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- Stefan Steinerberger: The Ulam Sequence
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Three Conferences: Joel Spencer, April 29-30, Courant; Joel Hass May 20-22, Berkeley, Jean Bourgain May 21-24, IAS, Princeton
- Polymath10-post 4: Back to the drawing board?
- Polymath10: The Erdos Rado Delta System Conjecture
- Can Category Theory Serve as the Foundation of Mathematics?

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# Category Archives: Geometry

## Exciting News on Three Dimensional Manifolds

The Virtually Haken Conjecture A Haken 3-manifold is a compact 3-dimensional manifold M which is irreducible (in a certain strong sense) but contains an incompressible surface S. (An embedded surface S is incompressible if the embedding indices an injection of its … Continue reading

## Fractional Sylvester-Gallai

Avi Wigderson was in town and gave a beautiful talk about an extension of Sylvester-Gallai theorem. Here is a link to the paper: Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes by Boaz Barak, Zeev … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Geometry
Tagged Avi Wigderson, Codes, Greg Kuperberg, Sylvester-Gallai
4 Comments

## Polymath3 (PHC6): The Polynomial Hirsch Conjecture – A Topological Approach

This is a new polymath3 research thread. Our aim is to tackle the polynomial Hirsch conjecture which asserts that there is a polynomial upper bound for the diameter of graphs of -dimensional polytopes with facets. Our research so far was … Continue reading

Posted in Convex polytopes, Geometry, Polymath3
Tagged Hirsch conjecture, Polymath3, Topological combinatorics
37 Comments

## János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem

Click here for the most recent polymath3 research thread. Erdős and Pach celebrating another November day many years ago. The Wolf disguised as Little Red Riding Hood. Pach disguised as another Pach. This post is authored by János Pach A … Continue reading

Posted in Combinatorics, Geometry, Guest blogger, Open problems
Tagged Larry Guth, Nets Hawk Katz
13 Comments

## Benoît’s Fractals

Mandelbrot set Benoît Mandelbrot passed away a few dayes ago on October 14, 2010. Since 1987, Mandelbrot was a member of the Yale’s mathematics department. This chapterette from my book “Gina says: Adventures in the Blogosphere String War” about fractals is brought here on this … Continue reading

Posted in Geometry, Obituary, Physics, Probability
6 Comments

## Answer to Test Your Intuition (3)

Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading

## Test Your Intuition (3)

Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in .