Tverberg's theorem

Jesus De Loera: Tverberg-type theorems with altered nerves

Abstract: The classical Tverberg's theorem says that a set with sufficiently many points in R^d can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is b

From playlist Combinatorics

Daisuke Kishimoto (8/12/21): Tverberg’s theorem for cell complexes

Tverberg’s theorem states that any (d+1)(r-1)+1 points in R^d can be partitioned into r subsets whose convex hulls have a point in common. There is a topological version of it, which is often compared with an LS-version of the Borsuk-Ulam theorem. I will talk about a generalization of the

From playlist Topological Complexity Seminar

On the Colored Tverberg Problem - Benjamin Matschke

On the Colored Tverberg Problem Benjamin Matschke Institute for Advanced Study February 14, 2012 In this talk I will present a colored version of Tverberg's theorem about partitioning finite point sets in R^d into rainbow groups whose convex hulls intersect. This settles the famous Bárány-

From playlist Mathematics

An Application of the Universality Theorem for Tverberg Partitions - Imre Barany

Computer Science/Discrete Mathematics Seminar I Topic: An Application of the Universality Theorem for Tverberg Partitions Speaker: Imre Barany Affiliation: Renyi Institute, Hungary and UCL, London Date: March 18, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Marek Filakovský: Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results

Title: Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results Abstract: We present two new results in computational topology. The first result, joint with Uli Wagner and Stephan Zhechev, concerns the algorithmic embeddability problem, i.e. given a k-dimensional s

From playlist ATMCS/AATRN 2020

Pablo Soberón on Tverberg-type results, weak epsilonnets and the probabilistic method

Date: March 16, 2018 Location: Worldwide Center of Mathematics Abstract: During this talk we will discuss some robust variations of Tverberg’s theorem. The aim is to seek partitions of a finite set of points in R^d such that the convex hulls of the parts intersect, even if our set of point

From playlist Center of Math Research: the Worldwide Lecture Seminar Series

Rade Zivaljevic (6/27/17) Bedlewo: Topological methods in discrete geometry; new developments

Some new applications of the configurations space/test map scheme can be found in Chapter 21 of the latest (third) edition of the Handbook of Discrete and Computational Geometry [2]. In this lecture we focus on some of the new developments which, due to the limitations of space, may have b

From playlist Applied Topology in Będlewo 2017

Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem

In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

Amzi Jeffs (6/3/20): Convex sunflower theorems and neural codes

Title: Convex sunflower theorems and neural codes Abstract: In the 1970s neuroscientists O'Keefe and Dostrovsky made a groundbreaking experimental observation: neurons called "place cells" in a rat's hippocampus are active in a convex subset of the animal's environment, and thus encode a

From playlist AATRN 2020

Theory of numbers: Congruences: Euler's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim

From playlist Theory of numbers

Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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

Statistics - How to use Chebyshev's Theorem

In this video I cover at little bit of what Chebyshev's theorem says, and how to use it. Remember that Chebyshev's theorem can be used with any distribution, and that it gives a lower proportion of what we can expect in the actual data. ▬▬ Chapters ▬▬▬▬▬▬▬▬▬▬▬ 0:00 Start 0:04 What is C

From playlist Statistics

Chebyshev's inequality

In this video, I state and prove Chebyshev's inequality, and its cousin Markov's inequality. Those inequalities tell us how big an integrable function can really be. Enjoy!

From playlist Real Analysis

Calculus 1 (Stewart) Ep 22, Mean Value Theorem (Oct 28, 2021)

This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f

From playlist Math 1171 (Calculus 1) Fall 2021

Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

Riemann Series Theorem

In this video, I explain a quite unbelievable fact about series: If a series converges, but does not converge absolutely, then we can rearrange it to have any limit that we want! Enjoy this beautiful analysis extravaganza, also known as the Riemann Rearrangement Theorem. Rearrange a serie

From playlist Series