### Welcome Message

The summer tutorial program offers some interesting mathematics to those of you who will be in the Boston area
during July and August. The tutorials will run for six weeks, meeting twice or three times per week in the
evenings (so as not to interfere with day time jobs). The tutorial will start early in July or late in June,
and run to mid August. The precise starting dates and meeting times will be arranged for the convenience
of the participants once the tutorial roster is set.
The format will be much like that of the term-time tutorials, with the tutorial leader lecturing in the
first few meetings and students presenting later on. Unlike the term-time tutorials, the summer tutorials
have no official Harvard status: you will not receive either Harvard or concentration credit for them.
Moreover, enrollment in the tutorial does not qualify you for any Harvard-related perks (such as a place to
live). However, the Math Department will pay each Harvard College student participant a stipend of
approximately , and you can hand in your final paper from the tutorial for your junior paper
requirement for the Math Concentration.

The topics and leaders of the tutorials this summer are:

## Representation Theory and Quantum Mechanics (Justin Campbell)

In classical mechanics, one can simplify many problems by imposing certain symmetries, which are efficiently expressed as groups acting on the space of physical states. Quantum mechanics distinguishes itself from classical mechanics in part by the principle of superposition, which says that states can be added to one another. More generally, states can be combined in linear combinations with coefficients which are complex (as opposed to real) numbers, and therefore form a complex vector space. When a symmetry group acts on the system it gives the state space the structure of a complex group representation, a very well-understood mathematical object.

## Binary Quadratic Forms and Class Field Theory (Zijian Yao)

You can sign up for a tutorial only by emailing me at
lurie@math.harvard.edu. Please indicate in your email a first and second choice of the tutorials you are
interested in taking. Please email me by noon, Monday, May 8.
Enrollment priority will be given to math concentrators. In the past summer tutorials have filled up quickly.
If you have further questions about any given topic, contact the tutorial leaders via e-mail.
Please contact me if you have questions about the administration of the tutorials.

Yours,
Jacob Lurie