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Abstract: Motivated by generalizations of the Ginsburg-Landau energy and the diffusion equation in which derivatives are replaced by fractional derivatives, Caffarelli, Roquejoffre, and Savin studied the minimizers of a fractional perimeter functional on sets involving a parameter between 0 and 1. Such minimizers have to satisfy a pointwise condition on their boundary, which can be used to define a notion of nonlocal mean-curvature. This definition only holds for surfaces which are the boundary of a set. I will describe how to define a nonlocal notion of mean-curvature for any surface by introducing a fractional area functional and considering its minimizers. Moreover, I will describe how these ideas can be extended to curves by defining a fractional length and an associated nonlocal curvature for a curve.
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Speaker: Dr. Tiago J. Arruda, University of São Paulo, Brazil
Language: English
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Speaker: Prof. Romain Bachelard, University of São Paulo, Brazil
Language: English
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Discussion on recent articles by D. Harlow and H. Ooguri "Symmetries in quantum field theory and quantum gravity" and "Constraints on symmetry from holography" with Linqing Chen leading the discussion.
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Dr. Masahiro Fukuda, Postdoc, Duke-NUS Medical School, Language: English
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Speaker: Dr. Kea Joo Lee, Korea Brain Research Institute
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Speaker: Dr. Jinseop Kim, Korea Brain Research Institute
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Language: English
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Prof. Yu Shen, UT MD Anderson Cancer Center
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Dr. Maxim Trushin, Centre for Advanced 2D Materials, NUS, Singapore