Scientific Series

In my talk, I will briefly review the representation theoretical construction of conformal blocks attached to an affine Kac-Moody algebra and a smooth algebraic curve with marked points. I will focus on the case when the algebraic curve is an elliptic curve. The bundle of conformal blocks carries a canonical flat connection: the Knizhnik-Zamolodchikov-Bernard (KZB) equation. There are various generalizations of the KZB equation. I will talk about one generalization that constructed by myself and Toledano Laredo recently: the elliptic Casimir connection. It is a holonomic system of differential equations with regular singularities on elliptic curve with marked points, taking values in a deformation of the double current algebra g[u, v] defined by Guay. The monodromy of elliptic Casimir connection leads to interesting representations of the elliptic braid groups. 

(1) Entanglement-enhanced quantum sensing: parameter estimation and hypothesis testing.
(2) Security from entanglement: quantum key distribution.
(3) Entanglement enhanced communication: channel capacity and additivity issues.
(4) Some open problems.

In this talk I will present new insights on a microscopic holographic theory for de Sitter space. I will focus on the static patch of dS, which describes our universe to a good approximation at late times. We use a conformal map between dS and the BTZ black hole times a sphere to relate the general microscopic properties of dS to those of symmetric product CFTs. In 2d CFT language, de Sitter space corresponds to a thermal bath of long string. The long string phenomenon exhibited by these CFTs implies that the excitation energy decreases at large distances in dS (contrary to the UV/IR relation in AdS/CFT). It also explains the smallness of the vacuum energy of dS. Similar results apply to Minkowski space and AdS below its curvature radius.

By the non-abelian Hodge theory of Carlos Simpson, harmonic bundles
interpolate between  bundles with connections on a curve and
 Higgs bundes (precise formulations requires some additional data like parabolic structure and stability structure).

I will explain the framework for a generalization of the non-abelian Hodge theory
which unifies Simpson's story ("rational case") with those  for q-difference
equations ("trigonometric case") and elliptic difference equations
("elliptic case").

This unification leads to a class of examples of the new notion of ``twistor families of categories".
In the rational,trigonometric and elliptic cases twistor families of categories  involve partially wrapped Fukaya categories of certain complex symplectic surfaces, categories of
holonomic modules over quantizations of these surfaces and categories of coherent sheaves on the surfaces
with certain restrictions on the support.

In the trigonometric and elliptic cases doubly and triply periodic monopoles give an alternative description of harmonic objects, hence playing the same role
as harmonic bundles play in the case of Simpson theory.

We discuss some applications of a result on the convex combination of the quantum states (that we refer to as convex-split technique) and its variants. In the framework of Quantum Resource theory, we provide an operational way of characterizing the amount of resource in a given quantum state, for a large class of resource theories. Our results use the convex-split technique in the achievability proof, with a matching converse in the one-shot setting.  Building upon the ideas involved in this achievability proof, we show how the technique (and its close counterpart of position-based decoding) can lead to a large family of entanglement-assisted protocols for quantum communication. We sketch close connections between these protocols and the port-based teleportation scheme of Ishizaka and Hiroshima [Phys. Rev. Lett. 101, 240501]. We exploit these connections to obtain a new protocol for entanglement assisted point to point quantum channel coding in the asymptotic and i.i.d. setting, with the rate of entanglement cost and achievable communication matching that of Bennett et. al. [IEEE Trans. Inf. Theory, 48, 2002].  Based on the works arXiv:1410.3031,  arXiv:1708.00381,   arXiv:1702.01940.

In his classic essay, “The Usefulness of Useless Knowledge,” Abraham Flexner, the founding director of the Institute for Advanced Study in Princeton and the man who helped bring Albert Einstein to the United States, describes a great paradox of scientific research. The search for answers to deep questions, motivated solely by curiosity and without concern for applications, often leads not only to the greatest scientific discoveries  but also the most revolutionary technological breakthroughs. In short, no quantum mechanics, no computer chips. Robbert Dijkgraaf, the Institute’s current director, explains how Flexner’s defense of the value of “the unobstructed pursuit of useless knowledge” may be even more relevant today than it was in the early twentieth century. Dijkgraaf describes how basic research has led to major transformations in the past century and explains why it is an essential precondition of innovation and the first step in social and cultural change.

The Standard Model of particle physics and its implications for cosmology leave several fundamental questions unanswered, including the strong CP problem and the origins of neutrino masses, dark matter, and dark energy. Previous directions of model building beyond the Standard Model have usually focused on new high-energy physics. As an alternative direction, we have developed a class of low-energy neutrino mass and axion models at a new infrared gravitational scale, which is numerically coincident with the scale of dark energy. In this seminar, I will present this novel class of models and expand on the aspect of gravitational neutrino mass generation. My talk will also cover the wide-ranging cosmological and phenomenological model predictions, in particular the invalidity of the cosmological neutrino mass bound, enhanced neutrino decays, and soft topological defects. 

In both Causal Set Quantum Gravity as well as in the String Landscape, we face the challenging tasks of sifting through large state spaces and searching for the set of solutions which best model our physical universe. I demonstrate in this talk how efficient parallel algorithms can give us access to areas of physics previously unstudied due to computational barriers. I first present new methods to accelerate the evolution of causal set Markov chains, which enables us to look for the spontaneous emergence of manifoldlike structure. Then, I use a similar graph theoretic approach to show how a dynamic vacuum selection mechanism naturally emerges in F-Theory and Type IIB String Theory in the context of eternal inflation. We will discuss in detail relevant numerical aspects, including practical limitations and algorithms from graph theory, and how machine learning can be used in future work.

Many researchers have been studying the time evolution of entanglement entropy in the sudden quenches where a characteristic mass scale suddenly changes. It is well-know that in these quenches, the change of entanglement entropy become thermal entropy which is proportional to a subsystem size in the late time. However, we do not know which quenches thermalize a subsystem. In our works, we have been studied the time evolution of quantum entanglement in the global quenches with finite quench rate (smooth quenches). Thus, we found that diabaticity plays an important role, so that quenches thermalize the subsystem.

If a component of the dark matter has dissipative interactions, it could collapse to form a thin dark disk in our Galaxy coincident with the baryonic disk. It has been suggested that dark disks could explain a variety of observed phenomena, including periodic comet impacts. Using the first data release from the Gaia mission, we search for a dark disk via its effect on stellar kinematics in the Milky Way. I will present new limits on the presence of a thin dark matter disk, as well as measurements on the matter density in the solar neighborhood.