In complex analysis, the monodromy theorem is an important result about analytic continuation of a complex-analytic function to a larger set. The idea is that one can extend a complex-analytic function (from here on called simply analytic function) along curves starting in the original domain of the function and ending in the larger set. A potential problem of this analytic continuation along a curve strategy is there are usually many curves which end up at the same point in the larger set. The monodromy theorem gives sufficient conditions for analytic continuation to give the same value at a given point regardless of the curve used to get there, so that the resulting extended analytic function is well-defined and single-valued. Before stating this theorem it is necessary to define analytic continuation along a curve and study its properties. (Wikipedia).
Using the monotonicity theorem to determine when a function is increasing or decreasing.
From playlist Calculus
Math 031 031017 Monotone Sequence Theorem
The rational numbers have holes: square root of 2 is irrational. Bounded sequences; bounded above, bounded below. Q. Does bounded imply convergent? (No.) Q. Does convergent imply bounded? (Yes.) Proof that convergent implies bounded. Statement of Monotone Sequence Theorem. Definition
From playlist Course 3: Calculus II (Spring 2017)
Monotone Subsequence Theorem (Every Sequence has Monotone Subsequence) | Real Analysis
How nice of a subsequence does any given sequence has? We've seen that not every sequence converges, and some don't even have convergent subsequences. But today we'll prove what is sometimes called the Monotone Subsequence theorem, telling us that every sequence has a monotone subsequence.
From playlist Real Analysis
Determine if an Expression is a Polynomial
This video explains how to determine if an expression is a polynomial.
From playlist Introduction to Polynomials
Monotone Sequence Theorem In this video, I prove the celebrated Monotone Sequence Theorem, which says that an increasing sequence that is bounded above must converge. This is the fundamental theorem of sequences, because it allows us to easily prove convergence of sequences Check out my
From playlist Sequences
In this video, I prove the monotone sequence theorem in calculus, which says that if a sequence is increasing and bounded above, then it must converge. It’s a great way of showing that a sequence converges, without actually finding the limit!
From playlist Real Analysis
How to determine if a term is a monomial or not
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Some algebro-geometric aspects of limiting mixed Hodge structure - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics December 16, 2014 This will be an expository talk, mostly drawn from the literature and with emphasis on the several parameter case of degenerating families of algebraic varieties. More videos on http://video.ias.edu
From playlist Mathematics
Umberto Zannier - Torsion values for sections in abelian schemes and the Betti map
November 14, 2017 - This is the second of three Fall 2017 Minerva Lectures We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear different
From playlist Minerva Lectures Umberto Zannier
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
The Generalized Ramanujan Conjectures and Applications (Lecture 2) by Peter Sarnak
Lecture 2: Thin Groups and Expansion Abstract: Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski dense in SL(n), arise in many geometric and diophantine problems (eg as reflection groups,groups connected with elementary geometry such as integral apollonian packings,
From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak
Thin Matrix Groups - a brief survey of some aspects - Peter Sarnak
Speaker: Peter Sarnak (Princeton/IAS) Title: Thin Matrix Groups - a brief survey of some aspects More videos on http://video.ias.edu
From playlist Mathematics
Hodge Theory -- From Abel to Deligne - Phillip Griffiths
Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
The pp-curvature conjecture and monodromy about simple closed loops - Ananth Shankar
Princeton/IAS Number Theory Seminar Topic: The pp-curvature conjecture and monodromy about simple closed loops Speaker: Ananth Shankar Affiliation: Harvard University Date: May 11, 2017 For more info, please visit http://video.ias.edu
From playlist Mathematics
Automorphic Cohomology II (Carayol's work and an Application) - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics April 6, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
R. Gutierrez - Quaternionic monodromies of the Kontsevich–Zorich cocycle
The monodromy group of a translation surface M is the Lie group spanned by all symplectic matrices arising from the homological action of closed loops at M (inside its embodying orbit closure). In the presence of zero Lyapunov exponents, Filip showed that these groups are —up to compact fa
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Monodromy of nFn−1 hypergeometric functions and arithmetic groups II - Venkataramana
Speaker: T. N. Venkataramana (TIFR) Title: Monodromy of nFn−1 hypergeometric functions and arithmetic groups II We describe results of Levelt and Beukers-Heckman on the explicit computation of monodromy for generalised hypergeometric functions of one variable. We then discuss the question
From playlist Mathematics
Thin groups as monodromy groups, Part I - Jordan Ellenberg (University of Wisconsin-Madison)
Thin groups as monodromy groups Jordan Ellenberg University of Wisconsin – Madison We discuss various algebro-geometric contexts in which thin groups appear as monodromy groups attached to families of varieties over curves. http://www.msri.org/workshops/652/schedules/14578
From playlist Number Theory
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
John Voight, Belyi maps in number theory: a survey
VaNTAGe Seminar, August 17, 2021 License CC-BY-NC-SA
From playlist Belyi maps and Hurwitz spaces