Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve. I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed […]
https://youtu.be/DMvmcTQuofE Speaker: Alex Davies, DeepMind Title: Machine learning with mathematicians Abstract: Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early computers to help formulate the Birch and Swinnerton-Dyer conjecture and using computer aid to […]
Abstract: Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such applications. Is schooling the result of vortex dynamics synthesized by individual fish wakes or the result of behavioral traits? Is fish schooling energetically favorable? I […]
Title: Polynomials vanishing at lattice points in convex sets Abstract: Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show that r_d / d converges to some positive number, which we compute for many (but maybe not […]
Speaker: Bong Lian Title: Singular Calabi-Yau mirror symmetry Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over […]
Speaker: Maria Tikhanovskaya (Harvard) Title: Maximal quantum chaos of the critical Fermi surface Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the […]
Abstract: We will consider the following problem: if (C,x_1,…,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,…,y_n, then how many maps f:C -> X in a given homology class are there, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory, the answer may be expressed in terms of […]
Speaker: Adam Smith (Boston University) Title: Learning and inference from sensitive data Abstract: Consider an agency holding a large database of sensitive personal information—say, medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. I will discuss recent (and not-so-recent) results on this problem with […]
https://youtu.be/7KMcXHwQzZs Speaker: Michael Bronstein, University of Oxford and Twitter Title: Neural diffusion PDEs, differential geometry, and graph neural networks Abstract: In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it is possible to provide a […]
Title: Kramers-Wannier-like duality defects in higher dimensions Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality […]
Abstract: The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The […]