# Random Algebraic Geometry

**Lecturer:**Paul Breiding**Date:**Tuesdays, 11:15-12:45**Room:**Leipzig University, SG 2-14**Keywords:**Algebraic Geometry, Probability, Expected Counting Problems, Average Topology**Prerequisites:**Basic understanding of algebraic and differential geometry and probability**Remarks:**Website of the course: https://pbrdng.github.io/rag.html

## Abstract

This course will deal with the basic problem of understanding the structure (e.g. the geometry and topology) of the set of solutions of real polynomial equations with random coefficients. The simplest case of interest is the count of the number of real zeroes of a random univariate polynomial whose coefficients are Gaussian random variabl2s – this problem was pioneered by Kac in the 1940s. More generally algebraic geometers might be interested, for example, in the number of components of a random real plane curve, or in the expected number of real solutions of more advanced counting problems. I will present the basic techniques for attacking this type of questions, trying to emphasize the connections of classical algebraic geometry with random matrix theory and random ﬁelds.To keep informed about changes to this lecture subscribe to lecture mailinglist

### Important information

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## Regular lectures: Winter semester 2021/2022

**Symmetry enriched fractionalization in quantum matter with emergent Z_2 and U(1) gauge fields**- Inti Sodemann
- Wednesdays 2 pm, starting January 19, 2022, MPI MiS G3 10

**Foundations of Algebraic Geometry**- Daniele Agostini
- Monday, 11.15-12.45, MPI MiS A3 01
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**Randomness and partial differential equations**- Felix Otto
- Tuesday, 09.15-11.00; first lecture on October 26, 2021, MPI MiS E1 05 (Leibniz)
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**Random Algebraic Geometry**- Paul Breiding
- Tuesdays, 11:15-12:45, Leipzig University, SG 2-14
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**Introduction to Toric Geometry**- Simon Telen
- Wednesday, 10.00-12.00, MPI MiS G3 10
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**Spectra of tensors and their applications**- André Uschmajew, Raffaella Mulas
- 6-8 lectures, on Wednesdays 2 pm, starting November 3, 2021, MPI MiS G3 10
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**Bielefeld-Leipzig online seminar: Mathematics of Machine Learning**- Benjamin Gess
- tent. Wednesdays 16:15-17:45, Videobroadcast

**Algebraic operads, Koszul duality and Gröbner bases: an introduction**- Pedro Tamaroff
- Friday, 09.00-10.30, MPI MiS A3 01
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**Mathematical problems and structures of the neurosciences**- Juergen Jost
- Friday, 2-3.30 pm, MPI MiS E1 05 (Leibniz)
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**Reading course on quasi-ergodic measures and related topics**- Zachary Adams, Voluntary, Maximilian Engel
- Fridays, 14:00-15:30 on October 22, 17:00-18:30 starting October 29, All lectures will be held online
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