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Welcome to my website! Since November 2024 I am a JSPS Fellow working at the Division of Mathematics of the Graduate School of Information Sciences of Tohoku University (東北大学 大学院情報科学研究科 数学教室) on algebraic combinatorics with a focus on Hadamard matrices and maximal determinant matrices. Here, I collaborate with my host Prof. Akihiro Munemasa (宗政昭弘先生).
I am also a Research Associate at the Worcester Polytechnic Institute, where I collaborate with Prof. Sergey N. Makaroff and his team on computational neuroscience. We are developers of the charge-based BEM-FMM solver for high-resolution bioelectric modeling. My focus is on theoretical aspects (integral equations, mathematical physics) as well as modelling and software development for EEG and MEG applications.
Below are some cool pictures related to my research in math and applications!
The bivariate polynomial x^2 + y^2 over the finite field of 193 elements visualized as a matrix. Certain Hadamard matrices can be constructed with blocks given by polynomials.
The adjacency matrix of the orthogonality graph on +/- 1 vectors of length 8. Here, two such vectors are adjacent if and only if their inner product vanishes. Any clique of size 8 in this graph corresponds to an Hadamard matrix of order 8.
The Gram matrix of a maximal determinant +/-1 matrix of order 23. The colors represent different entries. I am interested in computing maximal determinants for matrices with entries in the roots of unity.
The electric field induced by a fictitious current applied to a MEG gradiometer coil over the midsurface between the grey and white matter tissue of a subject. This TMS solution can be used to solve the forward MEG problem by the principle of electromagnetic reciprocity.
A source localization error map for an inverse model using simplified 3-layer models against synthetic data generated with high-resolution 5-layer models. This map showcases the need for fast high-resolution solvers for EEG/MEG source reconstruction.
Source reconstruction from measured MEG data. The inverse solution was calculated via a regularized system matrix obtained from reciprocal BEM-FMM TMS solutions.
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