From September 4 through September 6, 2018, Professor Russel E. Caflisch from the Courant Institute of Mathematical Sciences at NYU visited CCMA and gave three talks. He also had many insightful discussions with CCMA members on a variety of research topics.


On September 4th, Caflisch gave a talk about the deep relationship between differential equations to data science. His talk encompassed image processing and compressed sensing in addition to recent progress in deep learning. The talk stimulated much further discussion concerning the mathematical questions surrounding deep learning between Professor Caflisch and the CCMA professors and post-docs.


On September 5th, Professor Caflish met with Professor Jinchao Xu’s research group. Various members of the group presented their research. Highlights include Dr. Qingguo Hong presenting his recent work developing extended Galerkin methods and Dr. Shihua Gong giving a talk concerning this work developing finite element methods for the linear elasticity equations. To finish the meeting, Professor Xu presented his recent research progress, highlighted by his ideas to apply the theory of multigrid methods to better understand deep neural networks.


After meeting with Jinchao’s group, professor Caflisch gave his second talk on multiscale methods for modeling plasmas and dilute gases. He addressed the challenges of this modeling problem in the regime

where the plasma is too dense for a direct simulation of all particles, but not dense enough for a fluid approximation to be valid.


Then, on September 6th, Calflisch gave his final talk, which concerned signal fragmentation for low-frequency radio transmission. This recent work with his two graduate students, Edward Chou and Jonathan Siegel, studies the optimal decomposition of a low-frequency radio signal into pieces which can be efficiently transmitted using small antennas.


Professor Calflisch was the Director of the Courant Institute of MathematicalSciences at New York University (NYU) and a Professor in the MathematicsDepartment. Up until August 2017, Caflisch was the Director of the Institute for Pure & Applied Mathematics (IPAM) and a professor in theMathematics Department at UCLA. He is a fellow of the American Mathematical Society, the American Academy of Arts and Sciences, and the Society for Industrial and Applied Mathematics (SIAM), and was an invited lecturer at the SIAM National Meeting and at the International Congress of Mathematicians. Caflisch was previously an Alfred P. Sloan Research Fellow and a Hertz Foundation Graduate Fellow.



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