Erin Connelly

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20172025

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math.AG2025

Critical Points of Degenerate Metrics on Algebraic Varieties: A Tale of Overparametrization

Giovanni Luca Marchetti, Erin Connelly, Paul Breiding +1

We study the critical points over an algebraic variety of an optimization problem defined by a quadratic objective that is degenerate. This scenario arises in machine learning when…

math.AG2024

Geometric Interpretations of Compatibility for Fundamental Matrices

Erin Connelly, Felix Rydell

In recent work, algebraic computational software was used to provide the exact algebraic conditions under which a sixtuple ${F^{ij}}$ of fundamental matrices, corresponding to $4…

math.AG2023

Lines, Quadrics, and Cremona Transformations in Two-View Geometry

Erin Connelly, Rekha R. Thomas, Cynthia Vinzant

Given $7 \leq k \leq 9$ points $(x_{i}, y_{i}) \in P^{2} \times P^{2}$ , we characterize rank deficiency of the $k \times 9$ matrix $Z_{k}$ with rows $x_i^\top \otimes y_i^\t…

math.AG2023

The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products

Erin Connelly, Sameer Agarwal, Alperen Ergur +1

Given $k \leq 6$ points $(x_{i}, y_{i}) \in P^{2} \times P^{2}$ , we characterize rank deficiency of the $k \times 9$ matrix $Z_{k}$ with rows $x_{i}^{⊤} \otimes y_{i}^{⊤}$ in…