Scientific Series

Generative modeling via diffusion processes is already a vast field of literature. In this introduction, I will give an entry point to this field by going over the main concepts and deriving the essential results of the area. Thus, by the end of the talk, we would have a minimal pipeline for implementing the generative model. Furthermore, I will outline several alternative ways for learning such models that the community has developed in recent years. These directions bring novel perspectives and new capabilities of generative modeling.

Zoom link:  https://pitp.zoom.us/j/98786491081?pwd=U1cvZzBQT2VUZDl5Ykd0c1lqY29aZz09

Fast Radio Bursts (FRBs) are extremely energetic, millisecond-duration radio bursts coming outside our galaxy. The burst arrival time at different frequencies implies the number of electrons it has encountered in the foreground. Therefore, FRB is considered a promising new cosmology probe. The uncertainty of the circum-burst environment is one of the biggest concerns regarding its potential as a probe. In this talk, I will review the current understanding of the FRB progenitor and the recent study of the circum-burst environment. I will also discuss the many remaining mysteries, including the seemingly diverse nature of the sources, the magneto-environment, and the 16-day periodicity I found with one source. With the current and upcoming instruments, there will be more FRBs with orders of magnitude better spatial resolution detected in the next few years. The result will be an explosion of opportunity for understanding the burst origin and probing cosmic matter distribution at various spatial scales.

Zoom link: https://pitp.zoom.us/j/92030175800?pwd=dWlGVjV0Qnh5bGhLMk1pd01yRmNKQT09

Trace map on deformation quantized algebra leads to the algebraic index theorem. We investigate a two-dimensional chiral analogue of the algebraic index theorem via the theory of chiral algebras developed by Beilinson and Drinfeld. We construct a trace map on the elliptic chiral homology of the free beta gamma-bc system using the BV quantization framework. As an example, we compute the trace evaluated on the unit constant chiral chain and obtain the formal Witten genus in the Lie algebra cohomology. This talk is based on joint work with Si Li.

Zoom link:  https://pitp.zoom.us/j/91920988875?pwd=dUE1WDI5Q21KWTUxTGNsM21nblh5Zz09

For n≥3, we demonstrate the existence of quantum codes which are local in dimension n with V qubits, distance V^{(n−1)/n}, and dimension V^{(n−2)/n}, up to a polylog(V) factor. The distance is optimal up to the polylog factor. The dimension is also optimal for this distance up to the polylog factor. The proof combines the existence of asymptotically good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding theorem by Gromov-Guth.

Zoom link:  https://pitp.zoom.us/j/96227350980?pwd=TEFtamRmTXg3dnBMNEhKUkpHbmVoZz09

In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

Zoom link:  https://pitp.zoom.us/j/97435154387?pwd=OHYrRW9uSW5VeHRFUld1dmtVbmJiZz09

In any approach to quantum gravity, the quantum representation theory of the "algebra" of Cauchy hypersurface deformations plays a crucial role. Its faithful implementation is a key step towards constructing a valid theory of quantum gravity as it ensures quantum spacetime diffeomorphism covariance. Bergmann and Komar were the first to consider the possibilty of a corresponding quantum "group". Its construction is mathematically challenging in more than 1+1 spacetime dimensions because one leaves the realm of Lie algebras and Lie groups. After an introduction to these concepts, we show that the Bergmann Komar "group" can indeed be faithfully implemented in a weakly self-interacting truncation of 3+1 quantum gravity with two propagating polarisations. We then discuss possible implications for the actual, untruncated theory.

Zoom link:  https://pitp.zoom.us/j/91488383205?pwd=bkxGS0huMGNEYXc3Y2FJSGZHQ0pqQT09

Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing using no or few additional quantum resources, in contrast to fault-tolerant schemes that come along with heavy overheads. Error mitigation has been successfully applied to reduce noise in near-term applications. 

In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively `undone' for larger system sizes. We set up a framework that rigorously captures large classes of error mitigation schemes in use today. The core of our argument combines fundamental limits of statistical inference with a construction of families of random circuits that are highly sensitive to noise.

We show that even at poly loglog depth, a super-polynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. They also impact other near-term applications, constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.

Zoom link:  https://pitp.zoom.us/j/95736148335?pwd=akZLaHE5aStNQVZOeVFETlltNzVwdz09

I will use the S-matrix Bootstrap to carve out the space of unitary, crossing symmetric, and supersymmetric graviton scattering amplitudes in nine, ten, and eleven dimensions. I will introduce a novel extension of positivity for massless particles beyond the forward limit called “positivity in the sky” that significantly improves the convergence of the bootstrap algorithm.

I will show the bounds on the first leading correction to maximal supergravity, study the physics of the extremal amplitudes and compare them with the available nonperturbative String and M-theory results.

Zoom link:  https://pitp.zoom.us/j/99182927406?pwd=bWxIazFvUzhVQkpBdWluZURIM21wUT09

Recently, machine learning has become a popular tool to use in fundamental science, including lattice field theory. Here I will report on some recent progress, including the Inverse Renormalisation Group and quantum-field theoretical machine learning, combining insights of lattice field theory and machine learning in a hopefully constructive manner.

Zoom link:  https://pitp.zoom.us/j/95456375462?pwd=WmtZMloyclAyZzBwVEZHQ3gxVnkrUT09

Gamma ray bursts (GRBs) are the most luminous electromagnetic events in the universe. Short GRBs, typically lasting less than 2 seconds, have already been associated with binary neutron star (BNS) mergers, which are also sources of gravitational waves (GWs). The ultimate fate of a BNS, after coalescence, is usually expected to be a black hole (BH) with 2-3 solar masses. However, numerical relativity simulations indicate the possible formation of a short-lived hypermassive neutron star (HMNS), lasting for tens to hundreds of milliseconds after the BNS merger and before gravitational collapse forms a BH. The HMNS is expected to emit GWs with kHz frequencies that will be detectable by third generation ground-based GW detectors in the 2030s. I will present results from a recent analysis that revealed evidence for HMNSs by looking for kHz quasiperiodic oscillations in gamma-ray observations obtained in the 1990s with the Compton Gamma Ray Observatory.

Zoom link:  https://pitp.zoom.us/j/96687956901?pwd=MkgrUGlqY3IyRCs2bXJYVkhUVEpPZz09

The Lorentzian path sum in causal set theory(CST)  can be defined using the discrete EInstein-Hilbert or Benincasa-Dowker-Glaser(BDG)  action. It has been a long standing question  in CST whether  the path sum is  dominated by a class of non-continuum like layered posets — this would make it much harder to find a dynamically generated continuum approximation —  or whether the BDG action suppresses this contribution.  In this talk I will discuss a series of results that show that to  leading order in the saddle point approximation,  this dominating  class of layered posets is strongly suppressed. Moreover this is true for a  more general class of actions which include the BDG action.   We conclude with some remarks on the interpretation of these results and related  open questions. 

Zoom link:  https://pitp.zoom.us/j/91794153633?pwd=TTFnS0hpQ2s5eFVDM3k5ZDkxcndkUT09

In this talk I will show the equivalence of several different tests of the Jacobi identity for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT. Along the way I will clarify the role of the order of soft and collinear limits in obstructing the Jacobi identity for soft insertions and I will argue that, despite their current-algebra-like properties, soft insertions as formulated in this talk cannot be interpreted as local operators in celestial conformal field theory.

Zoom link:  https://pitp.zoom.us/j/99642885302?pwd=dWZhbzZUYnBuSlJ3UzBhSHdqdzVKdz09