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Daniel Scofield, NC State, Patterns in Khovanov homology
Khovanov homology is a recent link invariant that lifts the Jones polynomial. We analyze torsion in Khovanov homology by describing a related homology theory that lifts the chromatic polynomial. In particular, we describe torsion in Khovanov homology of several link families…
Find out more »Jichun Li, University of Nevada Las Vegas, Electromagnetic cloaking: mathematical analysis and simulation
In June 23, 2006's "Science" magazine, Pendry et al and Leonhardt independently published their papers on electromagnetic cloaking. In Nov.10, 2006's Science magazine, Pendry et al demonstrated the first practical realization of such a cloak with the use of artificially constructed…
Find out more »Joey Hart, NCSU, SIAM Tutorial Series: Introduction to Monte Carlo Methods
In this lecture we will present basis theoretical and algorithmic properties of Monte Carlo methods. In particular, their convergence properties and implementational simplicity will be highlighted. There are a variety of Monte Carlo methods but we will focus on two,…
Find out more »Adam Levine, Duke, Heegaard Floer invariants for homology $S^1 \times S^3$s
Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4-manifold X with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded 3-manifold Y representing a generator of H_3(X), a suitable version…
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