What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Math 131 Fall 2018 101218 Continuity and Connectedness; Discontinuities of Monotonic Functions
Recall definition of connected set. Theorem: continuous functions preserve connectedness. Proof by contraposition. Corollary: the Intermediate Value Theorem. Discontinuities on the real line: left-handed and right-handed limits. Left-continuous and right-continuous functions. Simple
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology
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
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
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
Commutative algebra 13 (Topology of Spec R)
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. In this lecture we discuss the topology of the spectrum Spec R of a ring, showing that it is compact, sometimes connected, an
From playlist Commutative algebra
Math 131 Spring 2022 022322 Continuity and Connectedness
Recall definition of connected set. Theorem: continuous image of a connected set is connected. Corollary: Intermediate Value Theorem. Proof of theorem (via contraposition). Discontinuities on R. Left limits and right limits. Simple discontinuities. Definition of monotonically increa
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
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
Pseudo-reductive groups by Brian Conrad
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Frédéric Campana: Special manifolds, the core fibration, rational and entire curves
Abstract: For complex projective manifolds X of general type, Lang claimed the equivalence between three fields: birational geometry, complex hyperbolicity, and arithmetic. We extend this equivalence to arbitrary X’s by introducing the (antithetical) class of “Special” manifolds and constr
From playlist Algebraic and Complex Geometry
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)
«Special» manifolds: rational points and entire curves. - Campana - Workshop 2 - CEB T2 2019
Frédéric Campana (Université de Lorraine) / 25.06.2019 «Special» manifolds: rational points and entire curves. We prove (joint with J. Winkelmann) for any rationally connected projective manifold X analytic analogues of several conjectural properties in arithmetic geom- etry: the “Poten
From playlist 2019 - T2 - Reinventing rational points
Weakly Connected Directed Graphs | Digraph Theory
What is a connected digraph? When we start considering directed graphs, we have to rethink our definition of connected. We say that an undirected graph is connected if there exists a path connecting every pair of vertices. However, in a directed graph, we need to be more specific since it
From playlist Graph Theory
Symmetry in Physics | Noether's theorem
▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Symmetry
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
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
Representations of p-adic reductive groups by Tasho Kaletha
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)