Talks

The evidence that the universe emerged 14 billion years ago from an event called \'the big bang\' is overwhelming. Yet the cause of this event remains deeply mysterious. In the conventional picture, the \'initial singularity\' is unexplained. It is simply assumed that the universe somehow sprang into existence full of \'inflationary\' energy, blowing up the universe into the large, smooth state we observe today. While this picture is in excellent agreement with current observations, it is both contrived and incomplete, leading us to suspect that it is not the final word. In this lecture, the standard inflationary picture will be contrasted with a new view of the initial singularity suggested by string and M-theory, in which the bang is a far more normal, albeit violent, event which occurred in a pre-existing universe. According to the new picture, a cyclical model of the universe becomes feasible in which one bang is followed by another, in a potentially endless series of cosmic cycles. The presentation will also review exciting recent theoretical developments and forthcoming observational tests which could distinguish between the rival inflationary and cyclical hypotheses. big bang, cosmology, universe, initial singularity, inflation, string theory, M-theory, pre-existing universe, cyclical model, cosmic cycle, particle physics, dark matter, dark energy

Coin flipping by telephone (Blum \'81) is one of the most basic cryptographic tasks of two-party secure computation. In a quantum setting, it is possible to realize (weak) coin flipping with information theoretic security. Quantum coin flipping has been a longstanding open problem, and its solution uses an innovative formalism developed by Alexei Kitaev for mapping quantum games into convex optimization problems. The optimizations are carried out over duals to the cone of operator monotone functions, though the mapped problem can also be described in a very simple language that involves moving points in the plane. Time permitting, I will discuss both Kitaev\'s formalism, and the solution that leads to quantum weak coin flipping with arbitrarily small bias.

At a very basic level, physics is about what we can say about propositions like \'A has a value in S\' (or \'A is in S\' for short), where A is some physical quantity like energy, position, momentum etc. of a physical system, and S is some subset of the real line. In classical physics, given a state of the system, every proposition of the form \'A is in S\' is either true or false, and thus classical physics is realist in the sense that there is a \'way things are\'. In contrast to that, quantum theory only delivers a probability of \'A is in S\' being true. The usual instrumentalist interpretation of the formalism leading to these probabilities involves an external observer, measurements etc.In a future theory of quantum gravity/cosmology, we will have to treat the whole universe as a quantum system, which renders instrumentalism meaningless, since there is no external observer. Moreover, space-time presumably does not have a smooth continuum structure at small scales, and possibly physical quantities will take their values in some other mathematical structure than the real numbers, which are the \'mathematical continuum\'. In my talk, I will show how the use of topos theory, which is a branch of category theory, may help to formulate physical theories in a way that (a) is neo-realist in the sense that all propositions \'A is in S\' do have truth values and (b) does not depend fundamentally on the continuum in the form of the real numbers. After introducing topoi and their internal logic, I will identify suitable topoi for classical and quantum physics and show which structures within these topoi are of physical significance. This is still very far from a theory of quantum gravity, but it can already shed some light on ordinary quantum theory, since we avoid the usual instrumentalism. Moreover, the formalism is general enough to allow for major generalisations. I will conclude with some more general remarks on related developments.