

Undergraduate Network Meeting
March 5, 2011
University of Toronto
Koffler House Building KP 108 (map
to site)
Organizers: Sergio Da Silva, Richard Cerezo
(Toronto)
For questions email Richard
Cerezo
Faculty Advisors: Matthias Neufang, James Colliander
The Fields Undergraduate Network (FUN) includes
a series of mathematical talks aimed at undergraduates,
and organized into a network involving the local universities.
We will be stating with trial run of four events for next
year with faculty members as consultants.

The Fields Undergraduate
Network (FUN) organizes monthly meetings to explore different areas
of mathematical research. The theme, as well as the host university
will vary from month to month. All interested undergraduates are welcome
to attend. We especially encourage participation by members of student
math societies.
Schedule:
10:00am  Networking
10:30am  Interview of Hugh Williams
11:00am  What keeps our secrets safe?
12:00pm  Lunch
1:30pm  Role of Lfunctions in number theory
2:30pm  Panel Discussion
3:00pm  Ergodic approaches to number theory
Hosting Student Group:
Math Union at University of Toronto
Interviewer and Discussion Moderator: Richard Cerezo, CoPresident
of Math Union and CoFounder of FUN
Talks:
What keeps our secrets safe?
Hugh Williams, The Cryptologic Institute and University of Calgary
Control over who knows what about us, for what purposes, and
to whom it is disclosed, is of profound concern to anyone making
use of electronic communication devices. In the eworld, personal
information is in a very real sense the person. Thus, it is essential
that we have confidence in the capacity of the information collector
to secure our personal information. This can only be achieved
through the very technology that threatens our privacy. One important
ingredient in these privacyenhancing technologies is cryptography.
Briefly put, cryptography is the study and development of techniques
for rendering information unintelligible to all but intended recipients
of that information. If a sender and receiver of a message wish
to communicate over an insecure channel (mobile phone, internet)
and want to ensure that no other unauthorized party can read their
transmission, they will make use of a particular cryptosystem.
A conventional cryptosystem can be thought of as a large collection
of transformations (ciphers), any one of which will render the
original message (plaintext) to unintelligible ciphertext, but
in order for the receiver to read the message, he must know which
particular transformation was used by the sender. The information
that identifies the transformation used by the sender is called
the key. It is important to point out that if an eavesdropper
acquires some message and its encrypted equivalent, he should
not be able to extract the key from this information. Nor should
the system be vulnerable to an adaptive attack; such attacks make
use of information previously acquired to obtain new information
from the sender and so on until the system is broken. This is
what makes cryptography fascinating. How can we protect our communications
against these kinds of attacks? Remember also that a good cryptosystem
must resist an attack even from the inventor of the system.
In this talk, which is intended for a nonspecialist audience,
I will describe from a historical perspective several features
of modern encryption techniques.
Role of Lfunctions in number theory
Henry Kim, University of Toronto
Lfunctions are very special type of meromorphic functions of
one complex variable. On the surface it is not clear why the Lfunctions
play decisive roles. Lfunctions are associated to arithmeticgeometric
objects such as Galois groups, elliptic curves, and also modular
forms. Riemann zeta function is used in the study of the distribution
of prime numbers. It gives rise to Riemann hypothesis. Lfunctions
attached to elliptic curves give rise to BirchSwinnertonDyer
conjecture. Those are two of the seven millennium prize problems
by Clay Mathematics Institute. I will try to survey very briefly
these and other roles Lfunctions play.
Ergodic approaches to number theory
Leo Goldmakher, University of Toronto
Ergodic theory is concerned with the long term statistical behaviour
of a dynamical system. Although the theory was originally motivated
by questions in statistical mechanics, in recent years it has
found spectacular applications to combinatorics, harmonic analysis,
number theory, and representation theory. In this talk I will
discuss some of the interactions between ergodic theory and number
theory, focusing on the pioneering work of Furstenberg on Szemeredi's
theorem.
List of Confirmed Participants as of March
1, 2011:
Full Name 
University Name 
Carmichael, Keegan 
University of Western Ontario 
Cerezo, Richard 
University of Toronto 
Chung, Ha Yoon 
University of Toronto 
da Silva, Sergio 
University of Toronto 
Dias, Manisha 
University of Waterloo 
Heidari Zadi, Amir Hossein 
University of Toronto 
Hill, David 
University of Toronto 
Hu, Samson 
University of Waterloo 
Isufllari, Henrieta 
University of Toronto 
Kang, Dongwoo 
University of Toronto 
Kinross, Alison 
McMaster University 
Lee, SeungJae 
University of Toronto 
Milcak, Juraj 
University of Toronto 
Moon, SeokHwan 
University of Toronto 
Pashley, Bryanne 
University of Waterloo 
Pistone, Jamie 
University of Toronto 
Shoukat, Affan 
York University 
Vlasova, Jelena 
University of Toronto at Mississauga 
Yee, Yohan 
McMaster University 
Zaidi, AliKazim 
University of Toronto 

