Data Loci course

Subscription
Subscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-sodomaco-s26-join@mis.mpg.de

---

Next lectures
27.04.2026, 10:00 (G3 10 (Lecture hall))
04.05.2026, 10:00 (G3 10 (Lecture hall))
07.05.2026, 10:00 (G3 10 (Lecture hall))
18.05.2026, 10:00 (G3 10 (Lecture hall))
21.05.2026, 10:00 (G3 10 (Lecture hall))
28.05.2026, 10:00 (G3 10 (Lecture hall))

---

Abstract

Many optimization problems can be represented by systems of parametric polynomial equations. The choice of parameters influences the geometry of the solutions associated with these polynomial systems. A sufficiently "generic'' or "random'' selection of parameters often results in solution sets that exhibit expected properties, such as the expected dimension or cardinality. In contrast, non-generic parameters give rise to algebraic subsets known as Data Loci. Each data locus is formed by imposing additional conditions on the solution sets.

In this course, we will provide an overview of the most relevant types of data loci in algebraic optimization, with a particular emphasis on data loci in distance optimization - a related field referred to as Metric Algebraic Geometry - and on the computation of Nash equilibria in Game Theory.

Each lecture will contain several examples and computations in Macaulay2 and Julia.

Lectures:

1) April 09 (10:00-12:00, G310): The intersection theory you need: polar classes and projective duality

2) April 13 (15:00-17:00, G3 10): Counting critical points

3) April 20 (10:00-12:00, G310): The first data loci: evolutes and distance discriminants

4) April 27 (10:00-12:00, G310): Offsets and distance polynomials

5) May 04 (10:00-12:00, G310): Relative polar classes and conditional data loci

6) May 07 (10:00-12:00, G310): Kalman varieties (CC equations meet RR equations)

7) May 18 (10:00-12:00, G310): Higher-order polar classes and higher-order distance loci

8) May 21 (10:00-12:00, G310): Data loci in Game Theory 1: Nash discriminants and resultants

9) May 28 (10:00-12:00, G310): Data loci in Game Theory 2: Nash Loci