Mr Terence Gaffney (Northeastern University)
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.
Mr Steven Dale Cutkosky (University of Missouri)
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.
Mr June Huh (Princeton)
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.
Mr Askold Khovanskii (University of Toronto)
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...
Mrs María Pe Pereira (ICMAT, Madrid)
Mr Mark Spivakovsky (Univ. Toulouse)
Mr Jean Lorenceau (Ecole Normale Supérieure)
Mr Krzysztof Kurdyka (Université de Savoie)
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...
Mr Tony Yue Yu (IMJ - Paris)
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...
Mr Alexandru Dimca (Université de Nice-Sophia Antipolis)
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.
Mr Jean Petitot
Mr Patrick Popescu-Pampu (Université de Lille)
Mr Mark McLean (Stony Brook)
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...
Mr Jan Draisma (Technische Universiteit Eindhoven)
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...
Mr Yimu Yin (Sun Yat-Sun University)
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...
Mr Mircea Mustata (University of Michigan)
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.
Mr Bernd Ulrich (University of Purdue)
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...
Mr Johannes Nicaise (University of Leuven)
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...
Mr Mikael Temkin (The Hebrew University of Jerusalem)
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.
Mr Georges Comte (Université de Savoie - Chambéry)
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...