Taras Lakoba

Taras Lakoba
Occupation	Professor of Mathematics
Employer	University of Vermont
Known for	Applied mathematics, numerical analysis, nonlinear optics

Taras Lakoba is a professor of mathematics at the University of Vermont, where his research spans applied mathematics, numerical analysis, and nonlinear optics. Over the course of his academic career he has built a body of work that bridges theoretical mathematics and practical engineering problems, particularly in the field of optical telecommunications and the mathematical modeling of nonlinear wave phenomena. His work has been supported by multiple grants from the National Science Foundation and has been published in a range of peer-reviewed journals covering mathematics, physics, and engineering.

Education

Lakoba received a Master of Science in physics from Moscow State University in 1989 and a Ph.D. in applied mathematics from Clarkson University in 1996, writing a dissertation titled "Perturbations and Stability of Solitary Waves in Nonlinear Optics" under the supervision of D. J. Kaup. He joined the Department of Mathematics and Statistics at the University of Vermont in 2003.

Career

Taras Lakoba has spent the majority of his academic career at the University of Vermont, where he holds a faculty position in the Department of Mathematics and Statistics. During his tenure at the university, he has served as a principal or co-principal investigator on several externally funded research projects, most notably through grants awarded by the National Science Foundation.

His funded research projects at the University of Vermont include a collaborative study titled "Multichannel All-Optical Signal-Processing Devices Based on a Group-Delay-Managed Nonlinear Medium," awarded on September 8, 2009, with a value of $99,708. This project examined the mathematical and engineering underpinnings of devices used for processing multiple channels of optical data simultaneously, work that connected his mathematical expertise to problems in photonics and telecommunications engineering.

Earlier in his career, Lakoba was awarded funding for a project titled "Mathematical and Engineering Study of Multi-Channel All-Optical Regenerator," which received $52,901 beginning June 24, 2005. This early project laid groundwork for his subsequent research into optical regeneration technologies, an area in which he continued to publish for more than a decade afterward.

In 2012, Lakoba received a larger NSF award of $181,836 for a collaborative research project titled "Instability Analysis of the Split-Step Method on Spatially-Varying Backgrounds, with Applications to Optical Telecommunications and Bose-Einstein Condensation," beginning September 12, 2012. This project extended his numerical analysis work to physical systems beyond optics, including the study of Bose-Einstein condensates, reflecting the broad applicability of the mathematical methods he develops.

More recently, in 2020, Lakoba participated in a collaborative research initiative titled "Expanding the Reach of Industrial Career Training for Graduate Students," which received $8,400 in funding beginning June 20, 2020.

Research

Lakoba's research portfolio, comprising 117 published papers with a combined citation count of 2,378 and an h-index of 23, spans several interconnected areas of applied mathematics and physics. His scholarship can be grouped into several broad categories: numerical methods for differential equations, nonlinear optics and optical signal processing, and applications of nonlinear wave theory to physical systems ranging from pulsar astrophysics to condensed matter physics.

One significant strand of his work concerns numerical methods for solving partial differential equations, particularly those with hyperbolic character. His 2021 paper, "Higher-order explicit schemes based on the method of characteristics for hyperbolic equations with crossing straight-line characteristics," published in Numerical Methods for Partial Differential Equations, develops computational techniques for handling complex characteristic behavior in hyperbolic systems. Related to this, his 2022 review article "Recent Progress in Studies of Stability of Numerical Schemes," published in Symmetry, surveys developments in the analysis of numerical scheme stability, an area central to reliable computational simulation of physical systems.

A second major research area concerns nonlinear optics, particularly the mathematics and engineering of optical signal regeneration and processing for telecommunications applications. His 2021 article "Recent Progress on Optical Regeneration of Wavelength-Division-Multiplexed Data," published in the IEEE Journal of Selected Topics in Quantum Electronics, has been cited 17 times and reviews techniques for maintaining signal quality across multiple wavelength channels in fiber-optic communication systems. Complementing this line of research, his 2022 paper "Numerical Treatment of Boundary Conditions to Reduce High-Frequency Artifacts in Simulations of Distributed-Feedback Lasers," also published in the IEEE Journal of Selected Topics in Quantum Electronics, addresses computational challenges in simulating laser systems used in telecommunications infrastructure. His 2022 conference paper presented at the Conference on Lasers and Electro-Optics, "Amplitude regeneration and phase noise suppression of an 8-PSK signal by an attenuation-imbalanced NOLM," further extends this work into specific signal formats used in modern optical communication systems.

Lakoba's mathematical methods have also found application in the study of nonlinear wave equations with broader physical significance. His 2021 paper "Dynamics of Plane Waves in the Fractional Nonlinear Schrödinger Equation with Long-Range Dispersion," published in Symmetry and cited 8 times, examines wave behavior in systems governed by fractional derivatives, a mathematical framework used to model long-range interactions in physical systems.

Beyond optics and numerical analysis, Lakoba has contributed to interdisciplinary research in astrophysics and condensed matter physics. His 2022 paper "Pulsar Radio Emission Mechanism II: On the Origin of Relativistic Langmuir Solitons in Pulsar Plasma," published in Monthly Notices of the Royal Astronomical Society and cited 11 times, applies nonlinear wave theory to the study of plasma dynamics in pulsar environments, illustrating the versatility of his mathematical techniques when applied to astrophysical problems. In condensed matter physics, his 2022 paper "Atomically Thin Superfluid and Solid Phases for Atoms on Strained Graphene," published in Physical Review B and cited 8 times, investigates the phase behavior of atoms adsorbed on graphene substrates under mechanical strain. A related 2021 paper, "Spinodal De-Wetting of Light Liquids on Graphene," published in the Journal of Physics: Condensed Matter, examines the physical mechanisms by which thin liquid films become unstable and de-wet from graphene surfaces.

Lakoba has also engaged with structural biology through computational methods, as seen in his 2022 paper "Towards Determining Amyloid Fibril Structures Using Experimental Constraints from Raman Spectroscopy," which applies mathematical and computational approaches to the problem of resolving protein fibril structures relevant to disease research.

Taken together, this body of work demonstrates an approach to applied mathematics research characterized by the transfer of numerical and analytical techniques across disciplinary boundaries, from optical engineering to astrophysics, condensed matter physics, and structural biology.

Recognition

Lakoba's research has been recognized through sustained funding from the National Science Foundation across multiple project cycles spanning nearly two decades, from 2005 to 2020, totaling $342,845 in grant support. His citation record, with an h-index of 23 across 117 publications, reflects consistent scholarly output and engagement across multiple subfields of applied mathematics and physics. His publications in journals such as the IEEE Journal of Selected Topics in Quantum Electronics and Monthly Notices of the Royal Astronomical Society indicate recognition within specialized scientific communities in optics and astrophysics, respectively.

Publications

Selected publications by Taras Lakoba include:

• Lakoba, T. (2022). "Numerical Treatment of Boundary Conditions to Reduce High-Frequency Artifacts in Simulations of Distributed-Feedback Lasers." IEEE Journal of Selected Topics in Quantum Electronics.
• Lakoba, T. (2022). "Amplitude Regeneration and Phase Noise Suppression of an 8-PSK Signal by an Attenuation-Imbalanced NOLM." Conference on Lasers and Electro-Optics.
• Lakoba, T. (2022). "Towards Determining Amyloid Fibril Structures Using Experimental Constraints from Raman Spectroscopy."
• Lakoba, T. (2022). "Pulsar Radio Emission Mechanism II: On the Origin of Relativistic Langmuir Solitons in Pulsar Plasma." Monthly Notices of the Royal Astronomical Society.
• Lakoba, T. (2022). "Recent Progress in Studies of Stability of Numerical Schemes." Symmetry.
• Lakoba, T. (2022). "Atomically Thin Superfluid and Solid Phases for Atoms on Strained Graphene." Physical Review B.
• Lakoba, T. (2021). "Dynamics of Plane Waves in the Fractional Nonlinear Schrödinger Equation with Long-Range Dispersion." Symmetry.
• Lakoba, T. (2021). "Recent Progress on Optical Regeneration of Wavelength-Division-Multiplexed Data." IEEE Journal of Selected Topics in Quantum Electronics.