Programme
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Planned courses:
- Antoine Ducros. Berkovich spaces.
- Charles Favre. Riemann-Zariski spaces.
- Martin Hils. Introduction to model theory.
- Ehud Hrushovski. Constructible sets over valued fields.
- Franz-Viktor Kuhlmann. Ramification, valuation and implicit functions.
- Hussein Mourtada. Arc spaces and valuations.
- Sam Payne. Berkovich and tropical.
- Ana Reguera. Arc spaces and resolution.
- Thomas Scanlon. Introduction to Motivic Integration.
- Joris van der Hoeven. Transseries.
Schedule of the first week. Segovia.
- 9:15 - 10:00. REGISTRATION.
- 10:00 - 11:30. DUCROS. Introduction to Berkovich analytic spaces.
- 11:30 - 12:00. COFFEE
- 12:00 - 13:00. BERKOVICH. F1-geometry
- 13:00 - 15:20. LUNCH
- 15:20 - 16:50. REGUERA. Arc spaces and resolutions.
- 16:50 - 17:15. COFFEE
- 17:15 - 18:45. KUHLMANN. Ramification.
- 9:15 - 10:45. FAVRE. Riemann-Zariski spaces.
- 10:45 - 11:10 COFFEE
- 11:10 - 12:40 REGUERA. Arc spaces and resolutions.
- 12:40 - 13:20 SARUSSI. Quasi-valuations extending a valuation.
- 13:20 - 15:20. LUNCH
- 15:20 - 16:50. DUCROS. Introduction to Berkovich analytic spaces.
- 16:50 - 17:15. COFFEE
- 17:15 - 18:45. HILS. Introduction to model theory.
- 9:15 - 10:45. FAVRE. Riemann-Zariski spaces.
- 10:45 - 11:10 COFFEE
- 11:10 - 12:40 HILS. Introduction to model theory.
- 12:40 - 13:20 CHERNIKOV. Model-theoretic weight in some valued fields.
- 13:20 - 15:20. LUNCH
- 15:20 - 16:50. SCANLON. Introduction to Motivic Integration.
- 16:50 - 17:15. COFFEE
- 17:15 - 18:45. PILTANT. Relative Local Uniformization in Function Fields.
- 9:15 - 10:45. MOURTADA. Arc spaces and valuations.
- 10:45 - 11:15 COFFEE
- 11:15 - 12:15 GUSEIN-ZADE. On equivariant versions of Poincaré series of filtrations and monodromy zeta functions.
- 12:15 - 13:00 PERUGINELLI. Good reduction for endomorphisms of the projective line.
- 13:00 - 15:20. LUNCH
- 15:20 - 16:50. SCANLON. Introduction to Motivic Integration.
- 16:50 - 17:15. COFFEE
- 17:15 - 18:45. VAN DER HOEVEN. Transserial Hardy fields.
- 9:15 - 10:45. MOURTADA. Arc spaces and valuations.
- 10:45 - 11:10 COFFEE
- 11:10 - 11:55 FABRI. Domains having a unique Kronecker function ring.
- 11:55 - 12:40 FINOCCHIARO. The ultrafilter topology on spaces of valuation domains and applications.
- 12:40 - 13:20 YUROVA. Ergodicity of the dynamical systems on 2-adic spheres.
- 13:20 - 15:20. LUNCH
- 15:20 - 16:50. F. V. KUHLMANN. Ultrametrics and Implicit Function Theorems.
- 16:50 - 17:15. COFFEE
- 17:15 - 18:45. VAN DER HOEVEN. Transserial Hardy fields.
Saturday 23th. An excursion is planned, starting from Segovia and
ending at El Escorial.
Schedule of the second week. El Escorial.
- 9:30 - 11:00. HRUSHOVSKI. Constructible sets over valued fields.
- 11:00 - 11:30 COFFEE
- 11:30 - 12:30 KNEBUSCH. Spaces of valuations.
- 12:30 - 13:30 GONDARD. On R-places and related topics.
- 13:30 - 15:30. LUNCH
- 15:30 - 16:30. HARBATER. Patching and local-global principles.
- 16:30 - 17:00. COFFEE
- 17:00 - 18:00. K. KUHLMANN. Spaces of R-places.
- 18:00 - 19:00. PAL. Multiplicative Valued Difference Fields.
- 19:15 - 20:00. ESTEROV. Corner loci of piecewise polynomials, and polynomially weighted tropical varieties.
- 9:30 - 11:00. HRUSHOVSKI. A model theoretic view of non-archimedean topology.
- 11:00 - 11:30 COFFEE
- 11:30 - 12:30 CLUCKERS. On transfer principles for motivic exponential integrals.
- 12:30 - 13:30 BUIUM. Differential calculus with integers.
- 13:30 - 15:30. LUNCH
- 15:30 - 16:30. POP. Large Fields: Old and New.
- 16:30 - 17:00. COFFEE
- 17:00 - 18:00. VAQUIE. Extension of valuation.
- 18:00 - 19:30. PAYNE. Nonarchimedean geometry, tropicalization, and metrics on curves.
- 19:30 - 20:15. FEHM. Hilbertian fields and families of valuations.
- 9:30 - 10:30. ARTAL. Pencils, dicriticals and curvettes.
- 10:30 - 11:30 MONTSERRAT. Algebraic foliations and dicritical valuations.
- 11:30 - 12:00 COFFEE
- 12:00 - 13:00 ABHYANKAR. Dicritical divisors of pencils.
- 13:00 - 13:45 COSSART. Dicritical divisors (after S. Abhyankar and I. Luengo).
- 13:45 - 15:30. LUNCH
- FREE AFTERNOON
- 9:30 - 10:30. CUTKOSKY. Semigroups of valuations dominating a Noetherian local ring.
- 10:30-11:30 SPIVAKOVSKY. Key polynomials, generalized Puiseux series and applications to local uniformization in arbitrary characteristic.
- 11:30-12:00 COFFEE
- 12:00-13:00 OLALLA. Extending a valuation centered in a local domain to the formal completion.
- 13:00-14:00 TEMKIN. Inseparable local uniformization.
- 14:00 - 16:00. LUNCH
- 16:00 - 17:00. VIRO. Valuations with complex values.
- 17:00 - 17:30. COFFEE
- 17:30 - 18:30. AZGIN. Extremal Valued Fields.
- 18:30 - 19:30. ZHUKOV. Approaches to ramification theory in the imperfect residue field case.
- 19:45 - 20:30. KHANDUJA. Some generalizations of Eisenstein-Schönemann Irreducibility Criterion.
- 9:30 - 10:30. MATUSINSKI. Hardy type derivations on generalized series fields.
- 10:30-11:30 YIN. Integration in certain o-minimal fields.
- 11:30-12:00 COFFEE
- 12:00-13:00 FERNANDEZ DE BOBADILLA. Nash problem for surfaces.
- 13:00-14:00 HALUPCZOK. Whitney stratifications in valued fields.
- 14:00 - 16:00. LUNCH
- 16:00 - 16:45. GRANJA. Real valuations on skew polynomial rings.
- 16:45 - 17:45. CAMPILLO. Valuations, multiindex filtrations and topology.
- 17:30 - - - - . CLOSING COFFEE