Number Theory Working Seminar

We are running a working number theory group seminar. The current group members are:

Lenny Fukshansky (CMC)
David Krumm (CMC)
Hiren Maharaj (CMC)
Xun Sun (CGU)
Arvind Suresh (CMC)

Also some former group members:

Michael Mei (Pomona)
John Shaughnessy (CMC)


In the Fall 2014 semester, we consider several different topics:

1. Mahler's measure and Salem numbers -- 3 lectures by Lenny Fukshansky, surveying material from:
The arithmetic and geometry of Salem numbers by E. Hironaka and E. Ghate
First chapter of Heights of Polynomials and Entropy in Algebraic Dynamics by G. Everest and T. Ward

2. Modular curves and related topics -- lectures by Hiren Maharaj, covering some material from
A First Course in Modular Forms by F. Diamond and J. Shurman


The topic for the Spring 2014 semester was Lattices and Codes. The seminar was led by
Hiren Maharaj, who got through the first two chapters of Ebeling's book.
We concluded with a lecture by Lenny Fukshansky on
Spherical designs and zeta functions of lattices by R. Coulangeon.


The topic for the Fall 2013 semester was Rational Points on Curves.
The seminar was led by David Krumm (with some lectures also by L. Fukshansky, M. Mei, J. Shaughnessy and X. Sun),
and the goal was to learn some basic arithmetic geometry with a potential view
towards the paper of McCallum and Poonen on the
method of Chabauty and Coleman.
Here is some of the reading we have done:

1. Mordell's paper on height bounds for points on conics
2. Legendre's theorem on zeros of ternary quadratic forms
3. Cassels' theorem on small zeros of quadratic forms
4. Hasse-Minkowski theorem, the local-to-global principle


 The topic for the Spring 2013 semester was Introduction to the Arithmetic of Function Fields.
The seminar was led by Hiren Maharaj, who took us through parts of Stichtenoth's famous book.




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