The Fields Institute will be
hosting a summer research program for undergraduates to be
held in July and August of 2011. The program will support
up to thirty students to take part in research projects supervised
by leading scientists from Fields partner universities or
thematic programs.
PROGRAM
Activities start July 4, 2011 at 9:30 a.m. at the Fields
Institute, 222 College Street. Map
to Fields
If you are coming from the Woodsworth residence, walk south
on St. George to College Street, turn right, Fields is the second
building on your right.
MONDAY JULY 4
9:3010:15 a.m. Orientation Meeting: Students meet with Fields
program staff
Re: computer accounts, offices, expense reimbursements, and
overview of Fields facilities.
10:15 a.m. Coffee break
10:30 a.m. Introductory Session: Introduction and presentation
of the program (Fields Director, Edward Bierstone)
Introduction to supervisors, and overview of theme areas
and projects:
Symmetries of Euclidean
tessellations and their covers
Supervisors: Isabel Hubard, Universidad Nacional Autónoma
de México (presenting by Skype); Mark Mixer,
Fields Institute; Daniel Pellicer, Fields Institute;
Asia Weiss, York University

Model Theory of Operator Algebras
Supervisers: Ilijas Farah, York University; Bradd
Hart, McMaster University (presenting)

Constraint Satisfaction
Group 1
Supervisors: Libor Barto, McMaster University; Matt
Valeriote, McMaster University; Ross Willard, University
of Waterloo

Constraint Satisfaction
 Group 2
Supervisors: Libor Barto, McMaster University; Matt
Valeriote, McMaster University; Ross Willard, University
of Waterloo

Mathematical Finance  Understanding
Financial Crisis
Supervisors: Matheus Grasselli, McMaster University
(presenting); Oleksandr Romanko, Mitacs  McMaster
University  Algorithmics Inc.

Combinatorial Rigidity
And Graph Constructions
Supervisor: Tony Nixon, Fields Institute (presenting),
Elissa Ross, Fields Institute

Study of the development
of glaucoma
Supervisors: Irwin Pressman, Carleton University (presenting);
Siv Sivologathan, University of Waterloo

12:30 p.m. Lunch provided at Fields for students and supervisors
Afternoon open for students to meet informally with supervisors.
*By 4 p.m. Hand in ranking sheet to Members Liaison, Sharon
McCalla, Room 330*
July 511
Tuesday July 5 (or Wednesday July 6) afternoon: Introduction
to the Fields SMART board and video conferencing facilities
which are useful for remote collaboration.
Friday July 8
Daniel Pellicer will meet with students involved with the
"Symmetries of Euclidean Tessellations and Their Covers"
Project in Room 210, 10 a.m.12 noon.
Lecture by Moshe Vardi,
Rice University Stewart Library at 1:30 pm
Title: P vs NP
The question of P vs. NP is one of the central questions
in computer science and mathematics. (It is one of the Clay
Institute Millenial Problems whose solution would yield
an award of $1,000,000.) In the first half of August 2010,
an HP researcher claimed to have solved the problem, using
tools from mathematical logic and statistical physics, including
a theorem proved by the speaker in 1982.
The claim generated a huge buzz in computer science, with
coverage also in the New York Times. This talk will explain
what the PvsNP problem is, what tools were employed in
the claimed proof, and what the status of the claim is.
July 811
The Mitacs Globalink students are invited to the Ontario
Conference for the Globalink Industry Conference. Opening
gathering on Thursday July 7
Saturday July 23
Students are invited to participate in a Fields Undergraduate
Network (FUN) event in Ottawa:
http://www.fields.utoronto.ca/programs/outreach/1112/undergradnet/
August 2227
During the final week, students are requested to prepare
a report on their projects and their experience in the Program
to be emailed to programs(PUT_AT_SIGN_HERE)fields.utoronto.ca
before August 27. These reports will be used in the Fields
Newsletter and Annual Report.
August 25
MiniConference: Undergraduate research students will present
their work. This Conference will form a special Fields Undergraduate
Network (FUN) event.
August 25
An excursion  sponsored and organized by Fields  is planned
for all students.
Project Overview
Symmetries
of Euclidean tessellations and their covers
Supervisors: Isabel Hubard, Mark Mixer, Daniel Pellicer, Asia
Ivic Weiss.
The study of Euclidean symmetries has origins in antiquity,
for instance with the Platonic solids. In the 19th and 20th
century, new ideas emerged, which revitalized the eld and
created numerous interesting topics of active research.
A symmetry of an Euclidean tessellation is an isometry of
the space that preserves it. Our study of these symmetries
will be focused on the number of orbits of some elements
of the tessellation, such as vertices, edges, ags, etc.,
under a given isometry subgroup.
Initially we start with a geometric approach, that will
lead into algebraic, combinatorial, and topological ones.
Various open problems related to Archimedean tessellations
in 2 and 3 space will be explored.
Students should consult the following literature:
1. First three chapters of "Regular Complex Polytopes"
by H.S.M. Coxeter.
2. "Uniform Tilling of 3Space" by B. Grunbaum,
Geombinatorics 4(1994), 49  56.
3. The attached notes by I. Hubard.
Constraint Satisfaction
(slides)
Supervised by : Ross Willard, Matt Valeriote, and Libor Barto
Many interesting and important questions from computer
science, combinatorics, logic, and database theory can be
expressed in the form of a constraint satisfaction problem.
Recently an algebraic approach to settling some central
conjectures in this area have been developed and have led
to the investigation of some novel properties of finite
algebraic and combinatorial systems. The proposed project
will involve experimenting with small algebraic and combinatorial
systems to test several conjectures and open problems that
are concerned with solving associated instances of the constraint
satisfaction problem.
Ideally students will have an interest and background in
abstract algebra and also in combinatorics, logic, and computational
complexity, but this is not essential.
Mathematical
Finance  Understanding Financial Crisis
Matheus Grasselli, McMaster University presenting and Oleksandr
Romanko
Abstract to follow
Model Theory
of Operators (slides)
Supervised by Bradd Hart & Ilijas
Farah
Model theory is a branch of mathematical logic which studies
the logical theories of classes of structures or models.
Traditionally this logic has been classical first order
logic and the techniques of first order model theory have
been used successfully in many areas of algebra, number
theory and geometry. Recently a new logic called continuous
logic has been developed and it is more suited for applications
in analysis. One area of application is operator algebras
(algebras of operators acting on a Hilbert space). A concrete
problem in this area is studying the asymptotic behaviour
of sentences in continuous logic in matrix algebras.
Some familiarity with basic logic would be helpful and
a solid grounding in linear algebra and analysis would be
an asset.
Study
of the development of glaucoma
Supervisors: Irwin Pressman, Carleton (presenting) and Siv
Sivologathan, University of Waterloo
Study of the development of glaucoma, this is a condition
in which the optic nerve is damaged and is often associated
with increased fluid pressure in the eye (occular hypertension).
The proposal is to model the flow of aqueous humor in the
eye using the partial differential equations governing buoyancydriven
flows (NavierStokes equations coupled to the heat equation).
Of course the full set of equations are too difficult to
solve (except numerically), and we will make some approximations
from lubrication theory that will lead to a set of equations
that are analytically tractible.
Combinatorial
Rigidity And Graph Constructions (course
introduction)
Supervisors: Tony Nixon, Fields Institute (presenting )
Rigidity theory is motivated by diverse applications in
computer aided design, materials science and structural
engineering. We consider realisations of graphs as physical
objects (called frameworks) where the vertices represent
joints and the edges bars between pairs of joints. A framework
is rigid if the only edgelengthpreserving continuous motions
of the vertices are induced by isometries. For almost all
frameworks it is the properties of the graph that determine
rigidity rather than the specific realisation.
The natural classes of graphs that arise in rigidity theory
are graphs G=(V,E) for which E=kVl (for natural numbers
k,l) together with a corresponding subgraph inequality.
Despite their innocent appearance these graphs have a rich
combinatorial flavour that the students can explore. Particularly
the proposed project would be based around one or more of
the following: inductive constructions, spanning subgraph
decompositions, algorithms, matroids and simple versus multigraphs.
Back to top
The Fields Institute will be hosting a summer research program
for undergraduates to be held in July and August of 2011. The
program will support up to thirty students to take part in research
projects supervised by leading scientists from Fields partner
universities or thematic programs.
Out of town students accepted into the program will receive
financial support for travel to Toronto, student residence
housing on the campus of the University of Toronto from July
4 to August 26, 2011, and a per diem for meals. NonCanadian
students will receive medical coverage during their stay.
Students will work on research projects in groups of three
or four. Some projects will be related to the Fields Thematic
Programs on The Mathematics of Constraint Satisfaction and
on Discrete Geometry and Applications. In addition, supervisors
will suggest other topics outside of these fields. In some
cases students may also have the opportunity to spend a week
off site at the home campus of the project supervisor(s).
Undergraduate students in mathematics and related disciplines
are encouraged to apply.
Note: Students requiring visas for travel
to Canada will need to make their own arrangements to obtain
the necessary documents.
Confirmed Program Students
Ferenc
Bencs Eötvös Loránd
University
Lucas Bentivenha  UNESP
Zoltan Blazsik Eötvös Loránd University
Luke Paul Broemeling University of Calgary
Kostiantyn Drach  V.N. Karazin Kharkiv National
University
Qian (Linda) Liu University of Toronto
Hao Liu  Nanjing University
HyungBin Ihm University of Toronto
Euijun Kim  University of Toronto
Maximilian Klambauer  University of Toronto
Avinash Kulkarni  University of Waterloo
Fernando Lenarduzzi  Universidade Estadual Paulista
“Julio de Mesquita Filho”
Daniel Perkins Bowie State University
Nikita Reymer University of Toronto
Rafael Rocha  Universidade Estadual Paulista “Julio
de Mesquita Filho”
Nigel Sequeira  McMaster University
Vishal Siewnarine  University of Waterloo
Maksym Skoryk V.N. Karazin Kharkiv National University
Garence Staraci Stanford University/McGill
Rebecca Tessier  Queen's University
LouisPhilippe Thibault  University of Montreal
Anna Tossenberger  Eötvös Loránd
University
Yiyang (Young) Wu  University of Waterloo
To
apply
We need the following by
April 30, 2011
(Note late applications are accepted dependent on funding)
(1) Brief covering letter outlining your background and experience,
sent by email to programs(PUT_AT_SIGN_HERE)fields.utoronto.ca
(2) Copy of your academic transcript sent in .pdf format as
an attachment to (1)
(3) An official copy of your transcript
send by issuing institution either by email to programs(PUT_AT_SIGN_HERE)fields.utoronto.ca
or by hard copy mailed to "Fields Manager of Scientific
Programs, 222 College Street, Toronto M5T 3J1"
(4)Two letters of reference. Please
ask referees to send letters directly to programs(PUT_AT_SIGN_HERE)fields.utoronto.ca
in .pdf format as an attachment.
Late applications will be accepted
funds allowing.
