Scientific Series

The core Python language is not particularly powerful or fast for numerical computing.  Fortunately, there is a large "numerical python" library, "numpy", that is a standard part of any Python-using scientist's toolkit.  I will present numpy, the associated "scientific python" library, "scipy", and the popular "matplotlib" plotting library.

I will talk about compact hyperkahler manifolds, which generalize the famous K3 surface to the higher dimensions. Given a compact simple hyperkahler manifold $M$, I will describe how the structure of cohomology algebra H*(M) is related with the so(b_2+2) Lie algebra action and the second cohomology group. I will explain how this is applied to the generalization of Kuga-Satake construction which allows us to assign for K3-type Hodge structure a Hodge structure of weight one (i.e. complex torus).

Advanced LIGO and Advanced Virgo are currently in the middle of their third observing run, and releasing open public event alerts for the first time. The LIGO-Virgo collaboration has issued 29 un-retracted candidate event alerts as of September 20th, 2019, potentially adding dozens more known compact binary object mergers to the eleven confident LIGO-Virgo detections from the first two Advanced-era observing runs. I’ll review novel LIGO-Virgo results to date, and discuss the challenges of extracting interesting new physics from noisy detector data. Finally, I'll summarize future prospects for astrophysics, cosmology, and tests of general relativity with gravitational waves, and the roadmap to future gravitational wave detectors on Earth and in space.

Hypermassive neutron stars (HMNS) can be briefly formed after a binary neutron star merger and are likely to be highly deformed and strongly oscillating. These oscillations may be seen as modulation of the associated short gamma-ray burst and could provide observational evidence for the HMNS phase. I will discuss the prospects for their detection and the important physical information that can be gained by their observation.

In this talk, I will describe some of the recent progress on computing holographic correlators using analytic bootstrap techniques combined with supersymmetric localization.  From taking a certain flat space limit of the holographic correlators, one can obtain scattering amplitudes of gravitons in string theory, and one can then reproduce some of the known results for these scattering amplitudes.  I will focus mostly on the case of the 4d {\cal N} = 4 super-Yang-Mills theory, but I will also mention related work in the 3d ABJM theory.

 Python is a widely used programming language for scientific
computing, data analysis, and machine learning. This tutorial will
feature an introduction for those with little or no background.

Non minimal couplings of scalar fields to gravity are a generic feature of Lagrangian formulations of gravity. Although challenging to probe at low energies and small curvature, such couplings can play a crucial role in cosmological setups. We focus on their impact in the production of scalar dark matter and its interplay with inflationary physics. We show how the standard non-thermal production mechanism of scalar dark matter, the misalignment mechanism, is modified, and explore how alternative scenarios like production from inflationary fluctuations become viable. We study potentially observable features of these scenarios, such as the enhancement of dark matter substructure at small scales and the generation of an isocurvature component in the fluctuations of the CMB.

A massive U(1)' gauge boson known as a “dark photon” or A', has long been proposed as a potential explanation for the muon g − 2 anomaly. Recently, experimental results have excluded this possibility for a dark photon decaying visibly and invisibly. I revisit this idea and consider a model where A' couples to inelastic dark matter, leading to a semi-visible decay mode. I show that for large mass splittings between the dark sector states this decay mode is enhanced, weakening the invisibly decaying dark photon bounds. As a consequence, A' resolves the g −2 anomaly in a region of parameter space the thermal dark matter component of the Universe is readily explained.

The category of coherent sheaves on an interesting variety X has an extremely annoying property: does not have enough projectives, so it cannot be equivalent to the category of modules over an algebra. However, if you pass to the derived category, this defect can be fixed in many interesting cases, by finding a tilting generator: that is, a vector bundle T such that any coherent sheaf can be resolved by a complex consisting of sums of copies of T, and Ext^i(T,T)=0 for all i>0. If A=End(T), then we obtain an equivalence of derived categories between finitely generated A-modules and Coh(X). This provides a bridge between representation theory and algebraic geometry. This bridge was largely built for us by Bezrukavnikov and Kaledin, but they did not make it very easy for the rest of us to cross it; in particular, while both ends of the bridge are in characteristic 0, the middle is in characteristic p. I’ll talk about how recent input from work in 3d field theory by Braverman, Finkelberg and Nakajima allows us in certain cases to reroute this bridge and avoid characteristic p, while getting a more concrete understanding of the algebra A on the other side.

Time is one of the most basic features of nature which has been extensively discussed in philosophy and physics. In contrast, time is rather neglected in neuroscience; here time is only conceived in terms of our perception and cognition of time. That leaves open the relevance of time itself, that is, how the brain constitutes its own temporal dynamics and how that is relevant for, for instance, consciousness and other mental features like self. My talk will discuss recent findings showing various features of the brain's temporal dynamics and how these are relevant in constituting mental features like consciousness and self as well as their changes in psychiatric disorders. 

I will discuss joint work with Roman Bezrukavnikov on a categorical version of Hikita duality, which relates coherent sheaves on a symplectic resolution to constructible sheaves on the loop space of the dual resolution. I will focus on a basic case, where this can be made very explicit, and finish with some wild speculation on further generalisations.

In this talk I review some of what we have learned from string theory about the criteria one needs for a quantum theory to be able to consistently couple to quantum gravity (the landscape) as opposed to one that looks consistent but cannot be consistently coupled to gravity (the swampland).  Moreover, I review some of the cosmological implications of these conditions for our universe.