Besides lectures and tutorials, we also organize guest talks for EPYMT students.


In 2012 summer, we will organize the following talks.


Guest Lecture in August

Topic: Primality test
Speaker: Mr. CHOW Chi Wang (CUHK)
Date: 22 August (Wed) 2012
Time: 2:30pm to 3:30pm
Venue: L1, Institute of Chinese Studies (ICS), The Chinese University of Hong Kong,
Map & Route Guidance

Abstract:Primality test is an algorithm that determines whether a given integer is prime. Since large prime numbers are essential ingredients in many real-life cryptographic protocols, efficient primality tests are therefore very important in practice. It was already known in early 1980s that the primality of an integer can be determined efficiently by probabilistic algorithms such as the Miller-Rabin test. Surprisingly, despite extensive research in the following two decades, an efficient deterministic primality test that is unconditional on any unproven hypothesis is not found. In 2002, Agrawal, Kayal, and Saxena proposed the ground-breaking AKS primality test, and this famous problem is finally resolved. In this talk, I will first give an overview of the primality test problem, and then I will discuss the key ideas of the Miller-Rabin primality test and the AKS primality test.

All are welcome. No registration and payment is required. First come first served.
* Tutorial session of Number Theory and Cryptography on that day will postpone to 3:30-6pm.

Topic: Algebra, Galois and Quintic Equations
Speaker: Mr. CHAN Edisy Kin-Wai (Indiana University Bloomington, USA)
Date: 15 August (Wed) 2012
Time: 2:30pm to 3:30pm
Venue: LT6, 1/F, Lady Shaw Building (LSB), The Chinese University of Hong Kong,
Map & Route Guidance

Abstract:It is well-known that quadratic equations are able to be solved by radicals, i.e., their roots can be given by a formula consisting of finitely many steps of rational operations and root extractions on their coefficients – this is exactly what we call “Quadratic Formula” and we should have learnt it in junior school. Indeed, such formulae can also be found for cubic and quartic equations. Unfortunately, the work on “Quintic Formula” must be in vain, since quintic equations are actually not solvable by radicals. The proof, surprisingly, requires many essential techniques in algebra, and even more astonishingly, deeply depends on an advanced theory in algebra – the renowned “Galois Theory”. In this talk, I will give a down-to-earth introduction to some algebra topics, such as Group Theory and Galois Theory, which serve as the background knowledge, and a concise but precise proof of the “main course”, radical insolvability of quintic equations.

All are welcome. No registration and payment is required. First come first served.
* Tutorial session of Number Theory and Cryptography on that day will postpone to 3:30-6pm.

Topic: What is Riemann Hypothesis?
Speaker: Dr. Kit-Ho Mak (Georgia Institute of Technology, USA)
Date: 7 August (Tue) 2012
Time: 2:30pm to 3:30pm
Venue: LT2, 1/F, Lady Shaw Building (LSB), The Chinese University of Hong Kong,
Map & Route Guidance

Abstract:In 1859, Riemann defined his famous zeta function and wrote down his celebrated conjecture regarding the (non-trivial) zeros of his function. Being widely regarded as the hardest and most important problem in number theory and even mathematics, the Riemann Hypothesis is still unresolved. In this talk, I will explain what Riemann Hypothesis is, and why it is so important. If time permits, I will also introduce the generalized Riemann Hypothesis.

All are welcome. No registration and payment are required. First come first served.
* Tutorial session of Number Theory and Cryptography on that day will postpone to 3:30-6pm.

Guest Lecture in June

Topic: Will a Random Walker Return Home?
Speaker: Mr. Ting-Kam Leonard WONG (University of Washington)
Date: 27 June (Wed) 2012
Time: 4pm to 5pm
Venue: LT5, UG/F, Lee Shau Kee Building (LSK), The Chinese University of Hong Kong, Map & Route Guidance

Abstract: Consider the simple random walk on the integer lattice Z^d, where d = 1, 2 or 3, starting at the origin. The question of interest is whether the random walker will revisit the starting point again. I will discuss Polya's famous result: for d = 1 and 2, it is certain (i.e. with probability 1) that the walker will return to the origin. But for d = 3, there is a positive probability that the walker will not visit the origin again. In fact, the walker will drift to infinity. To tackle this problem, I will relate the random walk with an infinite electric network. Then the probability of return can be interpreted in terms of the effective resistance of the network.

All are welcome. No registration and payment are required. First come first served.

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» Slides of the talk