DescriptionArtin Approximation concerns the solutions of algebraic or analytic equations in power series rings. Artin's celebrated theorem asserts that if a system f(x,y) = 0 admits a formal solution y(x), then it also admits a convergent solution y'(x). This result has seen many applications and has meanwhile obtained a fixed place in the mathematical landscape. Artin's proof is a very tricky combination of various reduction steps, but it just ensures the existence of one convergent solution. Later results of Ploski, Popescu, Spivakovsky, Grinberg, Kazhdan, Drinfeld and others aim at understanding the structure of the whole solution set nearby a given formal solution. As such, one is confronted with studying the infinite dimensional variety formed by all solutions. The study of these kind of solutions sets appears in different situations : in the study of arc spaces as be proposed by Nash, in non-archimedean analytic geometry or in tropical geometry for instance. The conference proposes to bring these different viewpoints together and to design a route map for further research and understanding. It addresses people from commutative algebra, algebraic and analytic geometry, differential geometry, complex analysis, and functional analysis. Also post-docs and graduate students are welcome -- they should be offered a panorama of fascinating problems to investigate. |
## Scientific Committee
- Javier Fernández de Bobadilla (Madrid)
- Herwig Hauser (Vienna)
- Melvin Hochster (Michigan)
- Leonard Lipshitz (Purdue)
- François Loeser (Paris)
## Organizing Committee
- Herwig Hauser (Vienna)
- Guillaume Rond (Marseille)
## Speakers
- Janusz Adamus (London - Ontario)
On relative Nash approximation of complex analytic sets (pdf)- Matthias Aschenbrenner (Los Angeles)
The algebra and model theory of transseries (pdf)- Raf Cluckers (CNRS Lille/Leuven)
Pfaffian functions: real and non-archimedean, and an application to counting rational points (pdf)- Jan Draisma (Eindhoven)
Stabilisation in algebraic geometry (pdf)- Jack Hall (Canberra)
Tannaka duality and formal glueings (pdf)- Shuzo Izumi (Osaka)
Zero-estimates from geometric point of view (pdf)- Pierre Lairez (Berlin)
Diagonals of rational functions (pdf)- Leonard Lipshitz (Purdue)
Artin Approximation, recursion relations, decidability and definability in local rings and fields (pdf)- Henri Lombardi (Franche-Comté)
Constructive steps towards Popescu desingularization theorem (pdf)- Nordine Mir (Doha)
Artin approximation and Cauchy-Riemann geometry (pdf)- Laurent Moret-Bailly (Rennes)
Topological aspects of strong approximation: the case of torsors over valued fields (pdf)- Hussein Mourtada (Paris Diderot)
Arc spaces and Rogers-Ramanujan identities (pdf)- Maria Pé Pereira (Madrid)
About the arc space of C2 and adjacencies of plane curves (tba)- Dorin Popescu (Bucarest)
On the regular local rings (pdf)- Ana Reguera (Valladolid)
How to obtain finiteness properties in the infinite dimensional scheme of the space of arcs (pdf)- David Rydh (Stockholm)
Equivariant Artin algebraization (pdf)- Hans Schoutens (New York)
The synergy between Artin Approximation and Ultraproducts (pdf)- Julien Sebag (Rennes)
The Grothendieck ring of varieties (pdf)- Mark Spivakovsky (CNRS Toulouse)
Popescu's theorem and (nested) Artin approximation (pdf)- Sebastian Woblistin (Vienna)
Geometry of analytic subset of power series spaces (pdf) |