Approximation algorithms | Computational hardness assumptions | Unsolved problems in computer science | Computational complexity theory | Conjectures
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the approximate value of a certain type of game, known as a unique game, has NP-hard computational complexity. It has broad applications in the theory of hardness of approximation. If the unique games conjecture is true and P ≠ NP, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem), but also impossible to get a good polynomial-time approximation. The problems for which such an inapproximability result would hold include constraint satisfaction problems, which crop up in a wide variety of disciplines. The conjecture is unusual in that the academic world seems about evenly divided on whether it is true or not. (Wikipedia).
The Unique Games Conjecture - O'Donnell
O'Donnell Carnegie Mellon University; Member, School of Mathematics April 20, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Existence & Uniqueness Theorem, Ex1.5
Existence & Uniqueness Theorem for differential equations. Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo For more calculus & differential equation tutorials, check out @justcalculus 👉 https://www.youtube.com/justcalculus To learn how to solve different types of d
From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Existence & Uniqueness Theorem, Ex1
Existence & Uniqueness Theorem, Ex1 Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo For more calculus & differential equation tutorials, check out @justcalculus 👉 https://www.youtube.com/justcalculus To learn how to solve different types of differential equations: Ch
From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Existence & Uniqueness Theorem, Ex2
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From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Unique factorization and its difficulties I Data Structures in Mathematics Math Foundations 198
The Unique Factorization Theorem is also called the Fundamental Theorem of Arithmetic: the existence and uniqueness of a prime factorization for a natural number n. It is a pillar of number theory, and goes back to Euclid. We want to have a look at the logical structure of this theorem.
From playlist Math Foundations
Existence & Uniqueness Theorem, Ex3
Existence & Uniqueness Theorem for differential equations. For more calculus & differential equation tutorials, check out @justcalculus 👉 https://www.youtube.com/justcalculus To learn how to solve different types of differential equations: Check out the differential equation playlist:
From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Existence & Uniqueness Theorem, Ex3.5
Existence & Uniqueness Theorem for differential equations. For more calculus & differential equation tutorials, check out @justcalculus 👉 https://www.youtube.com/justcalculus To learn how to solve different types of differential equations: Check out the differential equation playlist:
From playlist Differential Equations: Existence & Uniqueness Theorem (Nagle Sect1.2)
Small-set expansion in Grassman graph and the 2-to-2 Games Theorem (Lecture 1) by Prahladh Harsha
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
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Hermann Weyl Lectures Topic: Unique and 2:2 Games, Grassmannians, and Expansion Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor Affiliation: School of Mathematics Date: November 20, 2019 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
Bypassing UGC From Some Optimal Geometric Inapproximability Results - Rishi Saket
Bypassing UGC From Some Optimal Geometric Inapproximability Results Rishi Saket Princeton University February 8, 2011 The Unique Games conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a revers
From playlist Mathematics
Unique games, the Lasserre hierarchy and monogamy of entanglement - Aram Harrow
Aram Harrow Massachusetts Institute of Technology January 27, 2014 In this talk, I'll describe connections between the unique games conjecture (or more precisely, the closely relatedly problem of small-set expansion) and the quantum separability problem. Remarkably, not only are the proble
From playlist Mathematics
Rolf Nevanlinna Prize 2014 Subhash Khot
Subhash Khot is awarded the Nevanlinna Prize for his prescient definition of the “Unique Games” problem, and leading the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimization problems; his work has led to breakthroughs in algorithm
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Tight hardness of the non-commutative Grothendieck problem - Oded Regev
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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)
On the Approximation Resistance of Balanced Linear Threshold Functions - Aaron Potechin
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A Strange Product math problem
Here is a simple problem. Once you find the solution, you might want to try it on your friends, and even your teachers. Have fun! Next puzzle: http://www.youtube.com/watch?v=Jvygw_N_3OI Solution: http://www.youtube.com/watch?v=-Ouyg71Sbjw Previous puzzle: http://www.youtube.com/watch?v=6o-
From playlist Tricks and Math Puzzles