Talks

Zoom Link:  https://pitp.zoom.us/j/93581608531?pwd=d3NRQXRGNTNISkhuWmxLYkJMZllTUT09

Based on recent work arXiv:1902.08207 and arXiv:1911.02018 with E. Verlinde.

The discovery of gravitational wave signals from merger events of massive binary-black-hole (BBH) systems have prompted a renewed debate in the scientific community about the existence of primordial black holes (PBHs) of O(1-100) solar masses. These objects may have formed in the early Universe and could constitute a significant portion of the elusive dark matter that, according to standard cosmology, makes up the majority of the matter content in the universe. I will review the most recent developments of this field, with focus on multi-messenger prospects of detection. In the first part of the talk, I will present the prospects of discovery for both a hypothetical PBH population and the guaranteed population of astrophysical isolated black holes in our Galaxy, based on the radio and X-ray emission from the interstellar gas that is being accreted onto them (the “shiny dresses”). A future detection will be possible thanks to the expected performance of forthcoming radio facilities such as SKA and ngVLA. Then, I will turn my attention to scenarios where primordial black holes constitute a sub-dominant component of the dark matter, and study the impact of dark matter mini-spikes that are expected to form around them (the “dark dresses”) on several observables. In this context, I will first present an updated computation of the PBH merger rate as a function of DM fraction and redshift that takes into account the impact of the dark dresses. Then, I will discuss the observational prospects of these dresses in binary systems composed of a stellar-mass and an intermediate-mass black hole: I will show a novel calculation of the dephasing of the gravitational waveform induced by the DM spike, potentially detectable with the LISA space interferometer.DARK AND SHINY DRESSES AROUND BLACK HOLES DANIELE GAGGERO (UAM)July 6, 2020 Zoom Line: https://laurentian.zoom.us/j/92591146494

Over the last decade, the Effective Field Theory of Large Scale Structure (EFTofLSS) has emerged as a frontrunner in the effort to produce accurate models of cosmological statistics. Quantities such as power spectra can be fit with sub-percent precision, and there is a wealth of literature applying the formalism to more complex statistics. It is interesting to ask what lies ahead for the theory. Can it be used for cosmological parameter inference? And is it just for statistics based on the 3D density field?

 

In this talk, I will present a pedagogical introduction to the EFTofLSS, discussing its motivation and basic formalism, as well as a few of its theoretical challenges. To demonstrate the utility of the theory beyond the blackboard, I will discuss the analysis of galaxy power spectra. Using this model, competitive constraints can be placed on cosmology utilizing all the large-scale spatial information, not just the position of the Baryon Acoustic Oscillations. In particular, this yields the strongest CMB-independent measurement of H0. 

 

In answering the second question, I will introduce two less conventional applications of the EFTofLSS. Firstly, the marked density field. This is simply the matter field weighted by its local overdensity, and recent works have shown its power spectrum to be capable of placing strong constraints on the neutrino mass. I will discussing its perturbative modeling, highlighting its unusual features, and how the model allows us to shed light on the surprising constraining of the statistic. An additional statistic of interest is weak lensing. Creating an analytic model for this has its own complications, since it is sensitive to a large range of scales, requiring extensions to the usual EFTofLSS modeling. Crucial to this effort is the development of a matter power spectrum model which is accurate on all scales; I will present the results of recent modeling efforts within the ‘Effective Halo Model’, and discuss future applications to integrated statistics such as weak lensing.

Zoom Link: https://pitp.zoom.us/j/91697113596?pwd=OTh3ZjZ5SHd5Q09sTFdReUMyb0hpUT09

After the discovery of the Higgs boson in 2012, the Large Hadron Collider (LHC) at CERN has turned from a discovery machine to a precision machine. The highly boosted events measured by the LHC experiments are, for the first time, providing us a window on the details of the electroweak symmetry breaking mechanism. A crucial condition to maximise the reach of these studies is a profound understanding of the theoretical implications of perturbative Quantum Field Theory, and in particular of Quantum ChromoDynamics (QCD), for the physics of hadronic collisions at the LHC. In this talk, I will provide an account of the opportunities and the challenges that precision physics at the LHC can offer, focusing in particular on the recent developments in our understanding of higher order calculations in perturbative Quantum Field Theory and how they can help us understand the Higgs sector of the Standard Model.

Hessenberg varieties are a distinguished family of projective varieties associated to a semisimple complex algebraic group. We use the formalism of perverse sheaves to study their cohomology rings. We give a partial characterization, in terms of the Springer correspondence, of the irreducible representations which appear in the action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. We also prove a support theorem for the universal family of regular Hessenberg varieties, and we deduce that its fibers, though not necessarily smooth, always have the "Kahler package". This is joint work with Peter Crooks.

Categorical representation theory is filled with graded additive categories (defined by generators and relations) whose Grothendieck groups are algebras over \mathbb{Z}[q,q^{-1}]. For example, Khovanov-Lauda-Rouquier (KLR) algebras categorify the quantum group, and the diagrammatic Hecke categories categorify Hecke algebras. Khovanov introduced Hopfological algebra in 2006 as a method to potentially categorify the specialization of these \mathbb{Z}[q,q^{-1}]-algebras at q = \zeta_n a root of unity. The schtick is this: one equips the category (e.g. the KLR algebra) with a derivation d of degree 2, which satisfies d^p = 0 after specialization to characteristic p, making this specialization into a p-dg algebra. The p-dg Grothendieck group of a p-dg algebra is automatically a module over \mathbb{Z}[\zeta_{2p}]... but it is NOT automatically the specialization of the ordinary Grothendieck group at a root of unity! Upgrading the categorification to a p-dg algebra was done for quantum groups by Qi-Khovanov and Qi-Elias. Recently, Qi-Elias accomplished the task for the diagrammatic Hecke algebra in type A, and ruled out the possibility for most other types. Now the question is: what IS the p-dg Grothendieck group? Do you get the quantum group/hecke algebra at a root of unity, or not? This is a really hard question, and currently the only techniques for establishing such a result involve explicit knowledge of all the important idempotents in the category. These techniques sufficed for quantum \mathfrak{sl}_n with n \le 3, but new techniques are required to make further progress. After reviewing the theory of p-dg algebras and their Grothendieck groups, we will present some new techniques and conjectures, which we hope will blow your mind. Everything is joint with You Qi.

For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii) Kazhdan–Lusztig cells in the affine Weyl group. In this talk, I will review these results, and I will explain a (partly conjectural) analogous picture for reductive algebraic groups over fields of positive characteristic, inspired by a conjecture of Humphreys. This is joint work with W. Hardesty and S. Riche.

Koszul duality, as conceived by Beilinson-Ginzburg-Soergel, describes a remarkable symmetry in the representation theory of Langlands dual reductive groups. Geometrically, Koszul duality can be stated as an equivalence of categories of mixed (motivic) sheaves on flag varieties. In this talk, I will argue that there should be an an 'ungraded' version of Koszul duality between monodromic constructible sheaves and equivariant K-motives on flag varieties. For this, I will explain what K-motives are and present preliminary results.

Admissible representations of real reductive Lie groups are a key player in the world of unitary representation theory. The characters of irreducible admissible representations were described by Lustig—Vogan in the 80’s in terms of a geometrically-defined module over the associated Hecke algebra. In this talk, I’ll describe a categorification of this module using Soergel bimodules, with a focus on examples. This is work in progress.

Suzuki's functor relates the representation theory of the affine Lie algebra to the representation theory of the rational Cherednik algebra in type A. In this talk, we discuss an extension of this functor to the critical level, t=0 case. This case is special because the respective categories of representations have large centres. Our main result describes the relationship between these centres, and provides a partial geometric interpretation in terms of Calogero-Moser spaces and opers.

In this note we give an alternative presentation of the rational Cherednik algebra H_c corresponding to the permutation representation of S_n. As an application, we give an explicit combinatorial basis for all standard and simple modules if the denominator of c is at least n, and describe the action of H_c in this basis. We also give a basis for the irreducible quotient of the polynomial representation and compare it to the basis of fixed points in the homology of the parabolic Hilbert scheme of points on the plane curve singularity {x^n=y^m}. This is a joint work with José Simental and Monica Vazirani.