April 17, 2014

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.

10:00am - Networking
10:30am - Interview of Hugh Williams
11:00am - What keeps our secrets safe?
12:00pm - Lunch
1:30pm - Role of L-functions 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, Co-President of Math Union and Co-Founder of FUN

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 e-world, 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 privacy-enhancing 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 non-specialist audience, I will describe from a historical perspective several features of modern encryption techniques.

Role of L-functions in number theory
Henry Kim, University of Toronto

L-functions are very special type of meromorphic functions of one complex variable. On the surface it is not clear why the L-functions play decisive roles. L-functions are associated to arithmetic-geometric 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. L-functions attached to elliptic curves give rise to Birch-Swinnerton-Dyer 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 L-functions 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, Seung-Jae 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, Ali-Kazim University of Toronto

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