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
Eric Riedl: A Grassmannian technique and the Kobayashi Conjecture
Abstract: An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces X in ℙn: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie
From playlist Algebraic and Complex Geometry
The hyperbolic Ax-Lindemann conjecture - Emmanuel Ullmo
Emmanuel Ullmo Université Paris-Sud February 7, 2014 The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort
From playlist Mathematics
Periods Over Spherical Subgroups: An Extension of Some of the Langlands Conjectures - Y Sakellaridis
Yiannis Sakellaridis Member, School of Mathematics March 16, 2011 Periods of automorphic forms over spherical subgroups tend to: (1) distinguish images of functorial lifts and (2) give information about L-functions. This raises the following questions, given a spherical variety X=H\G: Loc
From playlist Mathematics
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
Ariyan Javanpeykar - Albanese maps and fundamental groups of varieties with many rational... - WAGON
Albanese maps and fundamental groups of varieties with many rational points over function fields In this talk we will discuss topological properties of varieties with many rational points over a function field, and present joint work-in-progress with Erwan Rousseau. More precisely, we def
From playlist WAGON
What is the Lang-Bombieri-Noguchi Conjecture?
Here we introduce the conjecture of Lang, Bombieri and Noguchi about the density rational points on varieties of general type.
From playlist One-off Explanations
Carlo Gasbarri: Arithmetic of algebraic points on varieties over function fields - Part 4
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
Andrew Wiles | Twenty Years of Number Theory | 1998
Notes for this talk: https://drive.google.com/file/d/1eJXPwL772Z00egvLjO3VHmvCv7mwcv6Q/view?usp=sharing Twenty Years of Number Theory Andrew Wiles Princeton University ICM Berlin 19.08.1998 https://www.mathunion.org/icm/icm-videos/icm-1998-videos-berlin-germany/icm-berlin-videos-2708
From playlist Number Theory
Panorama of Mathematics: Peter Scholze
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Peter Scholze: "Locally sym
From playlist Panorama of 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
Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of ... (Part 1)
We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyp
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Carlo Gasbarri: Arithmetic of algebraic points on varieties over function fields - Part 2
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
Analysis and topology on locally symmetric spaces - Akshay Venkatesh
Members' Seminar Topic: Analysis and topology on locally symmetric spaces Speaker: Akshay Venkatesh Affiliation: Stanford University; Distinguished Visiting Professor, School of Mathematics Date: October 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
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
Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of ... (Part 3)
We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyp
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Michael Harris "Shimura varieties and the search for a Langlands transform" [2012]
Michael Harris, Institut de mathématiques de Jussieu "Shimura varieties and the search for a Langlands transform" The Langlands reciprocity conjectures predict the existence of a correspondence between certain classes of representations of Galois groups of number fields and automorphic re
From playlist Number Theory