Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
André NEVES - Gromov’s Weyl Law and Denseness of minimal hypersurfaces
Minimal surfaces are ubiquitous in Geometry but they are quite hard to find. For instance, Yau in 1982 conjectured that any 3-manifold admits infinitely many closed minimal surfaces but the best one knows is the existence of at least two. In a different direction, Grom
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Existence of infinitely many minimal hypersurfaces in closed manifolds - Antoine Song
Variational Methods in Geometry Seminar Topic: Existence of infinitely many minimal hypersurfaces in closed manifolds Speaker: Antoine Song Affiliation: Princeton University Date: October 23, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Marc Levine: Refined enumerative geometry (Lecture 1)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Marc Levine: Refined enumerative geometry Abstract: Lecture 1: Milnor-Witt sheaves, motivic homotopy theory and Chow-Witt groups We review the Hoplins-Morel construction of the Miln
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Minimal Discrepancy of Isolated Singularities and Reeb Orbits - Mark McLean
Mark McLean Stony Brook University April 4, 2014 Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold calle
From playlist Mathematics
F. Coda Marques - Morse theory and the volume spectrum
In this talk I will survey recent developments on the existence theory of closed minimal hypersurfaces in Riemannian manifolds, including a Morse-theoretic existence result for the generic case.
From playlist 70 ans des Annales de l'institut Fourier
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
L. Mazet - Minimal hypersurfaces of least area
In this talk, I will present a joint work with H. Rosenberg where we give a characterization of the minimal hypersurface of least area in any Riemannian manifold. As a consequence, we give a lower bound for the area of a minimal surface in a hyperbolic 3-manifold.
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Xin Zhou - Recent developments in constant mean curvature hypersurfaces I
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well. Xin Zhou (Cornell)
From playlist Not Only Scalar Curvature Seminar
Ciprian Demeter (Bloomington): Restriction of exponential sums to hypersurfaces
We discuss moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter N apart from Nϵ losses. Joint work with Bartosz Lan
From playlist Seminar Series "Harmonic Analysis from the Edge"
Tamás Hausel : Toric non-abelian Hodge theory
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
D. Brotbek - On the hyperbolicity of general hypersurfaces
A smooth projective variety over the complex numbers is said to be (Brody) hyperbolic if it doesn’t contain any entire curve. Kobayashi conjectured in the 70’s that general hypersurfaces of sufficiently large degree in PN are hyperbolic. This conjecture was only recently proved by Siu. Th
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 2/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
The Four-Color Theorem and an Instanton Invariant for Spatial Graphs I - Peter Kronheimer
Peter Kronheimer Harvard University October 13, 2015 http://www.math.ias.edu/seminars/abstract?event=83214 Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional Z/2 vector space. The main result about the instanton hom
From playlist Geometric Structures on 3-manifolds
Recent progress on Overdetermined Elliptic Problems - Jose Espinar
Variational Methods in Geometry Seminar Topic: Recent progress on Overdetermined Elliptic Problems Speaker: Jose Espinar Affiliation: IMPA Date: October 30, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
3D convex contact forms and the Ruelle invariant - Oliver Edtmair
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: 3D convex contact forms and the Ruelle invariant Speaker: Oliver Edtmair Affiliation: Berkeley Date: January 29, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Julien Duval - Kobayashi pseudo-metrics, entire curves and hyperbolicity of algebraic varieties 1/2
An almost complex manifold is hyperbolic if it does not contain any entire curve. We start characterizing hyperbolic compact almost complex manifolds. These are the ones whose holomorphic discs satisfy a linear isoperimetric inequality. Then we prove the almost complex version of the Greee
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Restriction of Exponential Sums to Hypersurfaces - Ciprian Demeter
Special Year Research Seminar Topic: Restriction of Exponential Sums to Hypersurfaces Speaker: Ciprian Demeter Affiliation: Indiana University Date: February 21, 2023 The last decade has witnessed a revolution in the circle of problems concerned with proving sharp moment inequalities fo
From playlist Mathematics