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- Giving a talk at Eli and Ricky’s geometry seminar. (October 19, 2021)
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- Dream a Little Dream: Quantum Computer Poetry for the Skeptics (Part I, mainly 2019)
- To Cheer you up in difficult times 30: Irit Dinur, Shai Evra, Ron Livne, Alex Lubotzky, and Shahar Mozes Constructed Locally Testable Codes with Constant Rate, Distance, and Locality
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- Alef’s corner: Mathematical research
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- Giving a talk at Eli and Ricky's geometry seminar. (October 19, 2021)
- Academic Degrees and Sex
- The Argument Against Quantum Computers - A Very Short Introduction
- To Cheer You Up in Difficult Times 31: Federico Ardila's Four Axioms for Cultivating Diversity
- To cheer you up in difficult times 32, Annika Heckel's guest post: How does the Chromatic Number of a Random Graph Vary?
- Amazing: Karim Adiprasito proved the g-conjecture for spheres!
- To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
- Must-read book by Avi Wigderson
- Richard Stanley: How the Proof of the Upper Bound Theorem (for spheres) was Found

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# Tag Archives: Linear programming

## Projections to the TSP Polytope

Michael Ben Or told me about the following great paper Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds by Samuel Fiorini, Serge Massar, Sebastian Pokutta, Hans Raj Tiwary and Ronald de Wolf. The paper solves an old conjecture … Continue reading

## IPAM remote blogging: The Many Facets of Linear Programming

The many facets of Linear Programming Here is an extremely nice paper by Michael Todd from 2001. It gives useful background for many lectures and it can serve as a good base point to examine last decade’s progress. Background post for … Continue reading

## Günter Ziegler: 1000$ from Beverly Hills for a Math Problem. (IPAM remote blogging.)

Scanned letter by Zadeh. (c) Günter M. Ziegler left-to-right: David Avis, Norman Zadeh, Oliver Friedmann, and Russ Caflish (IPAM director). Photo courtesy Eddie Kim. Update: The slides for Friedmann’s talk are now available. The conference schedule page contains now the slides for … Continue reading

Posted in Computer Science and Optimization, Conferences, Guest blogger
Tagged Linear programming
4 Comments

## Subexponential Lower Bound for Randomized Pivot Rules!

Oliver Friedmann, Thomas Dueholm Hansen, and Uri Zwick have managed to prove subexponential lower bounds of the form for the following two basic randomized pivot rules for the simplex algorithm! This is the first result of its kind and deciding … Continue reading

## The Polynomial Hirsch Conjecture: A proposal for Polymath3

This post is continued here. Eddie Kim and Francisco Santos have just uploaded a survey article on the Hirsch Conjecture. The Hirsch conjecture: The graph of a d-polytope with n vertices facets has diameter at most n-d. We devoted several … Continue reading

## A Diameter problem (7): The Best Known Bound

Our Diameter problem for families of sets Consider a family of subsets of size d of the set N={1,2,…,n}. Associate to a graph as follows: The vertices of are simply the sets in . Two vertices and are adjacent if . … Continue reading

## A Diameter Problem (6): Abstract Objective Functions

George Dantzig and Leonid Khachyan In this part we will not progress on the diameter problem that we discussed in the earlier posts but will rather describe a closely related problem for directed graphs associated with ordered families of sets. The role models for … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems
Tagged Hirsch conjecture, Linear programming
7 Comments

## Diameter Problem (3)

3. What we will do in this post and and in future posts We will now try all sorts of ideas to give good upper bounds for the abstract diameter problem that we described. As we explained, such bounds apply … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems
Tagged Hirsch conjecture, Linear programming, Quasi-automated proofs
1 Comment