报告题目： EIT for once-differentiable conductivities at non-zero frequency
报告人： Evgeny Lakshtanov 首席研究员（University of Aveiro）
报告摘要： This talk concerns our recent progress in the Bukhgeim and Inverse Scattering Transform (IST) methods which allowed to get new results on the uniqueness in the 2D Inverse Conductivity Problem for Complex-Valued Conductivities. Both methods are reconstructional, but the first method is global while the application of the inverse scattering transform is generic in a manner similar to what exists in one-dimensional applications of IST to the Schrodinger or Zakharov-Shabat problems. The results are published in:
E. Lakshtanov, J. Tejero, B. Vainberg, Uniqueness in the Inverse Conductivity Problem for Complex-Valued Lipschitz Conductivities in the Plane, SIAM Journal on Mathematical Analysis, 49, 2017, 3766-3775.
E. Lakshtanov, B.Vainberg, On reconstruction of complex-valued once differentiable conductivities, J. Spectr. Theory 6, 4, (2016), 881-902, Special issue in memory of Yuri Safarov.
At the end we present our further plans as well as the general insight of further developments towards the wider utilization of EIT in daily practice.
Dr. Evgeny Lakshtanov, born in Khmelnitsky, USSR in 1979. After completing the Phys. Math. class in Chernogolvka in 1996 he studied Mathematics at Moscow State University. In 2004 he finished his PhD (Kand. Nauk.) under supervision of Robert Minlos. His thesis concerns applications of Functional Analysis and Catastrophe Theory in statistical physics, in particular in the description of properties of Gibbs fields. After defense of his thesis he took a decision to study a new area from the beginning enlarging his scientific background and accept the invitation of Alexander Plakhov to work on quantum analogue of Newton's minimal resistance problems. This led him to University of Aveiro where he was studying direct scattering problems and derivation of mathematical models of propagation of sound. Since 2009 he has a synergistic collaboration with Boris Vainberg. In 2011 Andreas Kirsch asked him to study the theory of Interior Transmission Eigenvalues and it marks the moment he turned from direct scattering problems to inverse scattering problems. He was fortunate to collaborate with Roman Novikov, Armin Lechleiter, Brian Sleeman, and others. Since 2013 he hold a position of Principal Researcher at University of Aveiro. Till now, he has published more than 40 research papers in SIAM J. Math. Anal., Rend. Istit. Mat. Univ. Trieste, Inverse Problems, Phys. Rev. E and other prestigious International journals.