Franz-Viktor Kuhlmann's
# Materials for recent courses

## Scientific English

Presentation 1: British vs American

Presentation 2: vocabulary

Presentation 3: spellchecker

Presentation 4: measures

Presentation 5: linking words

Presentation 6: conjuncts

Presentation 7: use of "the", :a"

Presentation 8: use of "in", "on"

Presentation 9: more vocabulary

Presentation 10: similar words

Presentation 11: avoid "get"

Presentation 12: irregular verbs

Presentation 13: punctuation

Presentation 14: pronunciation

Presentation 15: guidelines

Presentation 16: avoiding vagueness

Presentation 17: language

Presentation 18: mathematics content

Presentation 19: structure

Presentation 20: speech

Presentation 21: presentations

## Lecture series on valued function fields and the defect

This is a small course with eight lectures designed for graduate students at the University of Padova.

Here you can find the presentations given in the lectures:
Lecture I: Introduction - local uniformization - ramification
theory - elimination of ramification

Lecture II: Lemma of Ostrowski - the defect - examples of
defect extensions - defectless fields - tame fields

Lecture III: Valued function fields - valuations on rational
function fields - the Abhyankar inequality - Abhyankar valuations - immediate
extensions

Lecture IV: The Generalized Stability Theorem and
applications - reduction steps in its proof

Lecture V: Proof of the Generalized Stability Theorem:
reduction to extensions of prime degree and normal forms

Lecture VI: function fields with non-Abhyankar valuations -
alteration - the Henselian Rationality Theorem - first elements of the proof -
separable and inseparable local uniformization

Lecture VII: proof of the Henselian Rationality Theorem,
normal forms for Galois extensions of degree p, relative approximation degree,
reduction steps - embedding theorem for tame fields - application to the model theory
of tame fields

Lecture VIII: Zariski spaces of places of function fields - Zariski and patch topology - dense subsets - rational places - large fields.

*Last update: April 23, 2021*