Talks

Directional dark matter detectors using diamond as a target material offer a novel solution to overcome solar neutrino backgrounds. Sub-micron damage tracks from nuclear recoils can be read out via advanced quantum sensing techniques with nitrogen-vacancy (NV) centers. I will discuss recent advancements in strain-sensitive quantum interferometry that enable precise strain imaging, paving the way for directional particle detection. These developments highlight the potential of diamond-based detectors for advancing dark matter and neutrino physics, as well as material science applications.

Emergent Modified Gravity (EMG) is a post-Einsteinian theory of canonical gravity. In this formulation, modified constraints are required to preserve an algebra of hypersurface deformation form and will in general imply modified structure functions. This procedure leads to the conclusion that spacetime is an emergent object with a nontrivial dependence on the gravitational phase space variables through the modified structure functions. Consistency conditions are imposed on the modified constraints and the emergent spacetime metric to ensure general covariance. The resulting modifications allowed by EMG go beyond those obtained from adding higher curvature terms and can result in nonpolynomial dependencies on extrinsic curvature components. In this talk, we discuss how a particular interpretation of such modifications as holonomy terms makes it possible to use EMG as a covariant framework for effective (loop) quantum gravity. We then focus on dynamical solutions of the spherically symmetric model which include nonsingular black holes, new effects to gravitational collapse, and MOND-like effects at intermediate scales.

The groundbreaking detection of gravitational waves from merging black holes has forever changed how we observe the Universe. Upcoming detectors, like the Laser Interferometer Space Antenna (LISA), will unlock new opportunities by allowing us to detect mergers between stellar-mass black holes (tens of solar masses) and supermassive black holes (SMBHs, millions to billions of solar masses). These fascinating events, known as extreme-mass-ratio inspirals (EMRIs), provide a wealth of information about the dynamics near SMBHs. A key formation channel for EMRIs involves weak gravitational interactions—two-body kicks—from surrounding stars and compact objects that gradually alter the small black hole's orbit, eventually driving it into the SMBH. However, the picture changes when we consider the presence of SMBH companions, which can induce high orbital eccentricities, further enhancing EMRI formation. In this talk, I will show that combining these two processes is crucial for understanding the progenitors of EMRIs. Moreover, I will demonstrate that SMBH binaries create EMRIs more efficiently than either process alone, making it truly rain black holes! This scenario results in a substantial stochastic gravitational wave background for future detectors like LISA. Finally, I will also discuss how this mechanism affects tidal disruption events and address the tantalizing question: Is it raining stars, too?

I'll discuss the representation theory of line operators in 3d holomorphic-topological theories, following recent work with Wenjun Niu and Victor Py. Examples of the line operators we have in mind include half-BPS lines in 3d N=2 supersymmetric theories (reinterpreted in a holomorphic twist). We compute the OPE of line operators, which endows the category with a meromorphic tensor product, and establish a perturbative nonrenormalization theorem for the OPE. Then, applying Koszul-duality methods of Costello and Costello-Paquette, we represent the category of lines as modules for a new sort of mathematical object, which we call a dg-shifted Yangian. This is an A-infinity algebra, with a chiral coproduct whose data includes a Maurer-Cartan element that behaves like an infinitesimal r-matrix. The structure is a cohomologically shifted version of the ordinary Yangians that represent lines in 4d holomorphic-topological theories.

Over the three lectures and the tutorial, I want to explore some problems in enumerative algebra that can be understood by associating lattices to semistandard Young tableaux. I will introduce a family of rational functions called Hall--Littlewood--Schubert series (HLS series), which was recently introduced by Christopher Voll and myself. The enumerative problems we discuss will be solved by judicious substitutions of the variables of the HLS series.

Over the three lectures and the tutorial, I want to explore some problems in enumerative algebra that can be understood by associating lattices to semistandard Young tableaux. I will introduce a family of rational functions called Hall--Littlewood--Schubert series (HLS series), which was recently introduced by Christopher Voll and myself. The enumerative problems we discuss will be solved by judicious substitutions of the variables of the HLS series.