Talks

I will talk about a recent proof, joint with M. Gröchenig and D. Wyss, of a conjecture of Hausel and Thaddeus which predicts the equality of suitably defined Hodge numbers of moduli spaces of Higgs bundles with SL(n)- and PGL(n)-structure. The proof, inspired by an argument of Batyrev, proceeds by comparing the number of points of these moduli spaces over finite fields via p-adic integration.

Standard models of cosmology use inflation as a mechanism to resolve the isotropy and homogeneity problem of the universe as well as the flatness problem. However, due to various well known problems with the inflationary paradigm, there has been an ongoing search for alternatives. Perhaps the most famous among these is the cyclic universe scenario or scenarios which incorporate bounces. As these scenarios have a contracting phase in the evolution of the universe, it is reasonable to ask whether the problems of homogeneity and isotropy can still be resolved in these scenarios. In my talk, I will focus on the problem of the resolution of isotropy. In the contracting phase of the evolution, the mechanism of ekpyrosis is used in most cosmological scenarios which incorporate a contracting phase to mitigate the problem of anisotropies blowing up on approaching the bounce. I will start by studying anisotropic universes and I shall examine the effect of the addition of ultra-stiff anisotropic pressures on the ekpyrotic phase. I will then consider evolving such anisotropic universes through several cycles with increasing expansion maxima at each successive bounce. This eventually leads to flatness in the isotropic case. My aim will be to see if the resolution of the flatness problem also leads to a simultaneous resolution of the isotropy problem. In the last section of my talk, I will briefly consider the effect of non comoving velocities on the shape of this anisotropic bouncing universe.

Are we standing on the brink of a new scientific revolution that will radically change our views on space, time, and gravity?

In most circumstances, the theories of Einstein and Newton adequately describe gravity, but on cosmological scales, big questions arise, particularly surrounding the nature of dark matter and dark energy.

These questions are ushering in a revolution in theoretical physics – a completely new view on spacetime and gravity. Research in string theory and black hole physics, involving key concepts of quantum information theory, reveals a deep connection between the structure of spacetime and the origin of gravity.

This research suggests that gravity is not a fundamental force of nature, but rather an emergent phenomenon, similar to how temperature is an emergent phenomenon that arises from the movement of particles. That is, gravity is a side-effect, not a cause, of what happens in the universe.

In his public lecture, Dr. Erik Verlinde (University of Amsterdam) will explore the core ideas behind this research, and examine the implications of this fast-emerging revolution in our understanding of the universe.

We first summarize background on the quantum capacity of a quantum channel, and explain why we know very little about this fundamental quantity, even for the qubit depolarizing channel (the quantum analogue of the binary symmetric channel) despite 20 years of effort by the community.

Then, we focus on low-noise quantum channels, and present recent results on the quantum capacity to leading order in the noise parameter.  This in particular solves the quantum capacity problem (to leading order) for the qubit depolarizing channel, and provides a structure theorem for the capacity achieving codes.  For low-noise channels, degenerate codes provide negligible superadditivity effect.

Analoguous results on the private capacity will be presented.  Our results imply that for low-noise channels, there is negligible difference between coherence and privacy, and a key rate approaching the capacity can already be obtained using classical error correction and privacy amplification.

Joint work with Felix Leditzky and Graeme Smith

The observed deviations from the laws of gravity of Newton and Einstein in galaxies and clusters can logically speaking be either due to the presence of unseen dark matter particles or due to a change in the way gravity works in these situations. Until recently there was little reason to doubt that general relativity correctly describes gravity in all circumstances. In the past few years insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived from the quantum entanglement of the microscopic information that is underlying space-time. An essential ingredient in the derivation is of the Einstein equations is that the vacuum entanglement obeys an area law, a condition that is known to hold in Anti-de Sitter space due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de Sitter space and leads to a total entropy that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution on the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact that this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

Geometric invariant theory (GIT) is an essential tool for constructing moduli spaces in algebraic geometry. Its advantage, that the construction is very concrete and direct, is also in some sense a draw-back, because semistability in the sense of GIT is often more complicated to describe than related intrinsic notions of semistability in moduli problems. Recently a theory has emerged which treats the results and structures of geometric invariant theory in a broader context. The theory of Theta-stability applies directly to moduli problems without the need to approximate a moduli problem as an orbit space for a reductive group on a quasi-projective scheme. I will discuss some new progress in this program: joint with Jarod Alper and Jochen Heinloth, we give a simple necessary and sufficient criterion for an algebraic stack to have a good moduli space. This leads to the construction of good moduli spaces in many new examples, such as the moduli of Bridgeland semistable objects in derived categories. Time permitting, I will also discuss applications to enumerative geometry and wall crossing formulas.

Two seemingly different quantum field theories may secretly describe the same underlying physics — a phenomenon known as “duality". I will review some recent developments in field theory dualities in (2+1) dimensions and some of their applications in condensed matter physics, in particular in quantum Hall effect and quantum phase transitions.