In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. The theorem that every polytope is uniquely determined up to translation by this information was proven by Hermann Minkowski; it has been called "Minkowski's theorem", although the same name has also been given to several unrelated results of Minkowski. The Minkowski problem for polytopes should also be distinguished from the Minkowski problem, on specifying convex shapes by their curvature. (Wikipedia).
This is a basic introduction to Minkowski's inequality, which has many applications in mathematics. A simple case in the Euclidean space R^n is discussed with a proof provided.
From playlist Mathematical analysis and applications
Minkowski sums, mixed faces and combinatorial isoperimetry - Adiparsito
Computer Science/Discrete Mathematics Seminar II Topic: Minkowski sums, mixed faces and combinatorial isoperimetry Speaker: Karim Adiprasito Date: Tuesday, February 23 I want to sketch some algebraic and geometric tools to solve a variety of extremal problems surrounding Minkowski sums of
From playlist Mathematics
The (Counter-Intuitive) Geometry of Cut and Flow Polytopes - Ankur Moitra
Ankur Moitra Massachusetts Institute of Technology; Institute for Advanced Study October 3, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Emanuel Milman - The log-Minkowski Problem - IPAM at UCLA
Recorded 09 February 2022. Emanuel Milman of Technion - Israel Institute of Technology presents "The log-Minkowski Problem" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The classical Minkowski problem asks to find a convex body K in Rn having a prescrib
From playlist Workshop: Calculus of Variations in Probability and Geometry
Extremal Problems for Convex Lattice Polytopes - Imre Barany
Imre Barany Alfred Renyi Mathematical Institute, Hungarian Academy of Sciences March 15, 2010 In this survey I will present several extremal problems, and some solutions, concerning convex lattice polytopes. A typical example is to determine the smallest area that a convex lattice polygon
From playlist Mathematics
Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality
The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
[ANT05] Minkowski's geometry of numbers
Unsurprisingly, many of the pictures we've drawn are honest geometric objects, leaving them open to geometric attacks.
From playlist [ANT] An unorthodox introduction to algebraic number theory
Thomas Eliot - undergraduate talk
Thomas Eliot delivers an undergraduate research talk at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Polynomial systems and mixed volumes - Ricky I Liu
Computer Science/Discrete Mathematics Seminar II Topic: Polynomial systems and mixed volumes Speaker: Ricky I Liu Affiliation: Member, School of Mathematics Date: March 16, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
What are the names of different types of polygons based on the number of sides
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Connecting tropical intersection theory with polytope algebra in types A and B by Alex Fink
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Tropical Geometry - Lecture 8 - Surfaces | 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
Gaussian Brunn-Minkowski Theory by Mokshay Madiman
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Random concave functions on an equilateral lattice with periodic hessians by Hariharan Narayanan
DISCUSSION MEETING : STATISTICAL PHYSICS OF MACHINE LEARNING ORGANIZERS : Chandan Dasgupta, Abhishek Dhar and Satya Majumdar DATE : 06 January 2020 to 10 January 2020 VENUE : Madhava Lecture Hall, ICTS Bangalore Machine learning techniques, especially “deep learning” using multilayer n
From playlist Statistical Physics of Machine Learning 2020
QUESTION SESSION ON GRASSMANNIANS, POLYTOPES AND QUANTUM FIELD THEORY - Nima Arkani-Hamed
Nima Arkani-Hamed Professor, School of Natural Sciences April 7, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Word Problems with trigonometry and triangles
👉 Learn how to solve the word problems with trigonometry. Word problems involving angles, including but not limited to: bearings, angle of elevations and depressions, triangles problems etc are solved using trigonometry. To be able to solve these problems it is important that you have a gr
From playlist Evaluate Inverse Trigonometric Functions
Seminar on Applied Geometry and Algebra (SIAM SAGA): Jesús A. De Loera
Title: The Geometry of the Space of ALL Pivot Rules of a Linear Optimization Problem Speaker: Jesús A. De Loera, University of California Davis Date: Tuesday, April 12 2022 at 11:00am Eastern For more information, see our website: https://wiki.siam.org/siag-ag/index.php/Webinar
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)