I am a mathematician specializing in algebraic geometry. I completed a postdoctoral research position at the Institute of Mathematics, University of Bern (UniBe), where I was part of the Applied Algebraic Geometry Group led by Prof. Dr. Jan Draisma . Prior to that, I earned my PhD at the Institute of Mathematics of the Polish Academy of Sciences (IMPAN) and my master's degree at the Faculty of Mathematics, Computer Science, and Mechanics of the University of Warsaw (MIMUW), both under the supervision of Prof. Dr. Jarosław Buczyński . Although I am currently not holding a formal position at these institutions, I maintain collaborations with them.

My research is focused on tensors, their geometry and properties, with applications to complexity theory. In particular:

• tensor ranks (rank, border rank, asymptotic rank, etc.)
• Veronese, Segre and Segre-Veronese varieties
• Secant varieties
• Polynomial functors

In addition to my work in mathematics, I develop scripts and work on data analysis and machine learning projects. Examples of my programs and scripts can be found in the "Miscellaneous" section at the bottom of this website.

For a complete list see here.

For additional materials see here.

Fall semester 2026/2027:

• Python for scientific applications (Blok laboratoryjny L)
• Numerical Methods
• Introduction to Numerical Methods
• Introduction to Mathematica

Fall semester 2023/2024:

• Varieties and algebraic groups
• Mathematics für Naturwissenschaften

Spring semester 2023/2024:

• Seminar: Algebraic Statistics
• Mathematics für Naturwissenschaften

Fall semester 2022/2023:

• Linear Algebra 1
• Mathematics für Naturwissenschaften

Spring semester 2022/2023:

• Seminar: algebra and expander graphs
• Galois Theory

List of courses taught before:
Calculus, Discrete Mathematics, Mathematical Analysis, Linear Algebra

List of courses taught before:
Calculus, Discrete Mathematics, Mathematical Analysis, Linear Algebra

For the list of projects possibly not included below see gitlab.com/frupniew and huggingface.co/frupniew.

🚀 Advanced AI, LLMs & Complex Architectures

• gitlab.../llm_macaulay - An end-to-end RAG and fine-tuned LLM pipeline for generating, validating, and executing Macaulay2 scripts in a secure Docker sandbox, optimized for 4GB VRAM edge deployment.
• huggingface..../macaulay2-rag-coder-3b-gguf - Q4_K_M quantized 3B coding model fine-tuned for Macaulay2 (algebraic geometry), engineered to fit in 4GB VRAM for local deployment and automated RAG pipelines.
• gitlab.../speech_to_protocol - An automated system for transcribing meetings and generating organized summaries with action items. It uses a modular architecture that currently leverages cloud models for speed, but can be easily switched to fully local execution for strict data privacy. (Pairs with local_transcript_editor below.)

📊 Formal Machine Learning & Data Analysis

• github.../ml_challange - My solution for a Machine Learning Optimization and Multimodal Challenge, together with the report (containing a description of the challenge) and a dockerfile.
• github.../used_cars - A collection of graphs, tables, and raw data analyzing the used car markets in Poland and Switzerland, based on web-scraped data from 2024.

💻 Full-Stack Web

• gitlab.../local_transcript_editor - Local-first web app (Python/Flask & Vanilla JS) for editing and synchronizing audio transcripts, featuring high-precision playback and client-side state management. (Pairs with speech_to_protocol above.)

👁️ Applied Computer Vision

• github.../receipt_parsing - Python script that automatically extracts data from photos of Swiss retail and discount receipts, outputting neat, structured CSV files for easy analysis.

🛠️ Desktop Utilities

• github.../pytacz4 - A Python program (with both CLI and GUI versions) that uses an adaptive occurrence-count algorithm and text-to-speech to help you master vocabulary.
• github.../booklet_printing - A Python script for Linux that automates the preparation of PDF files for double-sided booklet printing by cropping margins and rearranging pages.

🗄️ Archived Project

• filip-covid.github.io - Daily updated charts on the spread of the epidemic of COVID-19 in Poland caused by SARS-CoV-2 (last updated in 2022).