Algebra events
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Monday, 16/7/2007, 11:00 - 12:00, room R223
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| Speaker:
James Lewis (University of Alberta, Edmonton, Canada)
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| Title:
Algebraic cycles and Mumford-Griffiths invariants.
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| Abstract:
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Monday, 10/12/2007, 11:00 - 12:00, room M143
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| Speaker:
Victor Abrashkin (Durham University, Durham, United Kingdom)
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| Title:
Faltings's strict modules as a characteristic p analogue of finite flat p-group schemes.
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| Abstract:
The classical concept of a finite flat group
scheme loses many interesting properties when
considered over a base of characteristic p.
Instead, Faltings suggested the concept of a
finite flat module scheme with a 'strict action'.
In this talk we will explain the classification
of such modules, as well as properties that
are analogous to those of classical group schemes.
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Friday, 29/2/2008, 11:00 - 15:15, room M129
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L-functions and friends
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A day devoted to L-functions and related topics
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| Time: 11:00-12:00
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| Speaker:
Tejaswi Navilarekallu (Vrije Universiteit, Amsterdam, The Netherlands)
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| Title:
Galois actions and L-values.
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| Abstract:
Let K/Q be a finite Galois extension with Galois group
G. For every character χ of G, the special value L(χ,0)
of the Artin L-function carries arithmetic information about the
extension. The equivariant Tamagawa number conjecture predicts the precise relation
between the L-values and certain arithmetic invariants. In this talk,
we shall give a formulation of the conjecture and indicate some
techniques of verification.
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| Time: 13:00-14:00
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| Speaker:
Don Zagier (Collège de France, Paris, France, and MPIM, Bonn, Germany)
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| Title:
Modular Green's functions.
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| Abstract:
The functions of the title arose many years ago in connection with heights of Heegner points
and special values of L-functions, but turned out to have further interesting properties, including
a conjectural algebraicity statement for their special values. This conjecture has recently been proved
in many cases by Anton Mellit. We will discuss this and related work.
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| Time: 14:15-15:15
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| Speaker:
Xavier-François Roblot (Université Claude Bernard, Lyon, France)
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| Title:
Computing values of p-adic L-functions over a real quadratic field.
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| Abstract:
Following the works of P. Cassou-Nogučs, D. Barsky, N. Katz
and P. Colmez, I will give an explicit construction of a continuous
p-adic function interpolating (some of) the values at negative integers
of the Hecke L-function of a real quadratic field, the so-called p-adic
Hecke L-function. I will show how this construction allows one to
compute (approximations of) the values of this function.
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Thursday, 20/11/2008, 11:00 - 15:15, rooms F453 and R232
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K-theory and algebraic cycles
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| Time: 11:00-12:00
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| Room: F453
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| Speaker:
Rob de Jeu (Vrije Universiteit, Amsterdam, The Netherlands)
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| Title:
Bounding the kernel of the tame symbol on curves.
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| Abstract:
One can compute K2 of the rationals fairly easily by using division with remainder in the
integers. We discuss how, for a curve over an arbitrary field, a similar technique leads to the description of a
subgroup of K2 of its function field that contains the kernel of the tame symbol on the
curve. For example, for an elliptic curve defined by a Weierstrass equation, this
subgroup is generated by symbols {l1,l2} with li a non-zero constant or an equation of
a line.
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| Time: 13:00-14:00
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| Room: F453
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| Speaker:
Lenny Taelman (Universiteit Leiden, Leiden, The Netherlands)
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| Title:
Characteristic p special L-values.
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| Abstract:
I shall present a new conjecture about special values (i.e., values at
integral arguments) of L-functions of certain types of Galois
representations. These are representations of the absolute Galois group of a global
function field of characteristic p on vector spaces over local fields in
characteristic p. Although there is no reason to expect a direct relation, the
conjecture is surprisingly similar to Beilinson's conjecture on special values of L-functions over
number fields. In very special cases the conjecture specializes to known results
about characteristic p zeta values; beyond this there is at present only numerical
evidence.
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| Time: 14:15-15:15
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| Room: R232
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| Speaker:
James Lewis (University of Alberta, Edmonton, Canada)
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| Title:
Real regulators on Milnor complexes. Or, the Mumford-Manin conjecture revisited.
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Abstract:
Let X be a projective algebraic manifold. For non-negative integers k, m,
we consider a cycle group CHMk(X,m) defined in terms of
the Zariski cohomology of the sheaf of Milnor K-groups on X,
and a corresponding twisted variant CHTMk(X,m).
We construct real logarithmic type maps ('real regulators')
on the latter with values in Hodge cohomology, and as an example in the case
k=m=2 and X a curve, we deduce a weak version of the Mumford-Manin
conjecture. In some cases where the regulator image of CHMk(X,m)
is 'trivial' it can be shown that the regulator image
of CHTMk(X,m)
can be non-trivial.
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Friday, 20/3/2009, room 208, Minnaertgebouw, Universiteit Utrecht
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IC number theory/DIAMANT/GQT
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After the last talk there will be drinks in the library of the Mathematical Institute.
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| Time: 11:00-12:00
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| Speaker:
Spencer Bloch (University of Chicago, Chicago, USA)
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| Title:
Algebraic geometry associated to graphs.
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| Abstract:
The Feynman amplitude associated to a graph in
physics is a period of the hypersurface defined by the Kirchoff
polynomial, a classical invariant of the graph. I will explain work on
the "motive" of the graph.
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| Time: 13:15-14:15
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| Speaker:
Alex Quintero Velez (Universiteit Utrecht, Utrecht, The Netherlands)
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| Title:
McKay correspondence for Landau-Ginzburg models.
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| Abstract:
The McKay correspondence is a principle that relates the geometry
of a resolution of singularities of a quotient variety M/G and the
equivariant geometry of the group action. The classic case is McKay's
identification of the cohomology of the resolution of a Kleinian singularity
CC2/G with the representation theory of G. In this talk, we discuss an
analogue of the McKay correspondence for Landau-Ginzburg models. This leads
naturally to a generalized notion of the McKay correspondence as an
isomorphism of "noncommutative spaces" (in Kontsevich's sense).
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| Time: 14:30-15:30
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| Speaker:
Rob de Jeu (Vrije Universiteit, Amsterdam, The Netherlands)
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| Title:
K4 of curves over number fields.
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| Abstract:
We give a conjectural description (due to Goncharov) of K4 modulo torsion
of a curve over a number field, using certain complexes based on the function
field of the curve. We also discuss to which extent this has been proved.
Furthermore, we illustrate a method of finding non-zero examples for elliptic curves E defined
over Q, and numerically verify the relation between their regulators and L(E,3) predicted by the Beilinson
conjectures. The latter is joint work in progress with Sander Meinema.
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| Time: 16:00-17:00
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| Speaker:
Dmitri Orlov
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| Title:
Triangulated categories of singularities, D-branes in LG-models and mirror symmetry.
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| Abstract:
I am going to talk about triangulated categories of singularities and
categories of D-branes of type B in Landau-Ginzburg models and
sigma-models. Different properties of these categories will be described.
At the end of my talk I am also going to discuss mirror symmetry and a
generalized strange Arnold duality.
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Thursday, 25/2/2010, 15:30-16:30, room C624
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| Speaker:
Jean-Louis Colliot-Thélène (Orsay, Paris, France)
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| Title:
(Slides)
The Brauer-Manin obstruction for zero-cycles, the Tate conjecture for
cycles of dimension 1, and the third unramified cohomology group.
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Abstract:
It is an open question whether the Brauer-Manin obstruction to the
existence of a zero-cycle of degree one is the only obstruction for
arbitrary smooth projective varieties over a global field. in 1989 Shuji
Saito noticed that over global fields of positive characteristic, an
integral version of the Tate conjecture for dimension 1 cycles on varieties
over a finite field would give an affirmative answer. A weak form of the
integral Tate conjecture for such cycles was given some support by C.
Schoen. For surfaces over global fields of positive characteristic, one can
relate the hoped for Tate conjecture to the vanishing of the third
unramified ètale cohomology groups of threefolds over a finite field.
Which one may establish in some cases.
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Friday, 11/3/2011, room M623
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IC number theory seminar
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| Time: 11:15-12:15
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| Speaker:
James Lewis (University of Alberta, Edmonton, Canada)
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| Title:
An Archimedean height pairing on the equivalence relation defining Bloch's higher Chow groups.
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| Abstract:
The existence of a height pairing on the equivalence relation defining
Bloch's higher Chow groups is a surprising consequence of some recent joint work
by myself and Xi Chen on a non-trivial K1-class on a self-product of a general
K3 surface. I will explain how this pairing comes about.
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| Time: 13:15-15:15
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| Speaker:
Jean-Louis Colliot-Thélène (Orsay, Paris, France)
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| Title:
Lectures on the Hasse principle, I.
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| Abstract:
Hasse principle and weak approximation: elementary fibration method,
Brauer-Manin obstruction for rational and integral points, examples. To which
extent can we compute the Brauer group and the Brauer-Manin set?
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| Time: 15:30-16:30
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| Speaker:
Ronald van Luijk (Universiteit Leiden, Leiden, The Netherlands)
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| Title:
Computability of Picard numbers.
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| Abstract:
The Néron-Severi group of a variety is the group of its divisor
classes modulo algebraic equivalence. The rank of this group is called the
Picard number of the variety. After giving a short review of ad hoc methods that
compute the Picard number in certain cases, I will sketch an idea of Bjorn
Poonen to prove that the Picard number is computable in general. This is joint
work in progress with Damiano Testa.
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