Room: C583
Time:
12:00-12:50
PM
Speaker:
Brandon Fodden (PIMS/University of Lethbridge)
Title: A lower bound for fractional moments of certain
L-functions
Abstract:
We extend the method of Heath-Brown to
find a lower bound for the fractional moments of a certain class of
L-functions.
Wednesday, September
17, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Dragos Ghioca (University of Lethbridge)
Title: Algebraic Dynamics
Abstract: The classical Mordell-Lang
conjecture (proven by Faltings and Vojta) describes the intersection
between a finitely generated subgroup of a semiabelian variety G defined over the field of
complex numbers with a subvariety V of G.
We may view this subgroup of G as the image of 0 under the action of a finitely generated semigroup S of automorphisms of G (each automorphism being a
translation). We present extensions of the Mordell-Lang conjecture in
which S is any
finitely generated semigroup of endomorphisms of G.
Wednesday, September
24, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Amir Akbary (University of Lethbridge)
Title: Rankin-Selberg Convolutions
Abstract: We describe how the study of the analytic
properties of the convolution of the Dirichlet series leads to the
results on the size of the coefficients of the Dirichlet series.
Wednesday, October
1, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Nathan Ng (University of Lethbridge)
Title: Non-vanishing
of L-functions and application to a Fermat equation
Abstract: In
recent years, a popular research topic in analytic number theory has
the been the non-vanishing of L-functions. In
this talk I will discuss
some non-vanishing results which imply the Fermat
equation A^4+B^2=C^p for p a prime
larger than 5 has no non-trivial solutions.
Wednesday,
October 22, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker: Nathan
Ng (University of Lethbridge)
Title: The Mobius function summed over short intervals
Abstract: The
Central Limit Theorem in probability determines that a sum of
independent identically distributed random
variables is normally distributed.
A number theoretic model for a sequence of such random
variables is the Mobius function. In this
talk we discuss the
distribution of the sum of the Mobius function in
short and long intervals. We will see
that in short intervals the Mobius function behaves like a sum of independent random variables. However, over
longer intervals its behaviour
depends on the zeros of the zeta function.
Wednesday,
October 29, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Dave Morris (University of Lethbridge)
Title: Introduction
to Ratner's Theorems on unipotent flows (I)
Abstract: Unipotent
flows are very well-behaved dynamical systems. In particular, Marina
Ratner has shown that every orbit is uniformly distributed (on some
invariant submanifold). The first talk will present some important
number-theoretic consequences of this theorem, and the second talk will
explain a few of the ideas of the proof.
Wednesday,
November 5, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Dave Morris (University of Lethbridge)
Title: Introduction
to Ratner's Theorems on unipotent flows (II)
Abstract: Unipotent
flows are very well-behaved dynamical systems. In particular, Marina
Ratner has shown that every orbit is uniformly distributed (on some
invariant submanifold). The first talk will present some important
number-theoretic consequences of this theorem, and the second talk will
explain a few of the ideas of the proof.
Monday, November
10, 2008
Room: C620
Time:
12:00-12:50
PM
Speaker:
Chantal David (Concordia University)
Title: Almost prime orders of elliptic curves over
finite fields
Abstract: Let
E be an elliptic curve over the rationals. A conjecture of Neal
Koblitz predicts an exact asymptotic for the number of primes p
such that the order of E over the finite field with p
element is prime. This conjecture is still open. Using sieve
techniques, one can find a lot of primes p such that the order p+1-aP(E) is almost
prime. The best result that one may hope to achieve by sieve techniques
was obtained by Iwaniec and Jimenez Urroz for complex multiplication
curves using Chen's sieve. They showed that there are infinitely many
primes p such that p+1-ap(E)=P2,
where n=Pk means that the integer n
has at most k prime factors. For elliptic curves without
complex multiplication, it is not known how to apply the switching
principle of Chen's sieve to get such a result.
For curves without complex multiplication,
we show that there are many primes p such that p+1-ap(E)=P8
with an explicit lower bound (in terms of the constant C(E)
of Koblitz's conjecture), using Greaves' sieve and under the GRH. This
improves previous work of Steuding and Weng. One can also show that
there are many primes such that p+1-ap(E)
has at most 6 distinct prime factors, but still cannot
improve the number of (not necessarily distinct) primes from 8
to 6. This surprising result is related to the difficulty of
sieving square-free numbers in the sequence p+1-ap(E).
This is joint work with Jie Wu
(CNRS, Institut Elie-Cartan, Nancy).
Friday,
November 21, 2008
Room: D630
Time:
12:00-12:50
PM
Speaker:
Harald Helfgott (University of Bristol)
Title: Escape
and incidence: their role in growth in groups
Abstract:
There is, so far, one tool that geometric group theory (largely on
infinite groups) and recent work on non-commutative group combinatorics
(largely on finite groups) have in common: the idea of escape.
After a brief discussion of what escape is and how it can be used, we
shall pass to the possibility of restating much of "additive
combinatorics" as the combinatorics of an abstract projective plane.
There is a basic statement in the latter that does not seem to have a
clear analogue in classical additive combinatorics; we shall see how
the main idea of the proof is, again, escape.
Wednesday,
November 26, 2008
Room: D633
Time:
12:00-12:50
PM
Speaker:
Hadi Kharaghani (University of Lethbridge)
Title: On
mutually unbiased Hadamard matrices
Abstract: Two
Hadamard matrices $H$ and $K$ of order $n$ are called {\it unbiased} if
$HK^t=\sqrt n L$, where $L$ is a Hadamard matrix of order $n$. Mutually
unbiased Hadamard matrices have applications in quantum measurement,
quantum cryptography and design theory. I will try to give a simple
survey talk on the the existence, structure and applications of these
matrices.
This talk will be accessible to the senior
undergraduate mathematics students.
Wednesday, December
3, 2008
Room: C583
Time:
12:00-12:50
PM
Speaker:
Pablo Spiga (University of Padova)
Title:
Synchronization and homomorphisms
Abstract:
An automaton is a machine which can be in any of a set of internal
states which cannot be directly observed. A synchronizing automaton is
an automaton admitting a sequence of transitions which take the
automaton from any state into a known state. In this talk we present
some recent connections between synchronizing automatons, permutation
groups and graph homomorphisms. All relevant definitions would be
given during the talk.