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Course Announcement - Spring 2023

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Math 270: Metric Algebraic Geometry

**Contact:** bernd@berkeley.edu, bernd@mis.mpg.de

**Office hours:** e-mail me to set up an appointment.

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Lecture times: Tuesdays, 8:10-9:30

**
First Day: Tuesday, January 17**

Last Day: Tuesday, March 21

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

**Description:**
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. Our aim is to compute these quantities from defining polynomials.
The term ``metric algebraic geometry'' was coined in 2021 by the
PhD thesis of
Maddie Weinstein.

**Format:**
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.

**Course materials:**
Notes are posted below. These are to be developed further for the
Oberwolfach seminar

which will be led by
Paul Breiding,
Kathlén Kohn and myself during
the week of May 28 - June 3, 2023.

**Grading:**
Regular attendence is expected.
Active participation and written work are encouraged.

This is a research-oriented course:
You set your own goals; you decide how well you reached them.

** WEEKLY SCHEDULE: **

Jan 17: Critical Equations

Jan 24:
Svala Sverrisdóttir:
HomotopyContinuation.jl

Jan 31: Wasserstein Distance

Feb 7: Voronoi Cells

Feb 14: Maximum Likelihood

Feb 21: Kathlén Kohn:
Polar Classes

Feb 23: Tropical Geometry Methods (Thursday in 891 Evans!)

Feb 28: Maddie Weinstein: Curvature, Bottlenecks and Reach

Mar 2: Questions and Answers (Thursday in 891 Evans!)

Mar 7: Paul Breiding: Tensors

Mar 14: Volumes (starts 16:10 in Europe)

Mar 21: Vahid Shahverdi: Machine Learning (starts 16:10 in Europe)