Charlotte Charlotte

Do you want to get a Ph.D. in researching the Lightning Network?

One Ph.D. position in Computer Science with full financial support is available starting in Fall 2023 in Dr. Christian Kümmerle’s research group at the University of North Carolina at Charlotte (UNC Charlotte) in Charlotte, North Carolina, with a specfic focus on multipart pathfinding algorithms for the Lightning Network, the leading scaling solution for Bitcoin payments.

Position & Project Description

Successful applicants will receive full tuition support and monthly stipend. During their Ph.D., the candidate will work on addressing some of the challenges arising within the routing and pathfinding of large payments within the Lightning Network.

Using the pathfinding algorithms currently implemented in implementations of Lightning network nodes such as Core Lightning or LND, it is challenging to reliably and cheaply send large payments whose amounts are of the same order of magnitude as the channel capacities of a node, as they are designed to only use a single payment path. While atomic multi-path payments are possible on a protocol level by now, finding the optimal multi-path payment splits that simultaneously are reliable, cheap and efficiently computable results in a non-convex optimization problem within the class of minimum cost flow optimization problems, and currently no efficient algorithms have been developed to solve this problem.

In this Ph.D. project, we develop continuous optimization techniques tailored to the requirements of finding optimal multi-path payment splits, leveraging recent advances in non-convex, continuous optimization techniques for with (partially) combinatorial loss functions.

Dr. Kümmerle research interest is in the mathematical foundations of machine learning and the development and analysis of efficient algorithms for large scale data analysis. His research leverages continuous optimization to address computational and statistical challenges arising from data models involving graph, sparsity and low-rank structures, leading to scalable algorithms with provable guarantees, and been published at premier venues in machine learning (JMLR, ICML, NeurIPS) and mathematics. The applicants can expect a close supervision and research mentorship starting from the first year. Please refer to this website for an overview of the coursework expected in the first semesters designed to supplement your knowledge.


Applicants should have a Bachelor or Master degree (or expect to receive the degree before enrollment at UNC Charlotte) in Computer Science, Applied Mathematics, Operations Research, Electrical Engineering or related disciplines. Further admission requirements and necessary application materials can be found at the admissions page of the Computer Science Ph.D. track.

Further desired qualifications:

  • Strong knowledge of multivariate calculus, linear algebra
  • Background and/or interest in continuous optimization
  • Familiarity with the technologies underlying Bitcoin and/or the Lightning network

How to Apply

To apply for the positions, please apply for the Ph.D. program in CS at UNC Charlotte and mention Dr. Kümmerle’s name in your application. Recommendation letters can be arranged to be submitted in the online application system.

Please also email your resume in PDF (including relevant research experience) to Dr. Christian Kümmerle ( with subject line “PhD applicant - Lightning”.

To ensure consideration for Fall 2023, we encourage applicants to apply soon, at the latest by April 15, 2023.

All inquiries about the position should be made to Dr. Christian Kümmerle (

UNC Charlotte & City of Charlotte

UNC Charlotte Campus

UNC Charlotte is North Carolina’s urban research institution. A large public university with a small college feel, more than 27,200 students consider UNC Charlotte’s 1,000-acre campus their home away from home. The College of Computing and Informatics is a talent-generating powerhouse and the largest producer of Computer Science graduates in NC and the sixth largest in the nation. The Computer Science Ph.D. track is with around 50 students currently the largest at UNC Charlotte and provides ample opportunities for developing advanced competencies beyond your specific research program.

Charlotte is an excellent location for you to spend your PhD years. The campus is located in the Piedmont of North Carolina, just two hours from the mountains and three hours from the Atlantic Ocean. Also known as the Queen City, Charlotte is a vibrant, entrepreneurial center and the largest city in North Carolina. Charlotte has 10 Fortune 500 companies in its metropolitan area: Bank of America, Truist Financial, Lowe’s, Nucor, Duke Energy, Sealed Air Corp, Sonic Automotive, Family Dollar, SPX Corporation, and Domtar. The city was recently named on Forbes’ list of Best Places for Business and Careers and regularly ranks highly on lists of desirable places to live and buy a home. Ranked in 2020 as America’s #1 “Tech Town”, the city has a vibrant entrepreneurial ecosystem, currently with four locally-grown unicorns (privately-held startups of at least $1B valuation).