Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
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)
Math 131 Fall 2018 100818 Limits and Continuity in Metric Spaces
Limits of functions (in the setting of metric spaces). Definition. Rephrasal of definition. Uniqueness of limit. Definition of continuity at a point. Remark on continuity at an isolated point. Relation with limits. Composition of continuous functions is continuous. Alternate (topol
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
MAST30026 Lecture 8: Compactness I
This is the first of several lectures on compactness. I recalled the proof of the Bolzano-Weierstrass theorem, defined sequential compactness in metric spaces and the characterisation of continuity of functions in terms of limits, and proved that the image of a compact set is compact. Lec
From playlist MAST30026 Metric and Hilbert spaces
Math 131 092116 Properties of Compact Sets
Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 101 Introduction to Analysis 112515: Introduction to Compact Sets
Introduction to Compact Sets: open covers; examples of finite and infinite open covers; definition of compactness; example of a non-compact set; compact implies closed; closed subset of compact set is compact; continuous image of a compact set is compact
From playlist Course 6: Introduction to Analysis
Mumford-Tate Groups and Domains - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics March 28, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Math 101 Introduction to Analysis 113015: Compact Sets, ct'd
Compact sets, continued. Recalling various facts about compact sets. Compact implies infinite subsets have limit points (accumulation points), that is, compactness implies limit point compactness; collections of compact sets with the finite intersection property have nonempty intersectio
From playlist Course 6: Introduction to Analysis
Math 131 Fall 2018 100118 Properties of Compact Sets
Review of compactness. Properties: compactness is not relative. Compact implies closed. Closed subset of compact set is compact. [Infinite] Collection of compact sets with finite intersection property has a nonempty intersection.
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Cup Products in Automorphic Cohomology - Matthew Kerr
Matthew Kerr Washington University in St. Louis March 30, 2012 In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally d
From playlist Mathematics
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Introduction to geometric invariant theory 1: Noncommutative duality - Ankit Garg
Optimization, Complexity and Invariant Theory Topic: Introduction to geometric invariant theory 1: Noncommutative duality Speaker: Ankit Garg Affiliation: Microsoft Research New England Date: June 5. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
A. Höring - A decomposition theorem for singular spaces with trivial canonical class (Part 3)
The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the deve
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
Weil-Petersson currents by Georg Schumacher
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Algebraic curves, tropical geometry, and moduli - Sam Payne
Sam Payne Yale University February 11, 2015 Tropical geometry gives a new approach to understanding old questions about algebraic curves and their moduli spaces, synthesizing techniques that range from Berkovich spaces to elementary combinatorics. I will discuss an outline of this method,
From playlist Mathematics
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
The True Power of Model Theory – Compactness, Infinitesimals and Ax's theorem
Thanks for watching! Go check out all submissions to 3blue1brown's contest: https://3b1b.co/SoME1 Corrections and remarks: none yet, let me know in the comments if you have any. Sources and resources: – First-order logic, compactness theorem David Marker's book: https://www.springer.com
From playlist Summer of Math Exposition Youtube Videos