Matthew Kahle

Columbus, OH

http://matthewkahle.org/

I am a professor at Ohio State University, interested in various interactions of topology and geometry with probability, statistical mechanics, and combinatorics.

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Connectivity of the Erdős–Rényi random graph

co.combinatorics pr.probability graph-theory random-graphs asked Mar 30, 2011 at 14:50

mathoverflow.net

33 votes

chromatic number of the hyperbolic plane

co.combinatorics discrete-geometry graph-colorings hyperbolic-geometry asked Jan 20, 2012 at 17:30

mathoverflow.net

27 votes

What is the right notion of self-dual (two-dimensional) percolation in R^4?

pr.probability gt.geometric-topology co.combinatorics mp.mathematical-physics asked Jul 14, 2010 at 2:00

mathoverflow.net

24 votes

Monochromatic triangles in every two-coloring of the plane?

graph-theory ramsey-theory additive-combinatorics asked Jul 29, 2010 at 19:20

mathoverflow.net

21 votes

What are some good examples of non-monotone graph properties?

graph-theory pr.probability co.combinatorics asked Sep 28, 2010 at 0:12

mathoverflow.net

20 votes

Is there an analogue of the Erdős–Gallai theorem for simplicial complexes?

co.combinatorics simplicial-complexes graph-theory asked Sep 11, 2012 at 19:43

mathoverflow.net

19 votes

Covering a hexagon

discrete-geometry asked Jun 21, 2013 at 19:58

mathoverflow.net

17 votes

Is it true that a connected graph has a spanning tree, if the graph has uncountably many vertices?

combinatorics graph-theory set-theory asked Oct 25, 2011 at 22:15

math.stackexchange.com

16 votes

How many triangulations of the genus $g$ surface on $n$ vertices?

enumeration asymptotics simplicial-complexes co.combinatorics asked May 22, 2013 at 23:43

mathoverflow.net

16 votes

In an Erdős–Rényi random graph, what is the threshold for the property "every edge is contained in at least one triangle"?

co.combinatorics pr.probability graph-theory asked Jul 31, 2011 at 20:19

mathoverflow.net

Top Answers

Which math paper maximizes the ratio (importance)/(length)?

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Most intricate and most beautiful structures in mathematics

mathoverflow.net

Open problems with monetary rewards

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Configuration space of little disks inside a big disk

mathoverflow.net

Open problems in Euclidean geometry?

mathoverflow.net

Why tropical geometry?

mathoverflow.net

Why do wedges of spheres often appear in combinatorics?

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A set for which it is hard to determine whether or not it is countable.

mathoverflow.net

What are some mathematical sculptures?

mathoverflow.net

Small simplicial complexes with torsion in their homology?

mathoverflow.net

Is it true that a connected graph has a spanning tree, if the graph has uncountably many vertices?

math.stackexchange.com

Number of non-Abelian groups of order $2^n$

mathoverflow.net

How many simplicial complexes on n vertices up to homotopy equivalence?

mathoverflow.net

Examples of non-simply connected manifolds with trivial H^1

mathoverflow.net

On the number of Archimedean solids

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Lower bounds for chromatic number of a graph

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Computational software in Algebraic Topology?

mathoverflow.net

What are some examples of colorful language in serious mathematics papers?

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Pennies on a carpet problem

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What is the inverse function of $\ x^2+x$?

math.stackexchange.com

Clique sizes in a unit disk graph

mathoverflow.net

Is there a dense subset of the real plane with all pairwise distances rational?

mathoverflow.net

Small simplicial complexes with torsion in their homology?

mathoverflow.net

Are "most" spaces aspherical?

mathoverflow.net

Counting in Two ways: $m^3 = 6 {m \choose 3} + 6 {m \choose 2} + m \quad \forall m \in \mathbb{N}$

math.stackexchange.com

Covering of a graph via independent sets

mathoverflow.net

The shortest path in first passage percolation

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Estimating the fractal dimension of a point cloud

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Is being simply connected very rare?

mathoverflow.net