Theorems in algebraic geometry | Real algebraic geometry
In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, gives the possible numbers of connected components that an algebraic curve can have, in terms of the degree of the curve. For any algebraic curve of degree m in the real projective plane, the number of components c is bounded by The maximum number is one more than the maximum genus of a curve of degree m, attained when the curve is nonsingular. Moreover, any number of components in this range of possible values can be attained. A curve which attains the maximum number of real components is called an M-curve (from "maximum") – for example, an elliptic curve with two components, such as or the Trott curve, a quartic with four components, are examples of M-curves. This theorem formed the background to Hilbert's sixteenth problem. In a recent development a is shown to be a curve whose amoeba has area equal to the Newton polygon of the polynomial P, which is called the characteristic curve of dimer models, and every Harnack curve is the spectral curve of some dimer model. (Wikipedia).
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Richard Hamilton | The Poincare Conjecture | 2006
The Poincare Conjecture Richard Hamilton Columbia University, New York, USA https://www.mathunion.org/icm/icm-videos/icm-2006-videos-madrid-spain/icm-madrid-videos-22082006
From playlist Number Theory
How to use right hand riemann sum give a table
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Risk-sensitive control for diffusions with jumps by Anup Biswas
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Peter TOPPING - Sharp local decay estimates for the Ricci flow on surfaces
There are many tools available when studying 2D Ricci flow, equivalently the logarithmic fast diffusion equation, but one has always been missing: how do you get uniform smoothing estimates in terms of local L^1 data, i.e. in terms of local bounds on the area. The problem is th
From playlist Trimestre "Ondes Non Linéaires" - May Conference
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
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
Ancient solutions to geometric flows IV - Panagiota Daskalopoulos
Women and Mathematics: Uhlenbeck Lecture Course Topic: Ancient solutions to geometric flows IV Panagiota Daskalopoulos Affiliation: Columbia University Date: May 24, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
How to use left hand riemann sums from a table
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Viscosity solutions approach to variational problems - Daniela De Silva
Women and Mathematics: Colloquium Topic: Viscosity solutions approach to variational problems Speaker: Daniela De Silva Affiliation: Columbia University Date: May 21, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Harnack-Medaille für Bundeskanzlerin Angela Merkel
In einer feierlichen Veranstaltung am 29. Juni im Humboldt Carré in Berlin überreichte Max-Planck-Präsident Martin Stratmann die Harnack-Medaille an Bundeskanzlerin Angela Merkel. Am 12. März 2021 hatte der Senat der Max-Planck-Gesellschaft beschlossen, der Bundeskanzlerin „für ihre Verd
From playlist Videos auf Deutsch
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation