### Seminar "Euklid trifft Bézout" 2023/2024

### - Wir beginnen am 24. Oktober/We start on the 24th of October -

Wir treffen uns im Raum S08 dienstags 16-18 Uhr

- SEMINARPROGRAMM -

### Einige Referenzen

1. Euclid Meets Bézout: Intersecting Algebraic Plane Curves with the Euclidean Algorithm, Jan Hilmar and Chris Smyth (2010), Artikel

2. A proof of Bézout's theorem using the Euclidean algorithm, R. P. Hulst (2011), Bachelor thesis

3. Plane Algebraic Curves, Andreas Gathmann (2018), Class Notes TU Kaiserslautern

4. Algebraic curves: An Introduction to Algebraic Geometry, W. Fulton (2008)

### May-June 2023 School - Involutions in Gauge theory and in algebraic geometry - Nantes

Exercise sheet 1th June

### 2023 - Real algebraic geometry- Universität Tübingen

### Some references

1. Real Algebraic Varieties, F. Mangolte

2. Real Algebraic Surfaces, R. Silhol

3. Real Algebraic and Semi-algebraic Sets, R. Benedetti, Jean-Jacques Risler

4. Topological properties of real algebraic varieties: du côté de chez Rokhlin, A.Degtyarev, V.Kharlamov

5. O. Viro notes

6. Algebraic Topology, A. Hatcher

We meet on Tuesday 14:15-16 Room S09 (C-Bau [Mathe/Physik]) and Wednesday 12:15-13:45 and 14-15 Room C5H41 Seminarraum S08 (C-Bau [Mathe/Physik]).

15th-19th of May

(recall that from the 29th of May to the 2nd of June the university is closed)

5th-9th of June

26th-30th of June

### Handwritten notes

Notes RAG till now

Complementary material presented in class:

Introduction singular homology

Some applications of Mayer Vietoris

Some examples, relative singular homology, excision, Poincaré duality

### Pdfs of the exercise sessions

### 2022/2023 - Algebraic curves- Universität Tübingen

Here the link to the web page of the Algebraic Curves course by Daniele Agostini of the Universität Tübingen

### 2022/2023 - Algebraic number theory - Universität Tübingen

Here the link to the web page of the Algebraic number theory course by Anton Deitmar of the Universität Tübingen

### 2022 - Geometric group theory- Universität Tübingen

Here the link to the web page of the Geometric Group Theory course by Hannah Markwig of the Universität Tübingen

### Book references

Geometric Group Theory by Clara Löh

### We meet on Wednesday from 16:15 to 17:45 in N16 Bau C

### Pdfs of the exercise sessions

Blatt1.pdf (German), ex1.pdf (English)
Blatt2.pdf (German), ex2.pdf (English)
Blatt3.pdf (German), ex3.pdf (English)
Blatt4.pdf (German), ex4.pdf (English)
Blatt5.pdf (German), ex5.pdf (English)
Blatt6.pdf (German), ex6.pdf (English)
Blatt7.pdf (German), ex7.pdf (English)
Blatt8.pdf (German), ex8.pdf (English)
Blatt9.pdf (German), ex9.pdf (English)
Blatt10.pdf (German), ex10.pdf (English)
Blatt11.pdf (German), ex11.pdf (English)
Blatt12.pdf (German), ex12.pdf (English)
### 2021/2022 - Algebraic Curves and Riemann surfaces - Universität Tübingen

Here the link to the web page of the Algebraic Curves and Riemann surfaces course by Hannah Markwig of the Universität Tübingen

### Book references

Arbarello, Cornalba, Griffiths,Harris: Geometry of Algebraic Curves

Cavalieri, Miles: Algebraic Curves and Riemann surfaces, a first course in Hurwitz theory

Miranda: Algebraic Curves

Moreover the class is in Hybrid format. The link to follow the class from home is the same as that to follow the course.
### Pdfs of the exercise sheets 1 to 13

ex1-13.pdf
### Pdfs of the exercise sessions 1 to 13

es1-13.pdf
### 2021 - Toric Geometry - Universität Tübingen

Here the link to the web page of the Toric Geometry course by Hannah Markwig of the Universität Tübingen

### Book references

Cox, Little, Schenck, Toric varieties

Fulton, Toric geometry

### Pdfs of the exercise sessions

Exercise sessions 1-13, Toric Geometry,
All_ex1_13.zip