Conference: "SINGULAR LANDSCAPES"

Europe/Paris
Centre Paul-Langevin AUSSOIS

Centre Paul-Langevin AUSSOIS

Centre Paul-Langevin 24, rue du Coin 73500 Aussois
Charles Favre, Evelia Garcia Barroso (Universidad de la Laguna), Marine AMIER, Patrick Popescu-Pampu (Laboratoire Paul Painlevé), Pedro Gonzalez Pérez (ICMAT , Departamento de Álgebra)
Description
This international conference is aimed at exploring various aspects of the geometry of analytic singular spaces. We shall especially emphasize the delicate interplay between commutative algebra and topology, and try to present new point of views on these problems that arose recently (valuations, non-archimedean geometry). This will be the opportunity to celebrate the accomplishments of B. Teissier in which all these aspects were always delicately interwoven. We shall also dedicate several talks to interactions between singularity theory and neuroscience.

Registration are now closed. Please contact the organizers by email if you want to attend.
Poster
Program
Participants
  • Alejandro Melle-Hernández
  • Alexandru Dimca
  • Ana Belén de Felipe
  • Ana José Reguera López
  • Ann Lemahieu
  • Anne Frühbis Krüger
  • Anne Pichon
  • Aron Simis
  • Arpan Dutta
  • Arturo Enrique Giles Flores
  • Askold Khovanskii
  • Bernard Teissier
  • Bernd Schober
  • Bernd Ulrich
  • Camille Plenat
  • Carlos GALINDO
  • Castro-Jimenez Francisco-Jesus
  • Charles FAVRE
  • David Eisenbud
  • David Massey
  • David Trotman
  • Denis Cheniot
  • Dung Trang LÊ
  • Enrique Artal Bartolo
  • Evelia Rosa García Barroso
  • Francisco Monserrat
  • Franz Viktor Kuhlmann
  • François Loeser
  • Félix Delgado de la Mata
  • Georges COMTE
  • goulwen fichou
  • Guillaume Rond
  • Hema Srinivasan
  • Herwig Hauser
  • Hussein Mourtada
  • Ignacio Luengo
  • Jan Draisma
  • Jawad Snoussi
  • Jean Lorenceau
  • Jean PETITOT
  • Johannes Nicaise
  • José Manuel Aroca Hernández-Ros
  • José Seade
  • June Huh
  • Justin Chen
  • Kevin Langlois
  • Krzysztof Kurdyka
  • Lee McEwan
  • Luis Narváez Macarro
  • Manuel Gonzalez Villa
  • Marc Chaperon
  • Marc Chardin
  • Maria Pe Pereira
  • Mark McLean
  • Mark Spivakovsky
  • Marko Roczen
  • Matteo Ruggiero
  • Meral Tosun
  • Michael Lönne
  • Michael Temkin
  • Michel VAQUIE
  • Mircea Mustata
  • Monique Lejeune-Jalabert
  • Olivier Piltant
  • Patrick Popescu-Pampu
  • Pedro González Pérez
  • Quy Thuong Le
  • Razieh Ahmadian
  • Rita Rodríguez Vázquez
  • Roberto Castellini
  • Rosario González Dorrego
  • Santiago López de Medrano
  • Steven Dale Cutkosky
  • Tamas Laszlo
  • Terence Gaffney
  • Tony Yue YU
  • Wael Mahboub
  • Walter NEUMANN
  • Wim Veys
  • Yimu Yin
    • 09:30 10:00
      Welcome
    • 10:00 11:00
      Morning session: GAFFNEY: Families of isolated singularities and three inspirations from Bernard Teissier La Parrachée

      La Parrachée

      Centre Paul-Langevin AUSSOIS

      Centre Paul-Langevin 24, rue du Coin 73500 Aussois
      • 10:00
        Families of isolated singularities and three inspirations from Bernard Teissier 50m
        Part of Bernard Teisier¹s work is a substantial contribution to equisingularity theory. In this talk I will discuss three of the many inspirations his work has given me, and their role in my current approach to the equisingularity of isolated singularities. The talk will use determinantal singularities as an illustration of these ideas.
        Speaker: Mr Terence Gaffney (Northeastern University)
        Slides
    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:30
      Morning session: CUTKOSKY: Local monomialization of analytic maps La Parrachée

      La Parrachée

      Centre Paul-Langevin AUSSOIS

      Centre Paul-Langevin 24, rue du Coin 73500 Aussois
      • 11:30
        Local monomialization of analytic maps 50m
        We prove that germs of analytic maps of complex analytic varieties can be made monomial by sequences of local blow ups of nonsingular analytic subvarieties in the domain and target along an arbitrary étoile. An étoile and the voûte étoilée is a generalization by Hironaka of valuations and the Zariski Riemann manifold to analytic spaces.
        Speaker: Mr Steven Dale Cutkosky (University of Missouri)
        Slides
    • 12:30 14:00
      Lunch break 1h 30m
    • 14:00 15:00
      Afternoon session: HUH: Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs La Parrachée

      La Parrachée

      Centre Paul-Langevin AUSSOIS

      Centre Paul-Langevin 24, rue du Coin 73500 Aussois
      • 14:00
        Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs 50m
        I will give an overview of a proof of a conjecture of Read that the coefficients of the chromatic polynomial of any graph form a unimodal sequence. There are two main ingredients in the proof, both coming from works of Bernard Teissier: The first is the idealistic Bertini for sectional Milnor numbers, and the second is the isoperimetric inequality for mixed multiplicities of ideals.
        Speaker: Mr June Huh (Princeton)
        Slides
    • 15:15 16:15
      Afternoon session: KHOVANSKII: Algebraic geometry, theory of singularities, and convex geometry La Parrachée

      La Parrachée

      Centre Paul-Langevin AUSSOIS

      Centre Paul-Langevin 24, rue du Coin 73500 Aussois
      • 15:15
        Algebraic geometry, theory of singularities, and convex geometry 50m
        I will review some results which relate these areas of mathematics. Newton polyhedra connect algebraic geometry and the theory of singularities to the geometry of convex polyhedra. This connection is useful in both direc- tions. On the one hand, explicit answers are given to problems of algebra and the theory of singularities in terms of the geometry of polyhedra. On the other hand, algebraic theorems of general character (like the Hirzebruch–Riemann–Roch theorem) give significant information about the geometry of polyhedra. In this way one obtains, for example, a multidimensional generalization of the classical one-dimensional Euler–Mclaurin formula. Combinatorics related to the Newton polyhedra theory allows to prove that in hyperbolic space of high dimension there do not exist discrete groups generated by reflections with fundamental polyhedron of finite volume (it was a longstanding conjecture). The theory of Newton–Okounkov bodies relates algebra, singularities and geom- etry outside the framework of toric geometry. This relationship is useful in many directions. For algebraic geometry it provides elementary proofs of intersection- theoretic analogues of the geometric Alexandrov–Fenchel inequalities and far-reach- ing generalizations of the Fujita approximation theorem. The local version of the theory provides a new proof of the famous Teissier’s inequalities for the multiplici- ties of primary ideals in a local ring. In geometry it suggests a transparent analog of Alexandrov–Fenchel inequality for coconvex bodies.
        Speaker: Mr Askold Khovanskii (University of Toronto)
        Slides
    • 16:30 17:00
      Coffee break 30m
    • 17:00 18:00
      Specific talk: POPESCU-PAMPU: How Teissier mixed multiplicities La Parrachée

      La Parrachée

      Centre Paul-Langevin AUSSOIS

      Centre Paul-Langevin 24, rue du Coin 73500 Aussois
    • 09:30 10:30
      Morning session: YU: Enumeration of curves via non-archimedean geometry
    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Morning session: NICAISE: Refined curve counting and Hrushovski-Kazhdan motivic integration
    • 12:30 14:00
      Lunch break 1h 30m
    • 14:00 15:00
      Afternoon session: ULRICH : Rees algebras of codimension three Gorenstein ideals
    • 15:15 16:15
      Afternoon session: YIN: Non-Archimedean Lipschitz stratification
    • 16:15 16:45
      Coffee break 30m
    • 16:45 17:45
      Afternoon session: PE PEREIRA: About the arc space of C2 and adjacencies of plane curves.
    • 09:30 10:30
      Neuroscience and Singularity theory: LORENCEAU: Continuities, discontinuities and singularities in Visual Perception
    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Neuroscience and Singularity theory: PETITOT: Geometry of some functional architectures of vision
    • 13:30 16:50
      Free afternoon 3h 20m
    • 09:30 10:30
      Morning session: DRAISMA: Noetherianity up to symmetry
    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Morning session: DIMCA: Free divisors and rational cuspidal curves in the plane
    • 12:30 14:00
      Lunch break 1h 30m
    • 14:00 15:00
      Afternoon session: MUSTATA: On some questions about valuations and minimal log discrepancies
    • 15:15 16:15
      Afternoon session: McLEAN: Minimal Log Discrepancy of Isolated Singularities and Reeb Orbits.
    • 16:15 16:45
      Coffee break 30m
    • 17:00 18:00
      Specific talk: SPIVAKOVSKY: An overview of Teissier's works on valuations
    • 09:00 10:00
      Morning session: KURDYKA: Convexifying positive polynomials and a proximity algorithm
    • 10:00 10:30
      Coffee break 30m
    • 10:30 11:30
      Morning session: TEMKIN: Resolution by alterations
    • 11:30 12:30
      Morning session: COMTE: Sets with few rational points
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