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ETH Zurich - D-MATH - Education - Bachelor - Student Seminars - Herbstsemester 2011 - p-adic Analysis Compared with Real

p-adic Analysis Compared with Real

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Organizers	Prof. Özlem Imamoglu, Prof. Alessandra Iozzi
Assistant	Pascal Rolli
Place	HG G 19.1
Time	Tuesday, 15:15-17:00
First meeting	Oct 4, 2011
Prerequisites	Analysis I/II, Topology

Schedule of talks

Date	Speakers	Topic	References
Oct 4		Organizational meeting
Oct 11	Felix Hensel Waltraud Lederle Simone Montemezzani	Completion of normed fields. Non-archimedean norms. p-adic norms. Definition of Q_p. [Report]	[K] §1.2-1.4 [S] §8
Oct 18	Ivo Aschwanden Adrian Clough Alexandros Grosdos Koutsoumpelias	Equivalence of norms. Ostrowski's theorem. The product formula. [Report]	[K] §1.9 [S] §9-10
Oct 25	Claudio Hüni Kathrin Naef Daniel Schmitter	Definition of Z_p using p-adic expansions. Arithmetic in Z_p. Definition of Z_p as an inverse limit. Q_p as the fraction field of Z_p. [Report]	[K] §1.4-1.6 [R] §1.1.1-1.1.3, §1.5.1
Nov 1st	Patrik Lengacher Linda Raabe Nicolas Wider	Hensel's lemma. Algebraic properties of Z_p and Q_p. Local-to-global for squares. [Report]	[K] §1.7-1.9 [R] §1.1.4-1.1.6
Nov 8	Giorgio Barozzi Esther Röder Samuel Trautwein	Topological properties of Z_p and Q_p. Euclidean models. [Report]	[K] §2.1-2.3 [R] §1.5.6
Nov 15 (in G19.2)	Hannah Hutter May Szedlak Philipp Wirth	Convergence of sequences and series. Power series. Strassman's theorem. p-adic logarithm and exponential. [Report]	[K] §3.1-3.6
Nov 22	Ciocan Nicolae Stephan Tornier	p-adic functions. Locally constant functions. Differentiability. [Report]	[K] §4.1-4.4
Nov 29	Nina Otter Berke Topacogullari	Antiderivatives. Dieudonné's theorem. [Report]	[S] §30
Dec 6	Jan Dumke Vladimir Serbinenko Raphael Steiner	Interpolation. Mahler series for continuous functions (and possibly for Lipschitz and differentiable functions). [Report]	[K] §4.6 [S] §50-53
Dec 13		Additional meeting, if necessary

Literature

Katok: p-adic Analysis Compared with Real. ISBN 978-0821842201
Robert: A Course in p-adic Analysis. ISBN 978-1441931504
Schikhof: Ultrametric Calculus. ISBN 978-0521032872 (available online)

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