On Zaremba's Conjecture on Continued Fractions - Jean Bourgain
Jean Bourgain Institute for Advanced Study February 14, 2012 Zaremba's 1971 conjecture predicts that every integer appears as the denominator of a finite continued fraction whose partial quotients are bounded by an absolute constant. We confirm this conjecture for a set of density one. Fo
From playlist Mathematics
Commutative algebra 32 Zariski's lemma
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We state and prove Zariski's lemma: Any field that is a finitely generated algebra over a field is a finitely generated modu
From playlist Commutative algebra
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of infinity, and give some examples of models where it does not hold. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG
From playlist Zermelo Fraenkel axioms
Yohann Genzmer : The Zariski problem for homogeneous and quasi-homogeneous curves
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
Zarhin's trick and geometric boundedness results for K3 surfaces - François Charles
François Charles Université Paris-Sud November 11, 2014 Tate's conjecture for divisors on algebraic varieties can be rephrased as a finiteness statement for certain families of polarized varieties with unbounded degrees. In the case of abelian varieties, the geometric part of these finite
From playlist Mathematics
Zagier's conjecture on zeta(F,4) - Alexander Goncharov
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Zagier's conjecture on zeta(F,4) Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics Date: November 10, 2017 For more videos, please visit http://video.ias.
From playlist Mathematics
Rahim Moosa: Around Jouanolou-type theorems
Abstract: In the mid-90’s, generalising a theorem of Jouanolou, Hrushovski proved that if a D-variety over the constant field C has no non-constant D-rational functions to C, then it has only finitely many D-subvarieties of codimension one. This theorem has analogues in other geometric con
From playlist Combinatorics
Ananth Shankar, Picard ranks of K3 surfaces and the Hecke orbit conjecture
VaNTAGe Seminar, November 23, 2021
From playlist Complex multiplication and reduction of curves and abelian varieties
Holly Krieger, Equidistribution and unlikely intersections in arithmetic dynamics
VaNTAGe seminar on May 26, 2020. License: CC-BY-NC-SA. Closed captions provided by Marley Young.
From playlist Arithmetic dynamics
Math 131 Fall 2018 100318 Heine Borel Theorem
Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Patrick Ingram, The critical height of an endomorphism of projective space
VaNTAGe seminar on June 9, 2020. License: CC-BY-NC-SA. Closed captions provided by Matt Olechnowicz
From playlist Arithmetic dynamics
Commensurators of thin Subgroups by Mahan M. J.
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Integral points on Markoff-type cubic surfaces - Amit Ghosh
Special Seminar Topic: Integral points on Markoff-type cubic surfaces Speaker: Amit Ghosh Affiliation: Oklahoma State University Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
E. Amerik - On the characteristic foliation
Abstract - Let X be a holomorphic symplectic manifold and D a smooth hypersurface in X. Then the restriction of the symplectic form on D has one-dimensional kernel at each point. This distribution is called the characteristic foliation. I shall survey a few results concerning the possible
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Complexes of tori and rational points on homogeneous (...) - Harari - Workshop 1 - CEB T2 2019
David Harari (Université Paris Sud) / 20.05.2019 Complexes of tori and rational points on homogeneous spaces over a function field We explain new arithmetic duality theorems for finite group schemes and 2-term complexes of tori defined over a global field of positive characteristic. We
From playlist 2019 - T2 - Reinventing rational points
Weil conjectures 6: etale cohomology of a curve
We give an overview of how to calculate the etale cohomology of a nonsinguar projective curve over an algebraically closed field with coefficients Z/nZ with n invertible. We simply assume a lot of properties of etale cohomology without proving (or even defining) them.
From playlist Algebraic geometry: extra topics
What is the Mordell-Lang problem?
It is my intention to eventually explain some things about the Mordell-Lang problem and the higher dimensional versions of these. The presentation in this video is due to Mazur and can be found in an MSRI article he wrote that introduces these things.
From playlist Mordell-Lang
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