Scientific Series

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.

Device-independent self-testing allows user to identify the measured quantum states and the measurements made in a device using the observed statistics. Such verification scheme only requires assuming the validity of quantum theory and no-signalling. As such, no assumptions are required about the inner-workings of the device. Hence, self-testing allows laymen to test the serviceability of a quantum device without needing its blueprint. This talk will be primarily focused on the self-testing of bipartite entangled pure states [Nat. Comms. 8, 15485 (2017)]. Also, I will be touching on the recent study of the geometry of the quantum set [In preparation].

We review recent developments concerning the dynamics of QCD in 2+1 dimensions. We will discuss the phases of the theory depending on the matter representations and the Chern-Simons level. We present several new dualities and conjectures about the behaviour of these theories in their strongly coupled phases.

One of the most concrete implications of the discovery of the Higgs boson is that, in the absence of physics beyond the standard model, the long term fate of our universe can now be established through precision calculations. Are we in a metastable minimum of the Higgs potential or the true minimum? If we are in a metastable vacuum, what is its lifetime? To answer these questions, we need to understand tunneling in quantum field theory.

This talk will give an overview of the interesting history of tunneling rate calculations and all of its complications in calculating functional determinants of fluctuations around the bounce solutions. Several problems has persisted for the last four decades, and we present new solutions to these problems that enabled us to calculate exact closed-form expressions of the functional determinant. Applied to the Standard model, we then get the first-ever complete calculation of the lifetime of our universe.

Moore and Tachikawa conjecture that there exists a functor from the category of 2-bordisms to a certain category whose objects are algebraic groups and morphisms between $G$ and $H$ are given by affine symplectic varieties with an action of $G\times H$.  I will explain a proof of this conjecture due to Ginsburg and Kazhdan, and its relation to Coulomb branches of certain quiver gauge theories which allows to make interesting calculations.

Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. By contrast, I will show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting. I will show that a subset of these novel phases are "time-crystals" in that they spontaneously break the underlying time-translation symmetry of the Floquet drive. Strikingly, the time-crystal phase is remarkably stable to all weak local deformations of the underlying Floquet drives, and the phase simultaneously also spontaneously breaks Hamiltonian dependent emergent spatial symmetries. Thus, the time-crystallinity goes hand in hand with spatial symmetry breaking and, altogether, these phases exhibit a novel form of simultaneous long-range order in space and time. I will describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states. 

Quantum effects render black holes unstable. In addition to Hawking radiation, which leads to the prediction of a long lifetime, there is the possibility of quantum tunneling of the black hole geometry itself. A robust possibility for treating the quantum tunneling of a spacetime geometry is through a complex path integral and Picard-Lefschetz theory. I will illustrate the semiclassical approximation of complex path integrals using these techniques with an analytically solvable 1D quantum potential—the inverse square barrier—and describe the setup of the calculation for spherically symmetric black holes. While the black hole calculation is incomplete, I will be able to describe a surprising extension of this setup to the more astrophysical rotating Kerr black hole.

The long-awaited detection of gravitational waves has provided us with another source of information about the Universe. In this talk I will give an overview of how we extract information from gravitational wave signals with a focus on signals for which we do not have a definitive and reliable model for what the signal looks like. In particular I will describe how we can analyze the signal emitted after two neutron stars have merged. I will describe how the information extracted from such a signal can be used to place constrains on the equation of state of dense matter.

 I will present several studies showing a surprising pattern. Not only can preschoolers learn abstract higher-order principles from data, but younger learners are actually better at inferring unusual or unlikely principles than older learners and adults. This pattern also holds for children in Peru and in Headstart programs in Oakland, California. I relate this pattern to computational ideas about search and sampling, to evolutionary ideas about human life history, and to neuroscience findings about the negative effects of frontal control on wide exploration. My hypothesis is that our distinctively long, protected human childhood allows an early period of broad hypothesis search, exploration and creativity, before the demands of goal-directed action set in.

We work out constraints imposed by channel duality and analyticity on tree-level amplitudes of four identical real scalars, with the assumptions of a linear spectrum of exchanged particles and Regge asymptotic behaviour. We reduce the requirement of channel duality to a countably infinite set of equations in the general case. We show that channel duality uniquely fixes the soft Regge behaviour of the amplitudes to that found in String theory, (-s)^(2t). Specialising to the case of tachyonic external particles, we use channel duality to show that the amplitude can be any one in an infinite-dimensional parameter space, and present evidence that unitarity doesn't significantly reduce the dimension of the space of amplitudes.
This talk is based on 1707.08135 by Pranjal Nayak, Rohan R. Poojary and RMS.

Galaxy clusters represent excellent laboratories to search for Axion-Like Particles (ALPs). They contain magnetic fields which can induce quasi-sinusoidal oscillations in the X-ray spectra of AGNs situated in or behind them. Ultra-deep Chandra observations of the Perseus cluster contain over 5 x 105 counts from the central NGC1275 AGN, and represent an extraordinary dataset for ALP searches. In this talk I will describe how we used these to search for spectral irregularities from the AGN. No irregularities were found at the ~30% level, allowing us to place leading constraints on the ALP-photon mixing parameter gaγγ  <1.5 × 10−12GeV−1 for ma < 10-12 eV. I will move on to discuss the upcoming Athena X-ray Observatory, due for launch in 2028. The X-ray Integral Field Unit (X-IFU) instrument onboard will be far better able to constrain ALPs than Chandra, due to its excellent energy resolution. Using the SIXTE simulation software, we estimate that non-observation of spectral modulations for a 200ks observation of NGC1275 will constrain gaγγ  <1.5 × 10−13GeV−1 , an order of magnitude improvement over that derived from Chandra data.

Thermodynamics is a closed field of research. The laws of thermodynamics, established in the nineteenth century, are still standing unchallenged.  However, they do not include gravity. Inclusion of gravity into the thermodynamical system can significantly modify the expected behavior of the system. We will demonstrate that gravity dynamically induces a maximal temperature that can be reached in a gas of particles.  We will also show how gravity can significantly change the Poincare recurrence theorem, and sometimes even prevent the recurrence from happening.