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Category Archives: Geometry
Symplectic Geometry, Quantization, and Quantum Noise
Over the last two meetings of our HU quantum computation seminar we heard two talks about symplectic geometry and its relations to quantum mechanics and quantum noise. Yael Karshon: Manifolds, symplectic manifolds, Newtonian mechanics, quantization, and the non squeezing theorem. … Continue reading
Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)
Wolfgang Haken found an algorithm to tell if a knot is trivial, and, more generally with Hemion, if two knots are equivalent. Joel Hass, Jeff Lagarias and Nick Pippinger proved in 1999 that telling that a knot is unknotted is … Continue reading
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
3 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 .
