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.

According to quantum theory, the outcomes of measurements are  generally not deterministic. "Single-world" theories (such as Bohmian  mechanics) add additional elements to quantum theory in order to restore determinism. In this talk, I will argue that such single-world theories  cannot be self-consistent in the following sense: any attempt to use a single-world theory to describe an observer who himself applies the  theory necessarily results in a contradiction.

The two concepts in the title stand for two distinct quantum phenomena whose relation to one another is not obvious although they often occur together.  Moreover, there is not a unique concept of superfluidity. In the talk I shall first comment on these general issues and then discuss a simple model involving a tunable random potential where some precise statements can be rigorously proved. The latter is joint work with M.Könenberg, T. Moser and R. Seiringer.

I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.

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In 1913, Niels Bohr wrote his groundbreaking paper "On the Constitution of Atoms and Molecules", were he already mentioned quantum jumps between energy levels. Later on, he was also the leader of the Copenhagen interpretation of measurement. A century later, thanks to major progresses in fast electronics and low temperature physics, the delicate manipulation of simple quantum systems, and the observation of quantum jumps and quantum trajectories, have become a reality. These observations teach us important things about measurement, with deep theoretical implications, but also with practical stakes for the conception of the still elusive quantum computers. After a brief overview, we shall focus on a few recent experiments dedicated to simple quantum systems and on their theoretical interpretation which involves some remarkable probabilistic results and structures.

I shall  introduce Bohmian Mechanics and present some basic notions for the analysis of the theory. Among them the notion of typicality, which is basic  for establishing Born’s statistical law in a Bohmian universe. The talk ends with a view on relativistic quantum physics seen from a Bohmian perspective.

The physics of many-body systems strongly depends on their dimensionality. With the realization of quantum wells for example, it has been possible to produce two-dimensional gases of electrons, which exhibit properties that dramatically differ from the standard three-dimensional case, some of them still lacking a full understanding.
 
During the last decade, a novel environment has been developed for the study of low-dimensional phenomena. It consists of cold atomic gases that are confined in tailor-made electromagnetic traps. The talk will discuss some experimental aspects of this research, including dynamical features like the emergence of coherence in the gas when it is rapidly cooled across the superfluid transition.