Scientific Series

The Langlands program is a grand organizing vision for a large slice of number theory and representation theory. A shockingly accurate metaphor for the Langlands program has emerged as electric-magnetic duality in four-dimensional gauge theory, but where the role of spacetime is played by objects from arithmetic. I will describe recent work with Yiannis Sakellaridis and Akshay Venkatesh, in which we apply ideas from QFT (the Gaiotto-Witten electric-magnetic duality for boundary theories) to a fundamental problem in number theory, predicting the relation between L-functions of Galois representations and integrals of automorphic forms.

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What happened in the earliest moments of the Universe? Despite decades of theoretical and observational work, a detailed understanding of the primordial Universe has remained elusive. In this talk, I will show how surveys of millions of galaxies can shed new light on these issues by constraining the statistics of the Universe just after inflation. By combining robust perturbative models with novel numerical techniques, I have placed some of the first (non-Gaussian) constraints on the dynamics and field content of inflation from galaxy surveys; these will sharpen considerably in the next decade as the volume of observational data grows. Through a combination of traditional perturbative approaches and new symmetry-based techniques, I will demonstrate how current and future galaxy surveys can be used to search for a wealth of new physics, including primordial scattering processes and parity violation, opening the door to constraining ultra-high-energy physics with low-energy data.

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Horizons of black holes in equilibrium and null infinity of asymptotically flat space-times are null 3-manifolds but have very different physical connotations. We first show that they share a large number of geometric properties, making them both weakly isolated horizons. We then use this new unified perspective to unravel the origin of the drastic differences in the physics they contain. Interestingly, the themes are woven together in a manner reminiscent of voices in a fugue.The talk is based on joint work with Simone Speziale (arXiv:2401.15618 and arXiv 2401:????).

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Fuzzy dark matter can form cored density distributions, named solitons, at the center of galaxies. Such cores can be viewed as approximate mass sheets and can affect the time delay cosmography Hubble constant (H_0) measurement via the mass sheet degeneracy. We show that a subdominant component of fuzzy dark matter can yield a 10 percent shift in the inferred H_0, if the particle mass is of order 10^-25 eV. The sensitivity of time delays on such cores (difficult to spot otherwise) may give a further probe in constraining the fuzzy dark matter scenario, if an H_0 prior is assumed.

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Brane Webs in Type IIB String Theory can be used to engineer 5d N=1 gauge theories and SCFTs. These brane webs can also be used to obtain so called magnetic quivers, whose 3d Coulomb branches gives the Higgs branch of the 5d theory in question. We will see how to obtain these magnetic quivers for brane webs possibly in the presence of orientifold planes. Then we will see how 3d Coulomb branch technology (such as quiver subtraction) can be used to understand Higgsings and mass deformations of 5d SCFTs.

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In this talk, I will discuss my exploration of the gravothermal collapse of isolated self-interacting dark matter (SIDM) halos, driven deep into the core-collapsed regime where interactions are frequent. We investigate how elastic collisions influence the central region of SIDM halos as they undergo core collapse. In our numerical findings, we discover a remarkable universality in the behavior of halos, allowing us to predict their evolution deep in the core-collapsed regime. We develop a semi-analytic method to characterize the core properties of the halo in the latest stages of evolution, which is crucial for making predictions of the mass of potential black holes forming at the heart of these dark matter halos.

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In my talk I will review motivation for and construction of an infinite derivative gravity. Especially a connection to the string field theory will be highlighted. Then I will demonstrate an exact embedding of the Starobinsky inflation in this construction. In final part I will speak about modifications to observable compared to local models of inflation: spectral indexes, tensor/to scalar ratio, shapes of non-gaussianities and related parameters, gravitational waves production.

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Recent developments point to a remarkable resistance of black holes to tidal deformations under the influence of external gravitational fields. Relying on hidden symmetries, compelling progress has been achieved to explain that the Love numbers, characterizing tidal deformations for Kerr black holes, vanish. How does the phenomenon of tidal squeezing manifest in broader dynamical contexts? An examination of the dynamical tidal deformations in rotating black holes will be presented.

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Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and faithfulness -- that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem stronger than Bell's theorem has been derived, based on extensions of Wigner's friend thought experiment: the Local Friendliness (LF) no-go theorem. Here we show that the LF no-go theorem poses formidable challenges for the field of causal modeling, even when nonclassical and/or cyclic causal explanations are considered. We first recast the LF inequalities, one of the key elements of the LF no-go theorem, as special cases of monogamy relations stemming from a statistical marginal problem; we then further recast LF inequalities as causal compatibility inequalities stemming from a nonclassical causal marginal problem, for a causal structure implied by well-motivated causal-metaphysical assumptions. We find that the LF inequalities emerge from the causal modeling perspective even when allowing the latent causes of observed events to admit post-quantum descriptions, such as Generalised Probabilistic Theories (GPT) or even more exotic theories. We further prove that no nonclassical causal model can explain violations of LF inequalities without violating the No Fine-Tuning principle. Finally, we note that these obstacles cannot be overcome even if one were to appeal to cyclic causal models.

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The Hitchin systems are a remarkable family of integrable models associated to the moduli space of principal bundles on a compact Riemann surface. In this talk, I explain how the loop group uniformization of this moduli space can be used to construct an r-matrix for the Hitchin systems. This r-matrix has been previously used in the description of the Friedan-Schenker connection on the space of conformal blocks.

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When additional degrees of freedom are considered during inflation, a crucial aspect of early universe physics emerges: the generation of isocurvature quantum fluctuations. In this talk, we will present generation and detection forecast for axionic blue-tilted isocurvature power spectra. The large blue-tilt readily evades current CMB bounds. Following a brief review, we will discuss a SUSY-embedded axion model which generates a strongly blue tilted (nI~4) isocurvature spectrum during inflation when the quantum modes are starting to be underdamped ( m/H > 3/2 ). Interestingly, there exist parametric regions with strong resonant spectral behavior that lead to rich isocurvature spectral shapes and large amplitude enhancements. These can be particularly interesting with observational consequences, in relation to the generation of PBH and GWs. The isocurvature spectral tilt is directly linked to the axion mass during inflation. Detecting blue-tilted isocurvatures can offer indirect evidence of a weakly interacting dark matter-like spectator field beyond conventional thermal-relic scenarios. Lastly, we will examine and forecast constraints for experiments such as Euclid (upcoming) and MegaMapper (proposed) using EFTofLSS based perturbative techniques. In the process we will comment upon the consistent renormalization requirements for mixed adiabatic and blue isocurvature primordial spectra.

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“Saturons" are macroscopic objects that saturate the field theoretic upper bound on microstate degeneracy. Due to their maximal microstate entropy, from a quantum information perspective, saturons and black holes belong to the same universality class with common key properties.  However, as opposed to black holes,  saturons do not require gravity and can emerge via ordinary renormalizable interactions, such as QCD, in the form  of soliton-like states. Due to this feature, saturons serve as laboratories for understanding certain properties of black holes. After reviewing the general properties of saturons, we discuss their implications for fundamental physics and cosmology. In particular, we explain how saturons can lead to a new form of phase transition. 

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