University of Illinois at Urbana-ChampaignDepartment of Mathematics
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RECENT PRESENTATIONS

[1] Sharp integrability condition of an exit time for stable processes from unbounded domains. [ pdf ]
[2] Isoperimetric inequalities for eigenvalues of triangles. [ pdf ]
[3] Heat kernel monotonicity for reflected Bessel processes. [ pdf ]


SCRIPTS IN MATHEMATICA

The scripts from my papers about eigenvalues are extremely slow in Mathematica 5.1 and newer (1000x slower than in Mathematica 5.0 !!!). Below are the new, fast scripts that work under Mathematica 5.0 and newer. They run in less than a minute and are around 10x faster than the old ones on Mathematica 5.0.
"Sharp bounds for eigenvalues of triangles": [ eigen.m ]
[ output: math -run "<<eigen.m" ]
"Isoperimetric inequalities for eigenvalues of triangles": [ iso.m ]
[ spectral gap: math -run "<<iso.m" ] [ ratio: math -run "bound=2;<<iso.m" ]

Department of Mathematics
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