Several complex variables | Algebraic geometry
In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L2 extension. The conjecture states the following: : Let R be an Riemann surface, which admits a nontrivial Green function . Let be a local coordinate on a neighborhood of satisfying . Let be the Bergman kernel for holomorphic (1, 0) forms on R. We define , and . Let be the logarithmic capacity which is locally defined by on R. Then, the inequality holds on the every open Riemann surface R, and also, with equality, then or, R is conformally equivalent to the unit disc less a (possible) closed set of inner capacity zero. It was first proved by for the bounded plane domain and then completely in a more generalized version by . Also, another proof of the Suita conjecture and some examples of its generalization to several complex variables (the multi (high) - dimensional Suita conjecture) were given in and . The multi (high) - dimensional Suita conjecture fails in non-pseudoconvex domains. This conjecture was proved through the optimal estimation of the Ohsawa–Takegoshi L2 extension theorem. (Wikipedia).
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 11) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
In this video I explain why so many physicists believe in string theory but that it also comes with a number of problems. It requires the existence of additional dimensions of space (which we do not see), of new particles (which we do not see), and of new fields (leading to deviations from
From playlist Physics
Yoshihiro Ohnita: Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces
An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form which is a compact embedded totally geodesic Lagrangian submanifold.
From playlist Geometry
What is the goal of string theory?
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From playlist Science Unplugged: String Theory
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
Tested in 2019: Jen's Favorite Things!
Fabricator Jen Schachter worked alongside Adam on this year's Savage Builds, and works with him on numerous projects in the cave. She shares a few of her favorite tools she uses for those builds, which are all about joining things together! Cleco pliers and ⅛-inch fastener kit: https://am
From playlist Staff Favorites
Winklevoss Twins in Hot Water!
Get 40% off Blinkist premium, only valid until February! Enjoy 2 memberships for the price of 1. Start your 7-day free trial by clicking here: https://www.blinkist.com/patrickboyle In today's video we look at the recent lawsuit against Gemini Trust Company, a crypto lending platform run b
From playlist What is Happening In The Market?
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
Large-scale structure response functions - F. Bernardeau - Workshop 1 - CEB T3 2018
Francis Bernardeau (IPhT, IAP) / 21.09.2018 Large-scale structure response functions ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com
From playlist 2018 - T3 - Analytics, Inference, and Computation in Cosmology
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Lecture 9 | String Theory and M-Theory
(November 23, 2010) Leonard Susskind gives a lecture on the constraints of string theory and gives a few examples that show how these work. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced
From playlist Lecture Collection | String Theory and M-Theory
Lecture 7 | String Theory and M-Theory
(November 1, 2010) Leonard Susskind discusses the specifics of strings including Feynman diagrams and mapping particles. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding of
From playlist Lecture Collection | String Theory and M-Theory
Engineering Single and N-Photon Emission from Frequency Resolved Correlations by Elena Del Valle
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Recent developments in non-commutative Iwasawa theory I - David Burns
David Burns March 25, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Giles Gardam: Kaplansky's conjectures
Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Giles Gardam - Kaplansky's conjectures
Kaplansky made various related conjectures about group rings, especially for torsion-free groups. For example, the zero divisors conjecture predicts that if K is a field and G is a torsion-free group, then the group ring K[G] has no zero divisors. I will survey what is known about the conj
From playlist Talks of Mathematics Münster's reseachers
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory