UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 16, 2012

939 Evans Hall


3:45PM: The F-pure threshold of a Calabi-Yau hypersurface

Anurag Singh

The F-pure threshold is a numerical invariant of prime characteristic singularities. It constitutes an analogue of a numerical invariant for complex singularities---the log canonical threshold---that measures local integrability. We will discuss, in detail, the calculation of F-pure thresholds of elliptic curves, and also indicate how this calculation extends to Calabi-Yau hypersurfaces. This is work in progress with Bhargav Bhatt.

5:00PM: Maximum Likelihood for Matrices with Rank Constraints

Jose Rodriguez

Maximum likelihood estimation is a fundamental computational task in statistics and it also involves some beautiful mathematics. We discuss this task for determinantal varieties (matrices with rank constraints) and show how numerical algebraic geometry can be used to maximize the likelihood function. Our computational results with the software Bertini led to surprising duality conjectures. This is joint work with Bernd Sturmfels and Jon Hauenstein.

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