My research interests are:
- Applied algebra
- Metric algebraic geometry
- Computational algebraic geometry
- Algebraic statistics
DresdenDIR - Algebraic Statistics
In the 6 weeks summer research program DresdenDIR in August–September 2026, I worked with maximum likelihood degree for toric models under linear changes of coordinates. We have worked with Veronese and Segre embeddings. The type of questions we were interested was the following:
- What is the maximum likelihood degree for generic matrix.
- What is the discriminant.
- What can we say about the stratification?
- How can we reach maximum likelihood degree equals to 1? Is every number between 1 and the generic number is reachable?
- What happens when its restricted to statistically meaningful matrices like stochastic matrices.
Master’s Thesis - Polar varieties and Applications
My master’s thesis, Polar Varieties and Applications (University of Copenhagen, 2026), was supervised by Nidhi Kaihnsa. It studies classical and reciprocal polar varieties, their degrees, and their applications to Euclidean and polyhedral distance optimization. It unifies several definitions of polar varieties, it introduces higher order osculating geometry. Defined higher-order polyhedral distance loci using it.
Polar variety of the twisted cubic with respect to line.
Higher-order polyhedral distance loci for the twisted cubic
Distance Optimization Questions
November 2025–January 2026 · with Nidhi Kaihnsa
I studied Euclidean and polyhedral distance optimization on real algebraic varieties, through a literature review that built my foundation in metric algebraic geometry. The project connected symbolic computations with numerical methods for finding nearest points on varieties.
I implemented algorithms in Julia using OSCAR and HomotopyContinuation.jl, and studied Voronoi diagrams for the corresponding norms.
Positive solutions of sparse polynomial systems
September–October 2025 · with Elisenda Feliu
I studied criteria for the existence and number of positive real solutions of sparse polynomial systems. Using Gale duality, I explored how the structure of a system yields certificates for the existence of a positive solution, and how sign variations give sharp upper bounds for systems supported on circuits.
I implemented results from the literature in OSCAR in Julia to check the criteria on examples. The project brought together real algebraic geometry, combinatorial sign conditions, and computational methods.
Geometric Combinatorics and Fitness Landscape Model
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Geometric combinatorics and polynomial posets, with Muhittin Mungan (2021–2023). Linear extensions subject to algebraic constraints, using polyhedral methods and linear programming.
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