It is well known that the observables for some classes of EFTs (eg the non-linear sigma model) naturally can be cast in terms of geometric quantities that are defined on a field space manifold.  One of the main benefits of this geometric approach is that it makes the field redefinition invariance of on-shell amplitudes manifest.  However, the standard approach does not apply to general EFTs; additionally, the field space geometry picture breaks down when one performs field redefinitions that involve derivatives.  In this talk, I will present a proposal for how to extend the notion of field space geometry to general EFTs in such a way as to accommodate general field redefinitions.  I will introduce the framework we call “functional geometry,” and will argue that this approach lays the groundwork for many new developments towards understanding properties of EFTs that circumvents issues associated with field redefinition ambiguities.
 
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I will examine Abrikosov–Nielsen–Olesen (ANO) vortex strings in variants of Abelian Higgs models. In the large flux limit, the equations governing them simplify, and the resulting giant strings realize two sharply distinct phases. I will explore qualitative features of these strings and identify patterns in their physical properties. I’ll also discuss the spectrum of small fluctuations and the associated low energy effective action. I will end by comparing these results to features of confining strings in Yang Mills theory.
 
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Fermi liquid theory is a cornerstone of condensed matter physics. However, Landau’s Fermi liquid theory does not fit into the paradigm of effective field theory in that it is formulated in terms of a kinetic equation rather than an action. We describe a new method that leads to a field-theoretical reformulation of Landau Fermi liquid theory. In this approach, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonization of the Fermi surface. The Berry phase that the Fermi surface acquires when changing shape is shown to be given bythe Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions and applications of the theory are described.

Fermi liquid theory is a cornerstone of condensed matter physics. However, Landau’s Fermi liquid theory does not fit into the paradigm of effective field theory in that it is formulated in terms of a kinetic equation rather than an action. We describe a new method that leads to a field-theoretical reformulation of Landau Fermi liquid theory. In this approach, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonization of the Fermi surface. The Berry phase that the Fermi surface acquires when changing shape is shown to be given bythe Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions and applications of the theory are described.

Fermi liquid theory is a cornerstone of condensed matter physics. However, Landau’s Fermi liquid theory does not fit into the paradigm of effective field theory in that it is formulated in terms of a kinetic equation rather than an action. We describe a new method that leads to a field-theoretical reformulation of Landau Fermi liquid theory. In this approach, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonization of the Fermi surface. The Berry phase that the Fermi surface acquires when changing shape is shown to be given bythe Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions and applications of the theory are described.

Fractional quantum Hall states are strongly interacting states of two-dimensional electrons moving in a high magnetic field. It has recently been found, theoretically and experimentally, that fractional quantum Hall fluids accommodate a quasiparticle excitations carrying spin equal to 2. I will describe the general theoretical arguments leading to this conclusion. I will also show that the existence of this spin-2 mode explains a strange feature of the numerical data on the spectrum of quantum Hall systems on a sphere.
 
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This talk is about a mixture of old and new work. First I will talk about how you can iterate Pappus’s theorem and construct a 2-parameter family of relatively Anosov representations of the modular group into Isom(X), where X = SL(3,R)/SO(3). Then I will explain how to interpret these representations as symmetry groups of patterns of geodesics in X that have the same asymptotic properties as the Farey graph in the hyperbolic plane. Finally I will say a few words about how this picture allows for a complete classification of the Barbot component of discrete faithful representations of the modular group into Isom(X).

A quasifuchsian manifold is a hyperbolic structure on the product of a surface and the line that is naturally compactified by two conformal structures at infinity. By a classical result of Bers, curves that have bounded length in the hyperbolic structures on these surfaces also have bounded length in the hyperbolic 3-manifold. However, the converse fails — one can construct examples of quasifuchsian manifolds that contain curves of bounded length in the 3-manifold while the curves are arbitrarily long in the hyperbolic structures at infinity. To rectify this, Minsky gave a description of the bounded length curves in the 3-manifold in terms of the data at infinity using the curve complex. These a priori bounds played a central role in the Brock-Canary-Minsky proof of the ending lamination conjecture. Bowditch later gave a new proof of these bounds. We will describe another proof of this result. While it uses many of the ideas of the approaches of Minsky and Bowditch, unlike their proofs the result is effective.

Human postnatal development is typically viewed from the perspective of our ‘human’ organs.  As we come to appreciate how our microbial communities are assembled following birth, there is an opportunity to determine how this microbial facet of our developmental biology is related to healthy growth as well as to the risk for and manifestations of disorders that produce abnormal growth. We are testing the hypothesis that perturbations in the normal development of the gut microbiome are causally related to childhood undernutrition, a devastating global health problem whose long-term sequelae, including stunting, neurodevelopmental abnormalities, plus metabolic and immune dysfunction, remain largely refractory to current therapeutic interventions. The journey to preclinical proof-of-concept, and the path forward to clinical proof-of-concept emphasize the opportunities as well as the experimental, analytic and other challenges encountered when developing microbiota-directed therapeutics.
 
 

The widely anticipated revolution in biology, driven by the superpowers of GAI, has been slow to materialize. In this talk, I will discuss the concept, the obstacles, and examine two specific projects involving language and image analysis. The first case study involves extracting information from a specific type of biological literature—model organisms’ lifespan extension under pharmacological perturbation—where we aim to agglomerate experimental parameters over an extensive body of published literature and automatically review and assess the quality of emerging studies in that context. The second project focuses on novel high-resolution image analysis, where we aim to characterize protein and lipid remodeling in various organs and tissues, to detect changes in a nested hierarchy of repetitive elements of tissue architectures and elucidate changes reflecting sex specificity, aging, and disease. We will anticipate what will be needed for a productive man-machine symbiosis to emerge in systems biology.
 

Beilinson defined the singular support of a constructible sheaf on a smooth scheme over a field as a closed conical subset on the cotangent bundle. He further proved its existence and fundamental properties, using Radon transform as a crucial tool. In first lectures, we formulate the definition in a slightly different but equivalent way, using an interpretation by Braverman–Gaitsgory of the local acycliciity. We also recall Beilinson’s proof of existence.
In mixed characteristics, the theory is still far from complete. As a replacement of the cotangent bundle, we introduce the Frobenius–Witt cotangent bundle, that has the correct rank but defined only on the characteristic p fiber. Using it, we define  the singular support and its relative variant. Finally, we show that Beilinson’s argument using the Radon transform gives a proof of the existence of the saturation of the relative variant.