November 17, 2008 – 9:00 am
Dear Professor. I want to ask you a maths question. Hope you don’t mind. What is the difference between and ? Where is the projection of on . I understand that the first expression is the magnitude of , which is the length of the projection, am i right? However, I’m uncertain about the second [...]
August 29, 2008 – 3:58 pm
Because of a rather hectic travel schedule, I was slow in putting up the reports that were submitted assiduously by Zhe and Alex. I apologize. Zhe’s reports on the book `Riemann’s Zeta Function’ by Edwards: Zhe’s report 4 Zhe’s report 5 Zhe’s report 6 Zhe’s report 7 Alex’s reports on elliptic curves: Points of finite [...]
Acyr’s report 2 Alex’s report 2
Three students are in the midst of summer reading projects under my supervision, Acyr Locatelli, Alex Tao, and Nikhil Mehrotra. Acyr is reading Ideals, Varieties, Algorithms by Cox, Little, and O’Shea, a very nice introduction to computational algebraic geometry. Alex is reading Rational Points on Elliptic Curves by Silverman and Tate. This book deals with [...]
March 15, 2008 – 12:20 am
Since arriving in the UK, I gave colloquium lectures at QMUL, Leeds, Durham, and Exeter. A `colloquium’ is when you lecture for about an hour to the whole mathematics faculty on the topic of your research. It’s considerably harder to prepare than specialized seminars (for example, the London-Paris number theory seminar) where you are speaking [...]
February 19, 2008 – 11:20 am
The great arithmetician Kazuya Kato visited twice over the last few weeks, so I thought I’d use the occasion to recommend some writings. An undergraduate level textbook on number theory is Number Theory I: Fermat’s Dream published by the American Mathematical Society. It is short and covers fairly standard material, but contains many unusual insights. [...]
February 11, 2008 – 12:22 pm
A few weeks ago, I gave a colloquium lecture at Leeds university and subsequently wrote up an exposition based on it. It’s still not entirely `popular,’ but may give a somewhat better sense than my previous remarks of at least a few ideas. Let me know if there are some points on which you would [...]
January 12, 2008 – 12:30 am
It’s something of a constant concern of mine to put students of every level in touch with mathematical culture. So I thought I’d call your attention to the Southwest Center for Arithmetic Geometry where I did most of my public service work from 1998 to 2005. If you browse through, you’ll find ten years’ worth [...]
December 19, 2007 – 3:25 pm
In June of next year, there will be a small workshop at UCL with the title `non-commutative constructions in arithmetic and geometry.’ I will write later in more detail about the goals of the meeting, but here is a link to a preliminary web page. MK
