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22-26 juin 2015

Centre Paul-Langevin AUSSOIS

Europe/Paris timezone

In honor of Bernard Teissier's 70th birthday

- teissier2015@listes.math.cnrs.fr

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## Liste des présentations

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contributions
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Session:
Afternoon session

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 the
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Présenté par Mr. Askold KHOVANSKII
on
22 juin 2015
à
15:15

Session:
Morning session

We prove that if f is a positive C^2 function on a convex compact set X then it becomes strongly convex when multiplied by (1+|x|^2)^N with N large enough. For f polynomial we give an explicit estimate for N, which depends on the size of the coefficients of f and on the lower bound of f on X. As an application of our convexification method we propose an algorithm which for a given polynomia
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Présenté par Mr. Krzysztof KURDYKA

Session:
Morning session

I will begin by explaining motivations from mirror symmetry. Then I will present some new results concerning tropical geometry and non-archimedean geometry. As an application, I will talk about the enumeration of curves in log Calabi-Yau surfaces. An explicit computation for a del Pezzo surface will be presented in detail. The enumeration is related to the notion of broken lines in the works by Gr
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Présenté par Mr. Tony Yue YU

Session:
Morning session

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.

Présenté par Mr. Terence GAFFNEY
on
22 juin 2015
à
10:00

Session:
Morning session

I will discuss a surprising relation between the free divisors in the complex projective plane (and a slight extension of them called the nearly free divisors) and the rational cuspidal curves. A number of conjectures express this relation and some of them are proved in special cases.

Présenté par Mr. Alexandru DIMCA

Session:
Morning session

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.

Présenté par Mr. Steven Dale CUTKOSKY
on
22 juin 2015
à
11:30

Session:
Afternoon session

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.

Présenté par Mr. June HUH
on
22 juin 2015
à
14:00

Session:
Afternoon session

Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a manifold called the link of A. The link has a natural hyperplane distribution called a contact structure. If the singularity is numerically Q-Gorenstein then we can assign an invariant of our singularity called the
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Présenté par Mr. Mark MCLEAN

Session:
Morning session

Many non-Noetherian rings and topological spaces equipped with the action of a large group or monoid are in fact Noetherian up to that action. This phenomenon is responsible for several recent finiteness results in algebraic geometry and commutative algebra. I will discuss examples concerning certain infinite-dimensional toric varieties with an action of the infinite symmetric group, and concerni
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Présenté par Mr. Jan DRAISMA

Session:
Afternoon session

I will discuss Lipschitz stratification from a nonarchimedean point of view and thereby show that it exists for definable sets, not necessarily bounded, in any polynomial-bounded o-minimal field structure. Unlike the previous approaches in the literature, our method bypasses resolution of singularities and Weierstrass preparation altogether; it transfers the situation to a nonarchimedean model, wh
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Présenté par Mr. Yimu YIN

Session:
Afternoon session

Minimal log discrepancies are invariants of singularities defined using the divisorial valuations centered at one point. They play an important role in birational geometry and several questions about them are widely open. In this talk I will give an introduction to this circle of ideas, I will discuss some of these questions and some partial results.

Présenté par Mr. Mircea MUSTATA

Session:
Morning session

We study the implicit equations defining the image and the graph of rational
maps between projective spaces, under the hypothesis that the base locus
has codimension at most three and is defined by a Gorenstein ideal. We provide
degree bounds for these implicit equations, and we describe them explicitly if
the syzygies of the Gorenstein ideal are all linear. This is joint work with Andy
Kusti
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Présenté par Mr. Bernd ULRICH

Session:
Morning session

Motivated by mathematical physics, Block and Göttsche have defined "quantized" versions of Mikhalkin's multiplicities for tropical curves. In joint work with Sam Payne and Franziska Schroeter, we propose a geometric interpretation of these invariants as chi_y genera of semi-algebraic analytic domains over the field of Puiseux series. In order to define and compute these chi_y genera, we use the t
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Présenté par Mr. Johannes NICAISE

Session:
Morning session

De Jong's famous theorem states that any integral variety can be resolved
by an alteration. Recently Gabber strengthened this by proving that for any
fixed prime l not equal to the characteristic, the alteration
can be taken of degree prime to l. In my talk I will tell about Gabber's
results and some newer progress on this topic.

Présenté par Mr. Mikael TEMKIN

Session:
Afternoon session

In the spirit of famous papers by Pila & Bombieri and Pila & Wilkie, I will explain how to bound the number
of rational points, with respect to their height, in various kinds of sets, such as algebraic varieties of a given degree,
transcendental sets definable in some o-minimal (or even not o-minimal) structure over the real field, and, after joint work
with R. Cluckers and F. Loeser, also def
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Présenté par Mr. Georges COMTE