Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is graph theory, which by itself has numerous natural connections to other areas. Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms. A mathematician who studies combinatorics is called a combinatorialist. (Wikipedia).
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 1) by Greg Blekherman
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)
Deep Dive into Combinatorics (Introduction)
What is combinatorics? What are the founding principles of combinatorics? Combinatorics is among the least talked about in the online world, especially for recreational mathematics. This video series will explore very deeply about one problem in combinatorics (about queuing in a bank), whi
From playlist Deep Dive into Combinatorics (DDC)
Large deviations for random hives and the spectrum of the sum of two random.. by Hariharan Narayanan
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)
Circular Fence Posets and Associated Polytopes with Unexpected Symmetry by Mohan Ravichandran
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)
Introduction to Combinatory Logic – #SoME2
This is Alexander Farrugia's and Giorgio Grigolo's submission to the second 3blue1brown Summer of Math Exposition. #some2 #mathematics #combinators #logic Music: Icelandic Arpeggios – DivKid
From playlist Summer of Math Exposition 2 videos
The Tropical Limit of String Theory and Feynman Integrals by Piotr Tourkine
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)
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 4) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study o
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Introduction to additive combinatorics lecture 1.0 --- What is additive combinatorics?
This is an introductory video to a 16-hour course on additive combinatorics given as part of Cambridge's Part III mathematics course in the academic year 2021-2. After a few remarks about practicalities, I informally discuss a few open problems, and attempt to explain what additive combina
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Timothy Gowers: Combinatorics, Szemerédis theorem and the sorting problem
Sir William Timothy Gowers is a British mathematician and a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. This video is a clip from the Abel Prize Announcement 2012. Gowers gives a brief introduction to t
From playlist Popular presentations
Combinatorics — Topic 97 of Machine Learning Foundations
#MLFoundations #Probability #MachineLearning Combinatorics is a field of mathematics devoted to counting that can be helpful for studying probabilities. In this video, we use examples with real numbers to bring this combinatorics field to life and relate it to probability theory. There a
From playlist Probability for Machine Learning
Quantum Computers: How They Work and What Can They Do?
We are beginning to evolve beyond classical computing into a new data era called quantum computing. The quantum computing power and speed will help us solve some of the biggest and most complex challenges we face.
From playlist Quantum Computing
Newton Polytopes and parameter estimation in reaction networks by Nidhi Kaihnsa
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)
Topics in Combinatorics lecture 1.0 -- welcome
This is the first video of a course entitled Topics in Combinatorics, which is given as part of the Part III Mathematics course at Cambridge University in the Michaelmas term of 2020. Because of the pandemic, all courses are online this year, and since we are allowed to post our lectures o
From playlist Topics in Combinatorics (Cambridge Part III course)
Zero-Sum Problems by R. Thangadurai
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
The Green - Tao Theorem (Lecture 2) by Gyan Prakash
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Squares in Arithmetic progression by Shanta Laishram
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Geometry of tropical varieties with a view toward applications (Lecture 1) by Omid Amini
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
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)