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I am a research associate at Dartmouth College, mathematics department with a PhD in mathematics from University of Arizona. I am passionate about both pure and applied mathematics. On the pure side, I look at problems in mathematical physics and geometry. I am interested in analytical and geometric aspects of quantum field theory, with a special interest in the rigorous construction of infinite-dimensional measures appearing in QFT. One the applied side, I enjoy using a mathematical lens to look at problems arising in data science.
Mohammad Javad Latifi
Research Associate
Dartmouth College, Department of Mathematics
Office:
Kemeny 209Research Interest:
Mathematical Physics and Geometry, Applied Mathematics and Data ScienceEmail:
mohammad.javad.latifi.jebelli@dartmouth.eduTeaching:
Math 22 - Linear Algebra Math 23 - Differential Equations (Spring 2022)Publications - Mathematical Physics and Geometry
1. On star Radon transform and real algebraic geometry , Gaik Ambartsoumian, Asher Auel, MJ Latifi, 2024 (in progress). 2. Tensor network approximation of Koopman operators , Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery, Philipp Pfeffer, Jörg Schumacher, Joanna Slawinska, 2024 (under review). 4. Kernel smoothing for discrete element models of sea ice dynamics , MJ Latifi, Dimitrios Giannakis, 2024 (under review) 3. Conversations with Flaschka: Kac–Moody groups and Verblunsky coefficients , MJ Latifi, Doug Pickrell, Physica D: Nonlinear Phenomena , Vol 445, 2023. 5. Lattice models and super telescoping formula, MJ Latifi, 2023, preprint. 6. Exponential of the S^1 trace of the free field and Verblunsky coefficients, MJ Latifi, Doug Pickrell, Rocky Mountain J. Math. 52(3), 2022. 7. Inversion and Symmetries of the Star Transform, G Ambartsoumian, MJ Latifi, The Journal of Geometric Analysis, 31 (2021), pp 11270-11291. 8. Generalized V-line transforms in 2D vector tomography, G Ambartsoumian, MJ Latifi, RK Mishra, Inverse Problems, Vol.36 (10),2020. 9. The V-line transform with some generalizations and cone differentiation, G Ambartsoumian, MJ Latifi, Inverse Problems, Vol.35 (3),2019. Publications - Applied Mathematics and Data Science
10. On the Literary Landscapes of Vector Embeddings, Daniel Rockmore, Jiayi Chen, Mohammad Javad Latifi Jebelli, Allen Riddell and Harrison Stropkay, 2024. (under review) 11. Numerical implementation of generalized V-line transforms on 2D vector fields and their inversions, MJ Latifi, Gaik Ambartsoumian, Rohit Kumar Mishra ,2023. SIAM Journal on Imaging Sciences. 12. Graph Spanners: A Tutorial Review, MJ Latifi, Reyan Ahmed, Alon Efrat, Keaton Hamm, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence, Computer Science Review, 2020. 13. Prediction of track geometry degradation using artificial neural network: a case study, MJ Latifi, Hamid Khajehei, Alireza Ahmadi, Iman Soleimanmeigouni, Mohammad Haddadzade, Arne Nissen, International Journal of Rail Transportation. 14. Approximation algorithms and an integer program for multi-level graph spanners, MJ Latifi, Reyan Ahmed, Keaton Hamm, Stephen Kobourov, FD Sahneh, Richard Spence. Analysis of Experimental Algorithms, SEA 2019. 15. A General Framework for Multi-level Subsetwise Graph Sparsifiers , MJ Latifi, Reyan Ahmed, Keaton Hamm, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence, 2019. See Google Scholar page for more.
Check out My CV.
Some visualizations that I made for my vector calculus students at University of Arizona.
Kernel Smoothing for Sea Ice Dynamic
During my time at Datrmouth , I have been working on a software to construct smooth representation of sea ice dynamic. Potential applications include using the smooth data to learn governing differential equations in large scale. We also establish a theoretical framework to prove \( L^p \) convergence theorems for such family of smooth approximations (Read more).
Orthogonal Polynomials on \( S^1 \) and Verblunsky Correspondence
Above animation visualizes the 5th orthogonal polynomial on the circle with respect to the background measure \( d\mu = (1-cos \theta) \frac{d\theta}{2\pi} \). This polynomial can be seen as a section of a fiber bundle on \( S^1 \) with the fiber being the set of complex numbers. In my current project, we study a new family of measures \( d\mu = (1-cos \theta)^a \frac{d\theta}{2\pi} \) establishing the corresponding Verblunsky sequence and orthogonal polynomials.
Radars and Autonomous Cars at Lunewave:
In the summer of 2019, I was involved in a project at Lunewave working on Radars and Autonomous Cars. During this period, I worked on algorithms to track and classify objects. I implemented a C++ GUI software for the analysis and visualization of the Radar data. Here is a video demonstration of the software where you can match the classified cars in the point cloud data with the camera video.