Harvard Mathematics Department : Summer Tutorials 2015

Archived Summer Tutorials:

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 tutorial 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 $700, and you can hand in your final paper from the tutorial for you junior paper requirement for the Math Concentration.
The topics and leaders of the tutorials this summer are:

Representation Theory of Finite Groups (Justin Campbell)
Combinatorial Game Theory (Erick Knight)
Knots and Links (Yi Xie and Boyu Zhang)

A description of the topics are below. You can sign up for a tutorial only by emailing me at [email protected]. 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 11. Places are filled on a first-come, first-served basis, but with priority being given to math concentrators. In the past, some 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.

Jacob Lurie

The topic and leader of tutorial this summer are:

Justin Campbell: Representation Theory of Finite Groups:

Representation theory is, roughly speaking, the use of linear algebra to study nonlinear algebraic objects such as groups. Group representations are not only studied for their own sake, but also have numerous applications in geometry, number theory, and physics. In this tutorial we will prove the main results about representations of finite groups using Wedderburn's theory of semisimple algebras. Finite groups being very concrete objects, we will see many examples and applications of the theorems.

Erick Knight: Combinatorial Game theory:

Combinatorial Game theory is sometimes referred to as the theory of "games of no chance". The games that will be studied are games with no random element and no hidden information. The most well known game that falls under this umbrella is NIM, but the tutorial will talk about both very general theory of such games, and apply the theory to well-known or "well-known" games such as dots and boxes, fox and geese, and many others.

Yi Xie and Boyu Zhang: Knots and Links

Are the two knots in the picture the same? Suppose you have a tied shoe lace. Is it possible to untie it by adding a reversed knot on the top? The first question is answered by studying a knot invariant called "signature", and the second one by studying genus. It turns out that the theory of knot invariants is a rich and fruitful subject, and it has many connections with other fields such as 3-manifold topology, gauge theory, and physics.

Archive: Old Summer Tutorials, since 2001

Summer Tutorials:

Last update, 5/3/2014