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We establish a direct connection between scattering amplitudes for bi-adjoint scalar theories and a classic polytope--the "associahedron"--known to mathematicians since the 1960s. We find an associahedron naturally living in kinematic space. The tree level scattering amplitude is simply a geometric invariant of the associahedron called its "canonical form" [2], which is a differential form on kinematic space with logarithmic singularities on the boundaries of the associahedron. We show that basic physical principles like locality and unitarity are "rediscovered" as properties of the geometry, and certain "soft" limits can be converted to geometric statements as well.

The associahedron in kinematic space plays an important role in the context of scattering equations. We discover that the scattering equations act as a diffeomorphism between the interior of the open string moduli space (yet another associahedron) and the associahedron in kinematic space. This observation provides the key to a novel derivation of the bi-adjoint CHY formula. Finally, we emphasize the importance of the scattering amplitude as a differential form, as suggested by the "canonical form" construction. We argue on general grounds that every color-dressed amplitude is dual to a form on kinematic space. This is motivated by the surprising observation that "projective" forms on kinematic space satisfy Jacobi identities and therefore have novel implications for color-kinematics duality.

References:

[1] Nima Arkani-Hamed, Yuntao Bai, Song He & Gongwang Yan. In preparation.

[2] Nima Arkani-Hamed, Yuntao Bai & Thomas Lam. Positive Geometries and Canonical Forms. arXiv 1703.04541

The radial acceleration relation is an empirical universal scaling relation between the total gravitational field and the Newtonian acceleration generated by baryons at any given radius within spiral galaxies. In this talk, I will discuss the possibility that such a relation arises from interactions between baryons and dark matter (DM), rather than from feedback processes or modifications of gravity. Starting from this premise, I will discuss what we can infer about the nature of baryon-DM interactions. In particular, I will argue that  such interactions must depend on the local DM density in order to correctly reproduce the observed behavior of spiral and elliptical galaxies. I will briefly revisit existing phenomenological, astrophysical and cosmological constraints on baryon-DM interactions in light of the unusual density dependence of our cross-section. I will conclude by mentioning possible ways of realizing this scenario in particle physics models, and discuss a non-relativistic toy model.

I will describe our recent work from 1709.07460, where we introduce a new renormalization group algorithm for tensor networks. The algorithm is based on a novel understanding of local correlations in a tensor network, and a simple method to remove such correlations from any network. It performs comparably with the best competing algorithms on 2D/(1+1)D systems, but is significantly simpler to implement, and easier to generalize to different lattices and graphs, including to higher dimensions. I will begin the talk by discussing renormalization group methods for tensor networks in general, then describe our algorithm and its advantages, show some benchmark results, and finally comment on the status of implementing real-space renormalization for 3D tensor networks.

The much-anticipated joint detection of gravitational waves and electromagnetic radiation was achieved for the first time on August 17, 2017, for the binary neutron star merger GW170817.  This event was detected by Advanced LIGO/Virgo, gamma-ray satellites, and dozens of telescopes on the ground and in space spanning from radio to X-rays.  In this talk I will describe the exciting discovery of the optical counterpart, which in turn led to several detailed studies across the electromagnetic spectrum.  The results of the observations carried out by our team include the first detailed study of a "kilonova", an optical/infrared counterpart powered by the radioactive decay of r-process nuclei synthesized in the merger, as well as the detection of an off-axis jet powering radio and X-ray emission.  These results provide the first direct evidence that neutron star mergers are the dominant site for the r-process and are the progenitors of short GRBs.  I will also describe how studies of the host galaxy shed light on the merger timescale, and describe initial constraints on the Hubble Constant from the combined GW and EM detection.        

In this talk I will define the quantum K-theory of Nakajima quiver varieties and show its connection to representation theory of quantum groups and quantum integrable systems on the examples of the Grassmannian and the flag variety. In particular, the Baxter operator will be identified with operators of quantum multiplication by quantum tautological classes via Bethe equations. Quantum tautological classes will also be constructed and, time permitting, an explicit universal combinatorial formula for them will be shown.
Based on joint works with P.Koroteev, A.Smirnov and A.Zeitlin

I present a one-function family of solutions to 4D vacuum Einstein equations. While all diffeomorphic to the extremal Kerr black hole, they are labeled by well-defined conserved charges and are hence distinct geometries. Out of the appropriate combination of these charges, we construct a Virasoro algebra and consistency conditions lead us to a proposal for identifying extreme Kerr black hole microstates, dubbed as extreme Kerr fluff. Counting these microstates, we correctly reproduce the extreme Kerr black hole entropy.

The Cosmic Web is the fundamental spatial organization of matter in the Universe on scales of a few up to a hundred Megaparsec, scales at which the Universe still resides in a state of moderate dynamical evolution. Galaxies, intergalactic gas and dark matter exist in a wispy weblike spatial arrangement consisting of dense compact clusters, elongated filaments, and sheetlike walls, amidst large near-empty void regions. The weblike pattern is marked by prominent anisotropic features, a distinct multiscale character, a complex spatial connectivity of its various morphological components and a clear asymmetry between voids and overdense regions.

This seminar will describe recent work on the structure and dynamics of the Cosmic Web. For the analysis of its complex and multiscale structural pattern, we invoke concepts from computational topology and computational geometry. We apply the explicit multi-scale -- parameter-free and scale-free -- Nexus/MMF Multiscale Morphology formalism to dissect the cosmic mass distribution into clusters, filaments, walls and voids. This results in a systematic study ofthe evolving size and volume distribution of these structural components. Subsequently, we assess the mass and halo distribution in the filaments and walls, and follow their evolution.

To study the dynamical evolution of the cosmic web, we describe our adhesion model of cosmic structure formation based on Voronoi and Delaunay tessellations. Subsequently, we will shortly describe how a full phase-space analysis allows us to understand the growth of structural complexity in terms of the emergence and spatial connectivity of singularities and caustics. Finally, we will discuss the migration flows of matter and galaxies along the cosmic web and prospects of using voids to constrain dark energy and dark matter.