Title: Heat flow of harmonic maps into CAT(0)-metric spacesAbstract: In this talk, I will describe an elliptic regularization approach, first proposed by De Giorgi, to study the heat flow of harmonic maps into CAT(0)-spaces, a generalization of manifolds with non-positive curvatures in the sense of Alexandrov. This leads to the existence of a unique suitable […]
35 events found.
Events
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Title: The Briançon-Skoda theorem revisitedAbstract: The Briançon-Skoda theorem is a comparison relating the integral closure of powers of an ideal with its ordinary power. The theorem was originally proved via analytic methods for coordinate rings of smooth varieties over the complex numbers. The full algebraic version for all regular local rings was obtained by Lipman-Sathaye. Since then, there have been […]
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Title: Symmetries of link homologyAbstract: We show that link homology over a field of characteristic p carries an action of a truncated polynomial algebra. This action gives rise to a categorification of the Jones polynomial at a prime root of unity. This is joint work with You Qi, Louis-Hadrien Robert, and Emmanuel Wagner. |
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Title: Linear stability of Kerr spacetimes Abstract: I will explain a result obtained in collaboration with P. Hintz and A. Vasy on the linear stability of rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure […] |
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Title: Positive Curvature Conditions and Contractible Manifolds Abstract: A classical theme in Riemannian geometry is that positive curvature imposes topological constraints on manifolds. In this talk, we investigate curvature conditions that distinguish Euclidean space among open contractible manifolds and the disk among compact contractible manifolds with boundary. We will show that an open manifold that […] |
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Title: Free fermions and the equivariant string orientation at the Tate curveAbstract: I will describe recent work (joint with Kiran Luecke and Langwen Hui) that constructs a geometric model for the (twisted) equivariant string orientation at the Tate curve. The primary ingredients come from loop group representation theory and the Stolz-Teichner program. As a warm-up […] |
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Title: Multivariate V-filtration and Strong Monodromy Conjecture for hyperplane arrangementsAbstract: In singularity theory, the Strong Monodromy Conjecture is a long-standing open problem predicting a deep connection between the poles of the p-adic, topological, and motivic zeta functions of a polynomial and the roots of its Bernstein-Sato polynomial. To date, this conjecture has only been verified in low […] |
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Title: On Breuil's Lattice Conjecture for GL_2 Abstract: Let $K$ be an extension of $Q_p$ and $E$ be a finite extension of $Q_p$ which is sufficiently large. We seek a -adic Langlands correspondence between a Galois representation $rho: Gal (overline{K}/K) to GL_2(E)$ and an admissible unitary Banach space representation of $GL_2(K)$ over $E$. This correspondence is […]
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Title: Solving the constraint equation for general free data Abstract: We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that once appropriate gauge conditions have been chosen […]
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Title: Learning Pseudo-Differential OperatorsAbstract: Pseudo-differential operators (PDOs) are a broad and fundamental class of operators in partial differential equations and mathematical physics. In this talk I will present recent work with Jiaheng Chen on learning elliptic PDOs from noisy data. Within a wavelet--Galerkin framework, we formulate this task as a structured infinite-dimensional regression problem with […] |
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Title: Moduli spaces of expanding Ricci solitons asymptotic to conesAbstract: Expanding Ricci solitons are a kind of self-similar solution of the Ricci flow. Asymptotically conical (AC) examples are interesting because they can be used to resolve conical singularities of 4D Ricci flow. I will describe a moduli space structure on spaces of AC expanding Ricci […] |
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Title: Existence, Non-existence, and Regularity of Minimizers in Weighted Fractional Cluster ProblemsAbstract: Recently, fractional partitioning problems have attracted significant attention: given a domain Omega, how should it be divided to minimize a weighted fractional perimeter? These problems arise naturally as sharp-interface limits of fractional vectorial Allen-Cahn equations. Unlike the classical setting, where the weights correspond […]
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Title: Type B websAbstract: This talk is about joint work in preparation with Elias—Rose on webs for Spin(2n+1) fundamental representations. Our approach is similar to Cautis—Kamnitzer—Morrison’s skew Howe duality approach to type A webs. We use ingredients from: Wenzl’s quantum spin Howe duality, Iorgov—Klimyk’s work on representation theory of iquantum groups, and our previous work […] |
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Title: Bounding the singular locus of the moduli of curves on a hypersurfaceAbstract: The space of rational curves on a Fano variety X serves as a powerful tool for probing the geometry of X. Even for hypersurfaces, characterizing these spaces is difficult; however, work by Riedl–Yang established they are irreducible and have the expected dimension. In this talk, […] |
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Title: Counting number fields of fixed degree by their smallest defining polynomial Abstract: When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of GL(2)xGL(1) on the space of polynomials of degree n so that for any two polynomials f and g in the same orbit, the […] |
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Title: Stability in the Free Boundary Curve Shortening Flow.Abstract: The free boundary curve shortening flow is natural Neumann analogue of the usual curve shortening flow; a geometric flow which arrises as the negative L^{2} gradient flow of arc-length. If the boundary curve is convex, Stahl in his PhD thesis established the convergence of convex initial […] |
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9:00–9:30 Breakfast 9:30–10:15 Christian Klevdal: Special and bi-analytic structures in p-adic geometry.10:15–10:45 Coffee break10:45–11:30 Foivos Chnaras: On the Iwasawa invariants of elliptic curves.11:30–12:00 Coffee break12:00–12:45 Rui Chen: Spherical functions on spherical varieties for unramified groups.12:45–2:30 Lunch break2:30–3:15 Junyan Zhao: K-moduli of Fano threefolds and their anticanonical K3 surfaces.3:15–3:45 Coffee break3:45–4:30 Myeong Jae Jeon: Compactification of torsors under reductive groups.4:30–5:00 […] |
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Title: On L-equivalence for K3 surfaces and hyperkähler manifolds (following Meinsma) |
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Negative Stepsizes Make Gradient-Descent-Ascent ConvergeSolving min-max problems is a central question in optimization, games, learning, and controls. Arguably the most natural algorithm is Gradient-Descent-Ascent (GDA), however since the 1970s, conventional wisdom has argued that it fails to converge even on simple problems. This failure spurred the extensive literature on modifying GDA with extragradients, optimism, momentum, […]
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Title: From Automorphic Periods to Arithmetic: The Case of Hilbert Modular Forms Abstract: The theory of Euler systems, first developed by Thaine and Kolyvagin, has become a central tool for proving cases of the Birch–Swinnerton-Dyer and Bloch–Kato conjectures. Many of the known examples are inspired from automorphic period integrals that capture special values of L-functions. […]
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Title: Anomalous superdiffusion of Brownian motion in random incompressible flowsAbstract: We study Brownian motion advected by a stationary, divergence-free random drift whose spatial correlations decay slowly. Such long-range dependence is expected to produce {it superdiffusion}: for a typical realization of the drift, the variance of the displacement of the particle grows faster than linearly in time, […] |
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Title: Entire area-minimizing surfaces in $R^4$ are algebraicAbstract: We classify entire 2-dimensional area-minimizing or stable surfaces in $R^4$ with quadratic area growth as algebraic, cut out by a finite union of holomorphic polynomials whose collective degrees are controlled by the density at infinity. As a consequence, we obtain bounds on the singular set size and […] |
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Title: Fast Diffusion Equations on Bounded Domains. Sharp Extinction Rates and singular asymptotic behaviourAbstract: We begin with an overview of the ``classical'' homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=Delta u^m$, posed in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $min (0,1)$.We then focus to the ``supercritical'' exponent range $m_s=(N-2)_+/(N+2)<m<1$ and focus on the […] |
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Title: What Deep Networks Can Represent — and What Training Can FindAbstract: Deep learning raises two basic questions: what functions deep networks can represent efficiently, and when training algorithms can actually find those representations. This talk brings these questions together through recent results on approximation and optimization. On the approximation side, depth and activation design […] |
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Title: Plateau borders and wet soap films Abstract: We discuss a model where soap films are understood as three-dimensional objects with small volume ("wet" soap films) rather than as two-dimensional surfaces satisfying the classical Plateau's laws ("dry" soap films). These wet films serve as physical approximations of their dry counterparts in the limit as the enclosed […] |
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Title: Towards a derived geometry for 2-rings with applications to the representation theory of finite groups |
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