The Ivan and Betty Niven Distinguished Lectures |
University of British Columbia |
March 7 - 10, 2006 |
The UBC Department of Mathematics is proud to present a series of
lectures by Ching-Li Chai
of the University of Pennsylvania. |
These lecture series were made possible through a generous bequest
received from Ivan and Betty Niven.
In honor of their generous support, the Department of Mathematics has
established a permanent endowment fund, "The Ivan and Betty Niven
Distinguished Lectures Fund", the income from which will fund a series of
annual lectures on a broad array of topics in Mathematics. |
Lecture #1 (Student Lecture) |
Tuesday, March 7, 4:00-5:00, MATH 105 |
Monodromy groups |
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A monodromy group is the group of symmetries of
a family of objects which are "locally isomorphic". These groups
frequently occur in several areas of mathematics, including algebra,
topology and number theory.
In many situations one would like to show that the monodromy group is
"as
large as possible", subject to the obvious constraints. We will consider
several examples of the monodromy problem in different flavors: local
versus global, p-adic versus l-adic. The first examples are from Galois
theory with finite monodromy groups. In other examples from number
theory
the monodromy groups will be infinite. |
Refreshements 3:30--4:00, MATX 1115
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Lecture #2 (Number theory / Algebraic geometry seminar) |
Thursday, March 9, 4:10-5:00, WMAX 110 |
Canonical coordinates for leaves of p-divisible groups |
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Let p be a prime number and g be a positive integer.
Let M be the moduli space of abelian varieties of PEL type.
A leaf in M is the locus corresponding to a fixed isomorphism
class of polarized p-divisible group with prescribed endomorphisms.
Although a leaf is defined by a "pointwise" condition, it turns out
that the formal completion (or jet space) of a leaf at a point
has a rigid structure: It is built up from a finite collection
of p-divisible formal groups via a family of fibrations.
This structural description can be regarded as a generalization
of the Serre-Tate coordinates of the local deformation space
of a ordinary abelian variety. We also explain a local rigidity
result related to the action of the local stabilizer subgroup
on the canonical coordinates.
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Lecture #3 Hecke orbits (Colloquium) |
Friday, March 10, 3:00-4:00, MATX 1100 |
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Let p be a prime number and g be a positive integer.
Let A_g be the moduli space of g-dimensional principally polarized
abelian varieties over the algebraic closure of the finite field with
p elements. There is a family of finite-to-one correspondences
on this moduli space generated by prime-to-p isogenies between
abelian varieties; these symmetries are known as Hecke correspondences.
Recently F. Oort defined a family of locally closed smooth algebraic
subvarieties of A_g, called "leaves"; a leaf is the locus in A_g
corresponding to a fixed isomorphism class of polarized p-divisible
group. Clearly every leaf is stable under all prime-to-p Hecke
correspondences. Oort conjectured that every Hecke orbit is dense
in the leaf containing it. We will explain methods motivated by
this conjecture, and how these methods can be used to prove the
conjecture.
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Colloquium tea 2:40--3:00, MATX 1115
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