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November 16, 2012 at 2:30pm Sieg 225 |
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| Max Warshauer
Texas State University |
Collaborations Between University Math Departments and Public Schools |
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In this talk, I will describe challenges in working with public schools and our
experiences with math camps, a curriculum project, and teacher training. This
discussion will outline steps in setting up collaborations, how they can benefit
all the parties, and problems that can occur. I will also describe lessons
learned, and where we are now in some of our current projects. |
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October 5, 2012 at 2:30pm Sieg 225 |
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| Matthew Kahle
Ohio State University |
Topology of Random Flag Complexes |
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Random flag complexes are a natural generalization of random graphs to higher
dimensions, and since every simplicial complex is homeomorphic to a flag complex
this puts a measure on a wide range of possible topologies. In this talk, I
will discuss the recent proof that according to the Erdős–Rényi measure,
asymptotically almost all \(d\)-dimensional flag complexes only have nontrivial
(rational) homology in middle degree \(\lfloor d/2 \rfloor\). The highlighted
technique is originally due to Garland -- what he called "\(p\)-adic curvature"
in a somewhat different context. This method allows one to prove cohomology-vanishing
theorems by showing that certain discrete Laplacians have sufficiently large
spectral gap. This reduces certain questions in probabilistic topology to
questions about random matrices. Some of this depends on new results for random matrices, in joint work with Chris Hoffman and Elliot Paquette. Proving central limit theorems for Betti numbers in the non-vanishing regime was done in joint work with Elizabeth Meckes.
The talk will aim to be self contained--I will not assume any particular
probability or topology prerequisites. |
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