Talks

Nonlinear dynamics aims to elucidate the basic mechanisms necessary to reflect the temporal behavior of a natural system. The data analysis and modeling techniques proposed by artificial intelligence (deep networks, computational reservoirs, recurrent networks, as examples), on the other hand, ostensibly resign the mechanistic vision for a data-oriented modeling paradigm.  In these lectures, these apparently antagonistic approaches will be analyzed in parallel, using as examples my work on the physics of birdsong production and vocal learning.

In 2010, Kontsevich and Soibelman defined Cohomological Hall Algebras for quivers and potential as a mathematical construction of the algebra of BPS states. These algebras are modeled on the cohomology of vanishing cycles, which makes these algebras particularly hard to study but often result in interesting algebraic structures. A deformation of a particular case of them gives rise to a positive half of Maulik-Okounkov Yangians. The goal of my talk is to give an introduction to these ideas and explain how for the case of tripled cyclic quiver with canonical cubic potential, this algebra turns out to be one-half of the universal enveloping algebra of the Lie algebra of matrix differential operators on the torus, while its deformation turn out be one half of an explicit integral form of the Affine Yangian of gl(n).

The next generation of extragalactic surveys will reveal the full diversity of the galaxy assembly process: from environment-dependent evolution to the build-up of mass inside galaxies, and with a complete accounting of all relevant processes/constituents ensured by multi-wavelength coverage. Observations at radio wavelengths carry a unique potential in that they can probe star-formation activity and cold gas content, i.e. place constraints on both galaxy growth rates and the fuel for future galaxy growth. With the construction of the Square Kilometre Array (SKA), radio astronomy will enter a new era; high-sensitivity, high-resolution and dust-unbiased radio imaging will provide a confusion-free census of star formation and black hole activity, regardless of whether these occur in dust-obscured or optically thin regions. I will review the high-priority science cases developed by the SKA extragalactic continuum science working group and outline the challenges brought about by our still only partial understanding of some of the astrophysical mechanisms producing radio emission (e.g. the relation between star formation rate and radio continuum luminosity).
Thanks to an order of magnitude increase in survey speed compared to existing radio telescopes, SKA surveys will detect millions of galaxies. I will summarize how - in addition to advancing our understanding of the drivers of the cosmic star-formation history - commensal survey design will ensure that information on galaxy shapes, redshifts, spatial distribution and polarization can be used for cosmological studies and to trace the evolution of magnetic fields in galaxies and the cosmic web.

I will introduce the Entanglement Bootstrap, a program to extract and understand the universal information characterizing a state of matter, starting from the local entanglement structure of a single representative state. This universal information is usually packaged in the form of a quantum field theory; the program therefore provides a surprising new perspective on quantum field theory. I will discuss what we can learn about gapped topological phases and their associated topological field theories, and about quantum critical points and their associated conformal field theories.