Commutative Algebra and Algebraic Geometry
Tuesdays, 3:45-6pm in Evans 939
Organizer: David Eisenbud
Date: Oct 16
3:45: Anurag Singh: The F-pure threshold of a Calabi-Yau hypersurface
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.
5:00 Jose Rodriguez: Maximum Likelihood for Matrices with Rank Constraints
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.