We would like to make various remarks on string amplitudes in type II string theory in which getting the exact and final form of the world sheet integrals up to five point mixed closed-open amplitudes to all orders are given.

We are also going to to talk about all kinds of effective actions involving DBI, Chern-Simons and more importantly new Wess Zumino actions. Indeed we try to provide a comprehensive explanation even for D-brane-anti D-brane systems. We also introduce various new techniques to be able to derive all order α’ corrections to all type II super string effective actions. If time allows, we then mention several issues related to those effective actions as well.

Dans ce cours nous étudierons plusieurs modèles de graphes aléatoires allant du plus classique (le modèle d'Erdös-Renyi introduit en 1960) aux plus récents (les cartes planaires aléatoires étudiées depuis le début des années 2000). Le fil conducteur du cours sera la notion de convergence locale et les propriétés des graphes limites dits dilués.

Contenu du cours :

– Modèle d'Erdös-Renyi, transition de phase et propriétés de base
– Convergence locale et "méthode objective" d'Aldous et Steele
– Arbre couvrant minimum et théorème de Frieze 
– Graphes aléatoires unimodulaires
– Limites locales d'arbres aléatoires
– Limites locales de cartes aléatoires (construction, épluchage, théorème de Benjamini-Schramm)

I shall briefly review the salient features of target space duality (T-duality) and recall some essential results. I shall outline a prescription to derive the S-matrix for the scattering of massless stringy states that arise in the compactification of closed bosonic strings on a torus at the tree level. It will be shown that the S-matrix elements can be expressed in a T-duality invariant form. The Kawai-Lewellen-Tye formalism plays an important role in our approach.

We point out that the (pseudo-)conformal Universe scenario may be realized as decay of conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study perturbations about the bubble and show that their leading late-time properties coincide with those inherent in the original models with homogeneously rolling backgrounds. In particular, the perturbations of a spectator dimension-zero field have flat power spectrum. (arXiv:1502.05897)

A twin building is a simplicial complex associated to a group G with a twin BN-pair. A complex hyperbolic Kac-Moody (KM) group G is associated with a hyperbolic KM Lie algebra g = g(A), where A is a hyperbolic type Cartan matrix. The invariant symmetric bilinear form (. , .) on the standard Cartan subalgebra h in g has signature (n-1,1) on the split real form of h, providing a Lorentzian geometry. The Cartan-Chevalley involution on g gives a « compact" real form k of g, a real Lie algebra whose complexification is g, whose Cartan subalgebra t also has Lorentzian form (. , .), and there is also a corresponding compact real group K. We are able to embed the twin building for G inside the union of all « lightcones" {x in k | (x,x) <= 0} which is in the union of all K conjugates of t.  This provides a geometrical realization of the twin building of G closely related to the structure of all Cartan subalgebras in k, and sheds light on the geometry of the infinite dimensional groups G and K. This is especially interesting in the case of rank 3 hyperbolic algebras whose Weyl groups are hyperbolic triangle groups, so that the building is a union of copies of the tesselated Poincaré disk with certain boundary lines identified. This is joint work with Lisa Carbone (Rutgers University) and Walter Freyn (TU-Darmstadt).

I will give an overview of a project aimed at understanding the motivic nature of l-adic sheaves. I will survey motivating questions about independence of l and past results of Lafforgue, Drinfeld, and others. I will then discuss how to incorporate correspondences into the theory, recent results, and open questions.

MicroRNAs are recently discovered regulators of gene expression, coordinating many biological processes. They are especially important for developmental processes, including cell differentiation, while their deregulation causes diseases like cancer.
In particular, microRNAs are key regulators of muscle differentiation, a complex process necessary for the formation of muscle fibers. I’ll describe the regulation of skeletal muscle differentiation by the miR-98 – E2F5 molecular pathway.

After overviewing the representation of biological molecules, I introduce the representation of interactions between modules in the proteins with the SO(3) rotation of the peptide unit introduced by Penner et al.. Using protein data in PDB, I will show our representation with the SO(3) rotation is useful in characterizing the structure and its change due to the mutation or the native dynamical change with time. I also discuss some possible potential extensions of our approach to the chromatin structure.

Deninger and Werner developed an analogue for p-adic curves of the classical correspondence of Narasimhan and Seshadri between stable bundles of degree zero and unitary representations of the fundamental group of a complex smooth proper curve. Using parallel transport, they associated functorially to every vector bundle on a p-adic curve whose reduction is strongly semi-stable of degree 0 a p-adic representation of the fundamental group of the curve. They asked several questions: whether their functor is fully faithful and what is its essential image; whether the cohomology of the local systems produced by this functor admits a Hodge-Tate decomposition; and whether their construction is compatible with the p-adic Simpson correspondence developed by Faltings. We will answer these questions in this talk.

This talk starts with the Bianchi orbifolds, which arise from the action of the Bianchi groups (SL2 matrix groups over imaginary quadratic integers) on hyperbolic 3-space (their associated symmetric space). Studying these orbifolds, one can obtain :
– dimensions of spaces of Bianchi modular forms;
– Algebraic K-theory of rings of imaginary quadratic integers;
– Group (co)homology and equivariant K-homology of the Bianchi groups;
– Chen-Ruan orbifold cohomology of the Bianchi orbifolds. The latter cohomology ring is conjectured to be isomorphic to the cohomology ring of a crepant resolution for the orbifold, which makes it interesting for string theory.
What makes Bianchi modular forms interesting, is that there are deep number-theoretical reasons for expecting that the Taniyama-Shimura correspondence can extend to the cuspidal Bianchi modular forms, attaching Abelian varieties to them. For the dimension calculations, use is made of the speaker’s constructive answer to a question of Jean-Pierre Serre on the Borel-Serre compactification of the Bianchi orbifolds, which had been open for 40 years. This has so far permitted heavy machine calculations joint with M. Haluk Sengun, locating several of the very rare instances of Bianchi modular forms in a large array of dicriminants and weights, such that these forms are not lifts of classical modular forms.
Complementary to this, studies of the torsion part of the cohomology of the Bianchi groups have given rise to a new technique (called Torsion Subcomplex Reduction; some procedures of the technique had beforehand been used as ad hoc tricks by Soulé, Mislin and Henn) for computing the Farrell-Tate cohomology of discrete groups acting on suitable cell complexes. This technique has not only already yielded general formulae for the cohomology of the tetrahedral Coxeter groups as well as, above the virtual cohomological dimension, of the Bianchi groups (and at odd torsion, more generally of SL2 groups over arbitrary number fields, in joint work with Matthias Wendt), it also very recently has allowed Wendt to refine the Quillen conjecture.
This talk will further discuss the adaptation of this technique to Bredon homology computations, yielding the equivariant K-homology of the Bianchi groups. The Baum-Connes conjecture, which has been proved for large classes of groups, constructs an (iso)morphism from the equivariant K-homology of a group to the K-theory of its reduced C*-algebra. For the Bianchi groups, this yields the isomorphism type of the mentioned operator K-theory, which would be very hard to compute directly.

Quantum theory is remarkably consistent and beautiful. Yet, as a theory on an experimental science, it ought to tell us what is measurable and how to extract information about Nature from these measurements. It also ought to tell us how Nature produces correlations between disconnected regions that can’t be described using only local variables that propagated gradually and continuously through space. Staring at these two problems might not help to find the next theory. But it provides much inspiration to design experiments that illuminate the situation and might, some day, help in finding the limits of quantum theory. I’ll discuss these two problems and their different status. Next, I'll present several such experiments.