Erin Connelly

collaborators

4 papers

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

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.AG2024

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…

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…