Spring 2023

MATH 270 001 - LEC 001

Advanced Topics Course in Mathematics

Metric Algebraic Geometry

Bernd Sturmfels

Jan 17, 2023 - May 05, 2023

Tu, Th

08:00 am - 09:29 am

Evans 891

Class #:19642

Units: 2

Instruction Mode: In-Person Instruction

Offered through Mathematics

Current Enrollment

Total Open Seats: 7

Enrolled: 8

Waitlisted: 0

Capacity: 15

Waitlist Max: 5

No Reserved Seats

Hours & Workload

1.5 hours of instructor presentation of course materials per week, and 4.5 hours of outside work hours per week.

Course Catalog Description

This course will give introductions to research-related topics in mathematics. The topics will vary from semester to semester.

How can we compute the distance from a point in 3-space to a given curve or surface? This question arises for many geometric shapes and in many contexts, notably in optimization and data science. Metric algebraic geometry studies real algebraic varieties, with focus on metric properties -- distances, volumes, angles, and curvature. The aim is to compute these quantities from defining polynomials. This 2-unit course offers an introduction to this field of research. Lectures by the instructor are supplemented by guest lectures and hands-on working sessions. Berkeley students will interact with participants from Germany and elsewhere.

Class Notes

Prerequisites: Basics of commutative algebra and algebraic geometry. Experience with computer algebra and numerical computing.

This course is for Graduate Students only.