Scientific Series

In 2008 jointly with Maxim Kontsevich we introduced the notion of stability data on graded Lie algebras. In the case of the Lie algebra of vector fields on a symplectic torus it underlies the wall-crossing formulas for Donaldson-Thomas invariants of 3-dimensional Calabi-Yau categories. In 2013 we introduced the notion of wall-crossing structure, which is a locally-constant sheaf of stability data. Wall-crossing structures naturally appear in complex integrable systems, Homological Mirror Symmetry and many other topics not necessarily related to Donaldson-Thomas theory. Recently, in 2020 we introduced a sublass of analytic wall-crossing structures. We formulated a general conjecture that analytic wall-crossing structure gives rise to resurgent (i.e. Borel resummable) series.

Many wall-crossing structures have geometric origin, and moreover they naturally appear in our Holomorphic Floer Theory program. Aim of my talk is to discuss wall-crossing structures associated with a pair of holomorphic Lagrangian submanifolds of a complex symplectic manifold (in most cases it will be the cotangent bundle). These wall-crossing structures underly Cecotti-Vafa wall-crossing formulas, and as such they appear naturally in the study of exponential integrals in finite and infinite dimensions. I am going to explain our conjectural approach to Chern-Simons theory  which is based on the idea of wall-crossing structure. In some aspects this approach is related to the work of Witten on analytic continuation of Chern-Simons theory.

Zoom link:  https://pitp.zoom.us/j/99446428842?pwd=aDRzbFJoNytDNURDUVFMNGQzNjBFQT09

The simplest large N gauge theory is, arguably, the Gaussian matrix (or more generally, one hermitian matrix) integral. We will explicitly show that arbitrary correlators of single trace operators in this theory (without any double scaling limit) are identical to corresponding physical correlators in a dual topological string description. We will present both a novel A-model dual and also a mirror B-model Landau-Ginzburg description. The equality of correlators arises via open-closed-open string triality and a surprising relation to the c=1 string theory. The goal will be, however, to go beyond demonstrating equality but rather to make the duality manifest. For the B-model description this involves Eynard's recasting of topological recursion relations in terms of intersection numbers on moduli space. For the A-model this goes through the relation of Gaussian correlators to the special Belyi covering maps or equivalently, discrete volumes of moduli space. Finally, we also briefly mention the significance of these results for the gauge-string duality of N=4 Super Yang-Mills theory.

Zoom Link: https://pitp.zoom.us/j/93961992131?pwd=MkxlekxWU1ZGbzNZeWpzeU1TMzMrdz09

This talk is motivated by the question: why do we put so much effort and investment into quantum computing? A short answer is that we expect quantum advantages for practical problems. To achieve this goal, it is essential to reexamine existing experiments and propose new protocols for future quantum advantage experiments. In 2019, Google published a paper in Nature claiming to have achieved quantum computational advantage, also known as quantum supremacy. In this talk, I will explain how they arrived at their claim and its implications. I will also discuss recent theoretical and numerical developments that challenge this claim and reveal fundamental limitations in their approach. Due to these new developments, it is imperative to design the next generation of experiments. I will briefly mention three potential approaches: efficient verifiable quantum advantage, hardware-efficient fault-tolerance, and quantum algorithms on analog devices, including machine learning and combinatorial optimization.

Zoom Link: https://pitp.zoom.us/j/96945612624?pwd=ckRKMFJqZ0Q0dGtFOU91c1hnMzIzZz09

Canonical Quantum Gravity can be considered as a gauge theory of translations. Just like in other gauge theories this implies that physical observables need to be gauge-invariant. Hence, quantities like the metric cannot be observables. This poses new challenges, as this requires to rephrase in the quantum theory how to characterize physics. Moreover, such observables are usually composite. To determine them, the Fröhlich-Morchio-Strocchi mechanism from QFT can be borrowed, to have an augmented perturbative approach.

Zoom Link: https://pitp.zoom.us/j/97927004145?pwd=ekFJaUJSc21UUGdkcDZDWCtpSmdIUT09

Numerical relativity continues to play a crucial role in interpreting gravitational wave detections as well as the first multi-messenger detection of GW170817. More so, state-of-the-art models for kilonvae, gravitational waves, and more rely on the thousands of numerical relativity simulations that have taken place over more than 20 years.  Simulations of binary systems including neutron stars are particularly taxing due to the equation of state of matter being a significant unknown.  In spite of this fact, there exists vast amount of literature on the independent influence mass asymmetry or spin can have on the merger and post-merger dynamics of neutron star binaries across a wide array of possible equations of state.

In this talk I will extend this topic to extremal configurations consisting of binaries that are not only asymmetric, but include appreciable spins on the component neutron stars.  To do so I will give an introduction into the initial data problem for numerical relativity, it's complexities, and its importance to current and future research.  Furthermore, I will discuss a collection of results for extremal binary configurations including neutron stars and why this line of research is important to enable the next generation of multi-messenger models.

Zoom Link: https://pitp.zoom.us/j/99895521696?pwd=T1VtN0RGbjZrVTNleXB3V0FtQjhldz09

Bell's theorem proves that quantum theory is inconsistent with local physical models and, from the perspective of causal inference, it can be seen as the impossibility of providing a classical causal explanation to quantum correlations. Bell's theorem has propelled research in the foundations of quantum theory and quantum information science. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more complicated causal structures allowing for communication between the parts and involving several independent sources which distribute shares of physical systems in a network. For the case of three observable variables, it is known that there are three non-trivial causal networks. Two of those, are known to give rise to quantum non-classicality: the instrumental and the triangle scenarios. In this talk, we introduce new tools to tackle the compatibility problem in the general framework of Bayesian networks and explore the remaining non-trivial network, which we call the Evans scenario. We do not solve its main open problem –whether quantum non-classical correlations can arise from it – but give a significant step in this direction by proving that post-quantum correlations, analogous to the Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.

Zoom Link: https://pitp.zoom.us/j/98549320714?pwd=QVllZXNpZTFqekI1ZVUrK3ZLdnRjZz09

I will introduce asymptotically safe quantum gravity, which is based on the quantum realization of scale invariance, as one candidate theory to describe nature at all scales. I will discuss the concept of an asymptotically safe fixed point, and how the realization of scale invariance at high energies might provide a predictive and UV-complete description of nature. In particular, I will focus on the interplay of gravity and matter, and highlight mechanisms how this interplay might lead to constraints and predictions of asymptotically safe gravity-matter systems.

Zoom Link: https://pitp.zoom.us/j/99056179498?pwd=SzlXK1R5dExNckFMM1pMS3IvS1VyQT09

The modern point of view is that the global symmetries of a quantum field theory are described by topological defects/operators of the theory. In general such symmetries are non-invertible, i.e. the associated topological defects do not admit an inverse under fusion. I will describe a general construction of such non-invertible topological defects by coupling lower-dimensional topological quantum field theories (TQFTs) to discrete gauge fields living in a higher-dimensional bulk. The associated symmetries would be referred to as theta symmetries, as this construction can be understood as a generalization of the notion of theta angle. Mathematically, this construction is connected to interesting fusion higher-categories like those formed by higher-representations of groups and higher-groups. I will briefly explain this mathematical connection. I will also describe how the study of theta symmetries includes within it, as a special case, the study of topological phases of matter pursued in condensed matter physics. Towards the end of the talk, I will discuss some works in progress regarding possible physical applications of non-invertible symmetries. Based on ArXiv: 2212.06159, 2208.05973.

Zoom Link: https://pitp.zoom.us/j/92668739313?pwd=ZmdteFQybU9SbTlPNVQxV3l5dE5FQT09

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realize and investigate topological quantum spin liquids (QSLs) phase. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases. In this talk, I will discuss how to construct Z2 QSLs states as the ground state of a static Hamiltonian with only local two-qubit interactions and a transverse field, and demonstrate its realization in the classical limit at the endpoint of quantum annealing protocol, using D-Wave DW-2000Q machine . I will also demonstrate how to probe signatures of Z2 QSLs fractional statistics in quantum simulators via quasiparticle interferometry. At the end, I will show the robustness of this probe against disorders and dephasing -- effects that are generally pervasive in quantum devices nowadays.

Zoom Link: https://pitp.zoom.us/j/99207971920?pwd=N3R3YUJtWXJWVjFQWlRoZ3hYSDlMZz09

Quantum algorithms have been found which are able to solve important problems exponentially faster than any known classical algorithm. The most well known example is Shor's algorithm which would be able to break all RSA encryption if fault tolerant quantum computers existed for it to be run on. It is currently not believed that quantum computers will be able to efficiently solve NP-Complete problems, but the answer is still unknown. I present a novel quantum algorithm which is able to solve 3-SAT along with numerical simulations to see how it performs on small instances, but new methods of analyzing the complexity of quantum algorithms will need to be developed before we can say exactly how it performs. This will be the goal of my PSI essay.

Zoom Link: https://pitp.zoom.us/j/95795655548?pwd=aU5jNFhFZHEzUWpLK1FvWjd2Q1c2Zz09

We describe a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the so-called Madelung transform between the Schrödinger-type equations on wave functions and Newton's equations on densities turns out to be a Kähler map between the corresponding phase spaces, equipped with the Fubini-Study and Fisher Rao information metrics. This is a joint work with G.Misiolek and K.Modin.

Zoom Link: https://pitp.zoom.us/j/92283820673?pwd=dXQzYWppaUdBVnhtVG1TZTFQQmx4UT09

We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) the mere presence of the horizon will eventually destroy the coherence of the superposition. This occurs because, in effect, the long-range fields sourced by the superposition registers on the horizon which forces the radiation of entangling soft gravitons/photons through the horizon. This allows the horizon to harvest “which path” information about the superposition. The electromagnetic decoherence arises only when the superposed particle carries electric charge. However, since all matter sources gravity, the quantum gravitational decoherence applies to all superpositions. We provide estimates of the decoherence time for such quantum superpositions. Additionally, we show that this decoherence is distinct from--and larger than--the decoherence resulting from the presence of thermal radiation from the horizon (i.e. Hawking/Bunch-Davies/Unruh radiation). We believe that the fact that Killing horizons will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes and horizons in quantum gravity. (Based on arXiv:2205.06279 and arXiv: 2301.00026).

Zoom link:  https://pitp.zoom.us/j/95263116767?pwd=amZ6SkROV1lxckVpdzhNbFhYc1ZiQT09