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## General Information

- Lecture: 2h, 5 LP
- official name: "Modul Algebra F5: Fortgeschrittene Themen der Algebra"

This course can serve as a preparation for the anticipated Thematic Einstein Semester Varieties, Polyhedra, Computation* *during the winter term 2019/20.

## News

**The last lecture will be on 4**^{th}July.- There will be NO lecture on 20
^{th}June. The REPLACEMENT lecture is on Wednesday, 26^{th}June at 16:15^{th}June takes place as usual.) - There will be NO lecture on 6
^{th}June. The REPLACEMENT lecture is on Wednesday, 5^{th}June at 16:15 in room MA 316. - There will be NO lecture on 30
^{th}May due to holiday (Christi Himmelfahrt).

## Schedule

Type | Day | Hours | Room | Lecturer |
---|---|---|---|---|

Lecture | Thursday | 16^{15}-17^{45} | MA 316 | Prof. Dr. Peter Bürgisser |

## Summary

Bezout's Theorem is a fundamental result of algebraic geometry. There are important extensions to polynomial system with few terms (fewnomials) that build a bridge to convex geometry (toric varieties, Newton polytopes, mixed volume). The goal of the lecture is to prove and discuss these results from different angles. We shall mainly work over the complex numbers and rely also on tools from differential geometry or integral geometry, that will be devoloped in the lecture.

## Literature

- Peter Bürgisser and Felipe Cucker.
*Condition: The Geometry of Numerical Algorithms.*Springer 2013. - Gregorio Malajovich.
*Nonlinear Equations*. Impa 2011.

Available as pdf under the following link - Frank Sottile.
*Real Solutions to Equations From Geometry.*University Lecture Series volume 57, AMS, 2011.

The book by Sottile is available as **e-book**. It has been licensed by the TU Berlin last year. Unfortunately, this information is not yet visible in Primo. Here is the legal link to the e-book: http://www.ams.org/books/ulect/057/ulect057.pdf

There is also an arXiv version with ID number 0609829.

**Semesterapparat:** We created for each of the lectures "Condition" and "Variations on Bezout's Theorem" a so called Semesterapparat. This ensures that some of the proposed books are always present for study in the mathematical library.