M.
Terence Gaffney
(Northeastern University)
22/06/2015 10:00
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.
M.
Steven Dale Cutkosky
(University of Missouri)
22/06/2015 11:30
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.
M.
Askold Khovanskii
(University of Toronto)
22/06/2015 15:15
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...
M.
Jean Lorenceau
(Ecole Normale Supérieure)
M.
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...
M.
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.
M.
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...
M.
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.
M.
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.
M.
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...
