics, and coined the term `cosmic Galois group'. One of my goals will be to describe how to set up such a theory rigorously, define a cosmic Galois group, and explore its consequences and unexpected predictive power. Topics to be addressed will include: 1) A Galois theory of periods, multiple zeta values. 2) Parametric representation of Feyman integrals and their mixed Hodge structures. 3) Operads and the principle of small graphs. 4) The cosmic Galois group: results, counterexamples and conjectures.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:55:07 Institut des Hautes Études Scientifiques (IHÉS) English 2015

4/4 Exponential Integral

  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:45:37 Institut des Hautes Études Scientifiques (IHÉS) English 2015

1/4 Singular support of coherent sheaves

Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference between "coherent" and "perfect" is responsible for the appearance of Arthur parameters in the context of geometric Langlands correspondence.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:03:48 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/3 Classical transversality methods in SFT

In this talk I will discuss two transversality results that are standard but perhaps not so widely understood: (1) Dragnev's theorem that somewhere injective curves in symplectizations are regular for generic translation-invariant J, and (2) my theorem on automatic transversality in 4-dimensional symplectic cobordisms (which generalizes earlier results for closed curves by Gromov, Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin). The common feature of these two theorems is that both can be proved by considering the restriction of the usual linearized Cauchy-Riemann operator to the "generalized normal bundle" of a (not necessarily immersed) holomorphic curve.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:20:05 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/3 Supersymmetric Vacua and Integrability

"I review the relationship between supersymmetric gauge theories and quantum integrable systems. From the quantum integrability side this relation includes various spin chains, as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalisations. From the gauge theory side one has supersymmetric gauge theories with four (and eight) supercharges in various space-time dimensions (compactified to two-dimensions, or in Omega-background). Gauge theory perspective provides the exact energy spectrum of corresponding quantum integrable system. Key elements, usually appearing in the topic of quantum integrability, such as Baxter equation, Yang-Yang function, Bethe equation, spectral curve, Yangian, quantum affine algebra, quantum elliptic algebra - all acquire meaning in the supersymmetric gauge theory." 22 avril 2015
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
2:22:26 Institut des Hautes Études Scientifiques (IHÉS) English 2015

1/3 Supersymmetric Vacua and Integrability

"I review the relationship between supersymmetric gauge theories and quantum integrable systems. From the quantum integrability side this relation includes various spin chains, as well as many well-known quantum many body systems like elliptic Calogero-Moser system and generalisations. From the gauge theory side one has supersymmetric gauge theories with four (and eight) supercharges in various space-time dimensions (compactified to two-dimensions, or in Omega-background). Gauge theory perspective provides the exact energy spectrum of corresponding quantum integrable system. Key elements, usually appearing in the topic of quantum integrability, such as Baxter equation, Yang-Yang function, Bethe equation, spectral curve, Yangian, quantum affine algebra, quantum elliptic algebra - all acquire meaning in the supersymmetric gauge theory."
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:10:44 Institut des Hautes Études Scientifiques (IHÉS) English 2015

1/2 Introduction to Polyfold Regularization

This lecture will discuss the overall ideas and challenges in regularizing moduli spaces, and introduce the two basic ideas behind polyfold theory: Making reparametrization actions "smooth" and making pregluing a "chart map". [related literature: Sections 2.1 and 3.3 of Polyfolds: A First and Second Look. Related videos: Lecture 8 and Lecture 20 from Wehrheim's special topics course.]
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:10:54 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/3 The rise of sc-retracts

In this talk, we discuss the second of two fundamental analysis concepts polyfold theory is built on: sc-retracts. In particular, we discuss how they arise naturally as a means of using pre-gluing maps to parametrize a neighborhood of nodal and non-nodal (or broken and unbroken) maps near a nodal (or broken) map. Despite locally varying dimensions, such retracts support a version of the sc-calculus on which the chain rule holds, and we define M-polyfolds (manifold-like polyfolds) to be those topological spaces locally modeled on such retracts. [Related literature: Sections 2.3 and 5.1 of Polyfolds: A First and Second Look.]
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:07:23 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/3 Knot contact homology and string topology

We show how to relate knot contact homology to a version of string topology. More precisely we express knot contact homology in terms of strings in the singular space which is the union of the three sphere and the Lagrangian conormal of the knot that split in a certain way when they hit the knot.
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:07:38 Institut des Hautes Études Scientifiques (IHÉS) English 2015

2/4 Polyfolds and the construction of Symplectic Field Theory

Topics: 1 Polyfold structures. 2 Consequences of polyfold structures. 3 Weighted categories and their smooth versions. 4 The polyfold of stable maps. 5 Bundle category
  • Published: 2015
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:05:21 Instituto de Ciencias Matemáticas (ICMAT) English 2006

Applications of Equivariant Cohomology

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular, we state a conjecture for the index of a transversally elliptic operator linked to a Hamiltonian action. In the last part, we describe algorithms for numerical computations of values of multivariate spline functions and of vector-partition functions of classical root systems.
  • Published: 2006
  • Publisher: Instituto de Ciencias Matemáticas (ICMAT)
  • Language: English
1:16:48 Institut des Hautes Études Scientifiques (IHÉS) English 2013

Wall-crossing and geometry at infinity of Betti moduli spaces

Linear algebraic differential equation (in one variable) depending on a small parameter produces a spectral curve, which is a point in the base of a Hitchin integrable system. Gaiotto, Moore and Neitzke discovered a remarkable structure on the Hitchin base, consisting in certain integer numbers (BPS counting) associated with cycles on the spectral curves, and satisfying universal wall-crossing constraint at hypersurfaces of discontinuity. For a generic spectral curve the wall-crossing structure leads to a preferred coordinate system on the Betti moduli space (a.k.a. the character variety, or the moduli space of monodromy data). I'll speak about interpretation of BPS counting as trees on the Hitchin base, about generalized Strebel differentials and associated quivers, and how one can effectively calculate BPS counting using algebraic curves in Betti moduli spaces.
  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:05:43 Institut des Hautes Études Scientifiques (IHÉS) English 2014

1/2 The orbital circle method and applications, toral eigenfuctions and their nodal sets

  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:59:46 Institut des Hautes Études Scientifiques (IHÉS) English 2013

4/4 Mathematical Structures arising from Genetics and Molecular Biology

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:03:54 Institut des Hautes Études Scientifiques (IHÉS) English 2014

3/4 Growth in groups and applications

  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
52:27 Institut des Hautes Études Scientifiques (IHÉS) English 2013

N = 4 Super Yang-Mills Theory on the Coulomb Branch

I will present a conjecture relating the world-volume action of a D3-brane in an AdS5 X S5 background to the effective action of N = 4 Super Yang-Mills Theory on the Coulomb branch.
  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:06:07 Institut des Hautes Études Scientifiques (IHÉS) English 2013

Where does quantum field theory come from?

This will be an interim report on a long-running project to construct a mechanism that produces spacetime quantum field theory; to indentify possible exotic, non-canonical low- energy phenomena in SU(2) and SU(3) gauge theories produced by this mechanism; and to calculate signals of these phenomena to see if they can be used to check whether the proposed mechanism operates in the real world. The last effort is still ongoing.
  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:09:30 Institut des Hautes Études Scientifiques (IHÉS) English 2013

Out of equilibrium

  • Published: 2013
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
1:00:04 Institut des Hautes Études Scientifiques (IHÉS) English 2014

2/4 Growth in groups and applications

  • Published: 2014
  • Publisher: Institut des Hautes Études Scientifiques (IHÉS)
  • Language: English
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