Researcher & Physicist
Lucas Kotz
Physics PhD · Data Scientist · Simulation and Modeling Specialist
I earned my PhD in Physics from Southern Methodist University, where I developed a strong foundation in data-driven analysis and predictive modeling. These skills have enabled me to tackle complex, data-intensive problems in areas like statistical modeling, uncertainty quantification, high-dimensional optimization, and data-driven theoretical analysis.
Learn about the particle that holds matter together within our universe: the pion. By learning about the internal structure of the pion at high energies, we can learn about the universe we interact with daily.
About
Background & Experience
About Me
I grew up in Valley Stream, NY, where my early curiosity for science was nurtured through museum visits and trips to the observatories across Long Island. That curiosity evolved into a passion for physics during high school, leading me to pursue a degree in physics at the University at Buffalo (UB).
At UB, I was exposed to a broad range of fields — from cosmology to condensed matter to particle physics. I discovered my interest in theoretical particle physics through hands-on labs and independent studies. I even designed a cosmic ray detector, which gave me a deep appreciation for the precision and ambition of high-energy physics experiments. A research experience at UB introduced me to the mathematical structure underlying quantum field theory and solidified my path toward graduate study.
I went on to earn my PhD in physics from Southern Methodist University (SMU), where I focused on studying the internal structure of pion, a particle that mediates the strong force between nucleons (protons and neutrons) at low energies. My research combined theoretical physics, statistical modeling, and computational tools to extract meaningful insights from various experimental datasets and theoretical predictions. I developed a novel approach using Bézier curves to represent parton distribution functions (PDFs), a probability density function of any given partons (constituent particle) within the pion. This allows us to systematically explore model uncertainty that has never been accounted for, specifically the pion in high-energy physics.
Today, I’m looking to apply the same analytical thinking, statistical analysis, coding expertise, and problem-solving mindset to data science, machine learning, and applied research challenges.
Research Interests
Lucas Kotz — Résumé
Full PDF available for download · Last updated 2025
Professional Summary
Data science-oriented physicist with 4+ years of doctoral experience in computational modeling, statistical analysis, and high-performance computing. Proficient in C++, Python, and Fortran.
- Rapidly acquired and applied expertise in complex theoretical frameworks and scientific computing tools across multiple languages and modeling domains.
- Communicated complex research findings to diverse audiences — from specialists to non-technical stakeholders — at international conferences and workshops.
- Applied advanced problem-solving to define research objectives, develop computational strategies, and collaborate in interdisciplinary, data-driven teams.
Education
Work Experience
- Designed and deployed C++ tools for advanced statistical modeling, including parameter estimation, Bézier curve parameterization, and uncertainty quantification.
- Validated and improved models using Bayesian inference, Hessian analysis, Monte Carlo methods, sensitivity analyses, and data visualizations.
- Presented technical research to audiences ranging from non-technical to expert, showcasing strong communication and adaptation skills.
- Independently managed projects while proactively collaborating with peers to ensure project alignment and progress.
- Kept up to date with emerging advances in high-energy physics by regularly reviewing publications, preprints, and conference proceedings.
- Supported undergraduate students in introductory physics courses (classical mechanics, electromagnetism, cosmology) in lab and classroom settings.
- Guided collaborative problem-solving exercises for lab groups within classes of up to 27 students.
- Tutored individual students and led after-hours sessions for any undergraduates in physics courses.
- Evaluated assignments, exams, and projects, providing detailed feedback for classes of up to 50 students.
Selected Publications
- L. Kotz, A. Courtoy, P. Nadolsky, F. Olness and M. Ponce-Chavez, Analysis of parton distributions in a pion with Bézier parameterizations, Phys. Rev. D 109 (2024) 074027, [arXiv:2311.08447].
- L. Kotz, A study of experimental sensitivities to proton parton distributions with xFitter, [arXiv:2401.11350].
- L. Kotz, A. Courtoy, P. Nadolsky, and M. Ponce-Chavez, Fantômas: epistemic and nuclear uncertainties for the parton distributions of the pion, [arXiv:2505.13594].
- L. Kotz, A. Courtoy, T. J. Hobbs, P. Nadolsky, F. Olness, M. Ponce-Chavez, and V. Purohit, Fantômas Unconfined: global QCD fits with Bézier parameterizations, [arXiv:2507.22969].
Technical Skills
Programming Languages
C++PythonFortran BashMakeLaTeXStatistical Modeling & Analysis
Bayesian InferenceMonte Carlo χ² MinimizationUncertainty Quantification Machine LearningSensitivity AnalysisTools & Platforms
MathematicaJupyterSQL CERN ROOTMATLABVS CodeSystems & Workflow
LinuxGitHPC SLURMgdb / dddResearch
Projects & Work
Research Overview
During my PhD at SMU, I focused on analyzing the internal structure of subatomic particles (like the pion) using parton distribution function models. Parton distribution functions (PDFs) are data-driven models derived from high-energy collider experiments, including the currently operating Large Hadron Collider (LHC) and the soon-to-be-built Electron-Ion Collider (EIC). These models describe how a particle’s momentum is distributed among its constituent quarks and gluons — a cornerstone of modern particle physics research.
I developed new modeling approaches for pion PDFs and analyzed how different experimental datasets affected the model’s results. The pion is crucial in holding atomic nuclei together (via the strong force), which is why it’s an important particle to study.
Although my work centers on structured, interpretable alternatives to neural networks, it draws on many of the same statistical foundations, including gradient descent optimization, chi-squared loss minimization, and model reliability techniques. I employed methods such as model verification, bootstrap-based uncertainty estimation, and comparative analysis across multiple parameterizations to assess assess model stability and robustness. This overlap gives me strong cross-compatibility with modern machine learning workflows and tools, and also enabled me to train and evaluate several baseline models as part of my broader data science development.
You can find all of my published work on Inspire HEP.
Fantômas4QCD →
The Fantômas4QCD project resulted in the development of a custom PDF modeling module using Bézier curves as the core technique (essentially using them as universal function approximators). This approach combines the transparency of a simple polynomial model with the flexibility of a neural network, allowing us to explore a much wider range of viable solutions in QCD models.
Lattice QCDC++ / MathematicaL2 Sensitivity →
To accurately interpret theoretical predictions, it's important to understand how individual datasets influence the fitted model. L2 sensitivity quantifies this by calculating how much the chi-squared value changes when PDFs are varied by one standard deviation.
This method highlights which datasets exert the most pull on the fit — helping identify potential outliers, inconsistencies, or overreliance on specific data.
StatisticsHEP FitsData Visualization →
Scientific results are only valuable if they can be effectively communicated. Throughout my research, I've emphasized clear data visualization to convey key findings in presentations, papers, and collaborations.
Using tools like Mathematica, ManeParse, and CERN's ROOT, I've created visualizations that reveal model behavior, compare datasets, and highlight statistical significance in an accessible and digestible way.
D3.jsPythonFantômas4QCD
Our team set out to create a new, flexible way to model parton distribution functions (PDFs) – the statistical profiles that show how a particle’s momentum is shared among its quarks and gluons.
We applied Bézier curves in our PDF modeling, giving our solution the clarity of a simple mathematical formula and the adaptability of a neural network – a unique combination not seen in previous models.
The Fantômas module we built quantifies uncertainties in the pion’s structure that earlier models could not measure, providing new insights for QCD analysis.
The xFitter program with the Fantômas module implemented is found here.
Bézier curves: From cars to physics
,_by_Klugschnacker_modified.webp)
To better describe the internal structure of the pion (and other hadrons), we use Bézier curves, originally developed for car design.
Invented by Paul de Casteljau (Citroën, 1958) and Pierre Bézier (Renault, 1960), Bézier curves were first used to model smooth car body shapes using only a few control points. The Citroën DS (left) was one of the first cars designed using this technology, which later became foundational in computer-aided design (CAD).
Today, more than 60 years later, we apply the same mathematical framework in high-energy physics. Bézier curves allow us to construct smooth, continuous, and highly adaptable functions for modeling PDFs. Their interpretability and flexibility make them ideal for capturing model-dependent uncertainty in a physically meaningful way.
How we extract PDFs using Bézier curves
Since parton distribution functions (PDFs) are not directly observable, we must infer them from experimental data — specifically, measurements from fixed-target and collider experiments.
Our module was implemented into xFitter, an open-source framework for global QCD analyses. xFitter predicts theoretical models by using a gradient-descent algorithm (Minuit) to minimize the chi-squared (χ²) goodness-of-fit value to identify the best-fit Bézier parameterization for the given data.
By adjusting the number and location of control points, the module can scan a wide range of model possibilities, giving us a more complete picture of the theoretical uncertainties in PDF extraction.
Extracted PDFs from pion data
From the hundreds of solutions generated by the Fantômas module, we selected five good fits that captured the full range of observed features.
These were combined into a single model that incorporates both aleatoric (statistical) and epistemic (model-based) uncertainties — providing a more comprehensive understanding of the pion's structure.
The complete pion PDF set is located here.
Visualizing pion data
After identifying the best-fit models, we analyzed their statistical behavior and interrelationships.
.webp)
L2 Sensitivity Analysis
The L2 sensitivity methodology provides a rigorous framework for assessing how individual data points or datasets influence the outcome of global QCD analyses. By examining the second-order (L2) response of the χ² function, one can quantify the statistical pull of each observable on extracted parton distributions or other fitted quantities.
This work extends existing sensitivity measures and applies them to [specific context — e.g., polarized parton distributions], providing actionable guidance for future experimental programs at facilities such as [EIC / Jefferson Lab / etc.].
Methodology Summary
[Summarize the core equations or steps of your methodology. Reference relevant papers, provide figures, or outline the algorithm in plain language accessible to a broad physics audience.]
Data Visualization
Effective communication of high-dimensional physics datasets requires purpose-built visualization tools. This project encompasses a suite of interactive dashboards and publication-quality figures developed to explore lattice QCD outputs, sensitivity maps, and global fit results.
Tools are built using Python (Matplotlib, Plotly) and D3.js for web-based interactive exploration. A particular focus is enabling physicists to interactively probe parameter spaces and understand correlations among fitted observables.
Gallery
[Embed or link representative figures and interactive demos here. Describe what each visualization shows and what physics insight it conveys. You can insert <img> tags or <iframe> embeds pointing to hosted demos.]
Dissertation
Doctoral Thesis
A Novel Approach to Model the Pion Structure Using Advanced Polynomial Functions
In the coming years, new experiments at the Electron-Ion Collider (EIC) and the Large Hadron Collider (LHC) will provide unprecedented insight into the building blocks of matter. To make the most of these opportunities, scientists must reduce uncertainties in the theoretical models that connect what we observe in experiments to what is happening inside particles like protons and pions. A critical part of these models involves describing how a particles momentum is shared among its internal components – quarks and gluons.
This work focuses on improving how we model the internal structure of the pion. We propose a new approach using smooth, flexible mathematical curves – called Bézier curves – to describe this structure without overly rigid assumptions. Integrating this method into commonly used analytical tools allows us to study how different modeling choices affect our results. As future experiments deliver more data, our approach will help uncover a broader understanding of the pions inner structure and the forces that hold nuclei together.
Full Thesis
The complete dissertation is archived in the SMU Institutional Repository. Includes the full text, appendices, and supplementary materials as submitted for the doctoral degree.
Hosted by: SMU Scholar · Southern Methodist University
Defense Slides
Presentation slides from the doctoral defense. Covers the core motivation, methodology, key results, and outlook of the dissertation research in a concise format.
Format: PDF · Defense presentation
Defense info
Defended: April 2025
Institution: Southern Methodist University
Advisor: Prof. Pavel Nadolsky, Michigan State University
Advisor: Prof. Fred Olness, Southern Methodist University
External: Prof. Aurore Courtoy, Universidad Nacional Autónoma de México
Member: Prof. Allison Deiana, Southern Methodist University
Member (Chair): Prof. Matthew Klein, Southern Methodist University