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 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.

Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that ‘anomalous’ weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401, arXiv:1409.1535]. We elaborate on and extend that result in several directions. Firstly, the original theorem requires certain perfect correlations that can never be realised in any actual experiment. Hence, we provide new theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values. Secondly, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight -- if any one of them is dropped, the anomaly can be reproduced classically. Thirdly, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. All in all, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.

We will review the bosonization approach to Fermi liquids in dimensions above one. We will use this to study a sharp change in the neutral excitation spectrum of fermi liquids that occurs beyond a critical interaction strength whereby an unconventional collective mode exits the particle-hole continuum. This mode is a collective shear wave that features purely transverse current oscillations, in analogy to the transverse sound of crystals. Because it is hard to “see" due to its transversal nature, the shear sound might be already “hiding`' in several metals. We will describe two strategies to “see” the shear sound: the appearance of sharp conductivity dips in ultra clean narrow channels and its coupling to charge-fluctuations under weak magnetic fields.