Number theory seminar this Thursday
4 views
Skip to first unread message
William Stein
Nov 13, 2012, 12:00:09 AM11/13/12
to ntuw, 581...@googlegroups.com, Rose Choi
Hi,
This is the number theory seminar announcement for this week.
DATE: Thursday, Nov 15 at 10:30am
SEMINAR: The Number Theory Seminar
SPEAKER: Aly Deines, University of Washington
TITLE -- Pseudobasis: Generalizing the idea of a basis to non-PIDs.
ABSTRACT -- Bases are a wonderful tool for representing algebraic
objects in a computational way. In this talk I will explore how
objects can fail to have bases and how we can use pseudo-bases to
represent and compute these objects. There will be many examples,
mostly drawn from number theory. This talk is geared towards the
students in this quarter's algebraic number theory class.
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
This is the number theory seminar announcement for this week.
DATE: Thursday, Nov 15 at 10:30am
SEMINAR: The Number Theory Seminar
SPEAKER: Aly Deines, University of Washington
TITLE -- Pseudobasis: Generalizing the idea of a basis to non-PIDs.
ABSTRACT -- Bases are a wonderful tool for representing algebraic
objects in a computational way. In this talk I will explore how
objects can fail to have bases and how we can use pseudo-bases to
represent and compute these objects. There will be many examples,
mostly drawn from number theory. This talk is geared towards the
students in this quarter's algebraic number theory class.
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
William Stein
Nov 26, 2012, 10:01:39 PM11/26/12
to ntuw, 581...@googlegroups.com, Rose Choi, Neal Koblitz, Simon Spicer
Hello,
Simon Spicer is back from Oberwolfach and will give this Thursday's
number theory seminar on something he learned there.
Speaker: Simon Spicer, University of Washington
Coordinates: 10:30am in Padelford C401 on Nov 29, 2012.
Title: Using CM Theory to construct curves over prime fields of a given order
Abstract: Modern day cryptographic protocols make use of finite cyclic
groups in which arithmetic is easy, but certain operations like the
discrete logarithm are computationally hard. Groups of points on
elliptic curves over prime fields are one such class of cryptographic
groups. A famous result of Hasse is that the number of points on an
elliptic curve modulo p lies in the interval (p+1-2*sqrt(p),
p+1+2*sqrt(p)), so for large N and a p close to N it unlikely that a
random elliptic curve E(F_p) will have cardinality N. In this
expository talk we show how the theory of Complex Multiplication can
be used to derive a polynomial time algorithm for constructing
elliptic curves over prime fields of any given order.
Simon Spicer is back from Oberwolfach and will give this Thursday's
number theory seminar on something he learned there.
Speaker: Simon Spicer, University of Washington
Coordinates: 10:30am in Padelford C401 on Nov 29, 2012.
Title: Using CM Theory to construct curves over prime fields of a given order
Abstract: Modern day cryptographic protocols make use of finite cyclic
groups in which arithmetic is easy, but certain operations like the
discrete logarithm are computationally hard. Groups of points on
elliptic curves over prime fields are one such class of cryptographic
groups. A famous result of Hasse is that the number of points on an
elliptic curve modulo p lies in the interval (p+1-2*sqrt(p),
p+1+2*sqrt(p)), so for large N and a p close to N it unlikely that a
random elliptic curve E(F_p) will have cardinality N. In this
expository talk we show how the theory of Complex Multiplication can
be used to derive a polynomial time algorithm for constructing
elliptic curves over prime fields of any given order.
William Stein
Dec 3, 2012, 4:49:31 PM12/3/12
to ntuw, 581...@googlegroups.com, Rose Choi, Andrew Ohana
Hi,
The number theory seminar this THURSDAY at 10:30am in Padelford C401 will be:
Speaker: Andrew Ohana (Graduate Student, University of Washington)
Title: Arithmetic of Ideals for Orders of Quadratic Fields
Abstract: Answering a question such as whether a fractional ideal I is
principal or finding a short representation I^100 is difficult when I
is given by multiple generators. In this talk we will show how by
using matrix representations for ideals, we are able to leverage
results in integral linear algebra and binary quadratic forms to
resolve these problems and many more.
The number theory seminar this THURSDAY at 10:30am in Padelford C401 will be:
Speaker: Andrew Ohana (Graduate Student, University of Washington)
Title: Arithmetic of Ideals for Orders of Quadratic Fields
Abstract: Answering a question such as whether a fractional ideal I is
principal or finding a short representation I^100 is difficult when I
is given by multiple generators. In this talk we will show how by
using matrix representations for ideals, we are able to leverage
results in integral linear algebra and binary quadratic forms to
resolve these problems and many more.
Reply all
Reply to author
Forward
0 new messages