Faisal Al-Faisal
Home university:
University of Waterloo
Supervisor:
K. Purbhoo
Project title:
Schubert Calculus
Comments:
I worked with Professor Kevin Purbhoo on a project that dealt with Schubert calculus and the Wronski map. More specifically, we looked at what the fibres of the Wronski map say (and don't say) about the intersection of certain Schubert varieties.
Working as a Undergraduate Research Assistant (URA) was definitely an enjoyable and interesting experience. I have no reservations about recommending it to anyone interested in pursuing mathematics at a higher level. This was my third time as a URA (although my first in the Combinatorics and Optimization (C and O) department), and each time I learned a great deal both about doing mathematical research and about myself. This knowledge will no doubt be very helpful when it comes to, say, getting the most out of graduate school.
Shalev Ben-David
Home university:
University of Waterloo
Supervisor:
J. Geelen
Project title:
Representability of Matroids
Comments:
I thought the research term went very well and was a very good experience. I ended up co-authoring two papers with my supervisor.
Carmen Bruni
Home university:
University of Waterloo
Supervisor:
D.M. Jackson
Project title:
Knots, Links and Invariants
Ming Ben Feng
Home university:
University of Waterloo
Supervisor:
C. Swamy
Project title:
Stackelberg Minimum Spanning Tree Game
Comments:
This
summer
research
program
provides
good
research
facilities
and
experience
to
every
participant,
and
is
an
extremely
good
platform
to
meet
talented
people
with
similar
interests.
I
did
research
on
a
specific
subclass
of
profit-maximization
pricing
problems,
which
can
be
modeled
as
a
combinatorial
game.
My
problem
is
to
set
prices
on
some
edges
in
a
graph,
so
that
my
revenue
is
maximized
when
a
minimum
spanning
tree
of
the
graph
is
purchased.
There
is
existing
approximation
algorithm
for
this
class
of
problems
based
on
trivial
pricing
strategy.
My
supervisor
and
I
tried
to
tackle
the
problem
based
on
a
somewhat
more
sophisticated
algorithmic
approach.
And
the
remaining
task
is
to
analyze
the
performance
of
our
algorithm.
Elyot Grant
Home university:
University of Waterloo
Supervisor:
J. Koenemann
Project title:
Solving and Approximating Priority Cover
Comments:
This summer, I worked on providing algorithms to find exact and approximate solutions to a family of covering problems known as Priority Covering Problems. Our initial research led us to many new and exciting techniques for solving them, with relevant applications to capacitated covering problems on lines and trees. Many of my results were incorporated into a research paper in the topic. Additionally, my research led to many unforseen connections between combinatorial optimization results and known problems in computational geometry and computational learning theory. Despite the fact that both me and my supervisor were not familiar with these topics, we dove right in, read some papers, and were able to make insightful connections that were immediately relevant to our research. The summer is almost over and I still feel like I have dozens of uncharted directions in which to continue exploring. The URA experience has, for me, been extremely satisfying.
Stacey Jeffery
Home university:
University of Waterloo
Supervisor:
M. Mosca
Project title:
Exact, Efficient and Information-Theoretically Secure Voting with an Arbitrary Number of Cheaters
Comments:
As
a
URA
this
summer,
and
in
the
previous
year,
I've
had
the
opportunity
to
work
on
several
interesting
projects
with
some
great
people.
With
Anne
Broadbent
and
Alain
Tapp,
I
worked
on
a
voting
protocol
which
is
secure
against
an
arbitrary
number
of
corrupt
participants.
This
was
a
really
interesting
and
important
result,
which
I
feel
very
lucky
to
have
been
a
part
of.
We
are
currently
finishing
up
the
paper.
Anne
and
Alain
have
been
really
great
to
work
with,
and
have
let
me
play
a
big
role
in
the
actual
writing
of
the
paper
and
proving
of
results,
which
has
been
very
useful
experience
for
my
future
as
a
researcher.
Another
project
I've
been
working
on,
under
the
supervision
of
Anne
Broadbent,
is
a
survey
of
nonlocality.
From
this
experience,
I
have
gotten
a
good
grounding
in
the
subject,
and
now
hope
to
attack
some
open
problems.
Nonlocality
is
a
very
broad
and
interesting
topic,
and
in
writing
this
survey
I've
had
a
chance
to
learn
all
the
relevent
background
and
important
results,
and
organize
them
into
a
paper,
which
will
also
be
useful
to
people
wanting
an
overview
of
the
subject
in
the
future.
Steven Karp
Home university:
University of Waterloo
Supervisor:
I.P. Goulden
Project title:
The Harer-Zagier Formula
Will Ma
Home university:
University of Waterloo
Supervisor:
P. Haxell
Project title:
Triangle Packings and Triangle Edge Covers
Comments:
I
liked
how
in
combinatorics
there
is
usually
less
background
material
to
read,
so
you
can
dive
into
your
problem
right
away.
I
really
enjoyed
the
term;
I
felt
like
I
was
really
immersed
in
the
subject.
My
supervisor
and
I
ended
up
co-authoring
a
paper
with
Professor
Qing
Cui
from
China.
Malcolm Sharpe
Home university:
University of Waterloo
Supervisor:
L. Tunçel
Project title:
Some Theory of Optimally Pricing Products
Vladimir Soukharev
Home university:
University of Waterloo
Supervisor:
D. Jao
Project title:
Evaluating Large Prime Degree Isogenies Efficiently
Comments:
This term we have worked in the area of elliptic curve isogenies. Previous best known results for evaluating isogenies of large prime degree had an exponential running time. We were able to develop an algorithm that solves this problem in subexponential running time for horizontal isogenies. I enjoyed working in the C and O department as a URA and will continue my studies here at the graduate level.
Leanne Stuive
Home university:
University of Waterloo
Supervisor:
B. Guenin
Project title:
Relationships between Grafts with the Same Even Cuts
Yi Su
Home university:
University of Waterloo
Supervisor:
D. Wagner
Project title:
The lattice of integer flow of a graph (regular matroid)
Comment:
The URA program is a great experience in my life. Here I learned so much knowledge from my supervisor and my fellow students. It also taught me how difficult the research is, which in some sense makes me realize how inadequate I am. I still have a lot to learn before I can conduct any sorts of research. But this motivates me to learn more mathematics. I think that's what I get from this program.
Rachael Taylor
Home university:
University of Waterloo
Supervisor:
A. Childs
Project title:
Quantum Query Complexity of Linear Functions
Comments:
We
considered
an
unknown
linear
function
mapping
points
on
the
n-dimensional
hypercube
to
the
real
numbers.
We
were
interested
in
how
many
queries
of
this
function
are
required
to
determine
the
function.
Thoughts
on
program:
I
was
exposed
to
many
of
the
areas
of
combinatorics
and
optimization
with
an
in-depth
look
at
quantum
algorithms.
This
was
a
very
well
organized
program
which
provided
a
first
hand
experience
in
mathematical
research
that
you
would
not
find
anywhere
else.
Nathan Yeung
Home university:
University of Waterloo
Supervisor:
H. Wolkowicz
Project title:
Perturbations and Sensitivity Analysis in Linear Programming