Below is a suggested list of topics to help students choose something to speak about. We welcome ideas for other topics; these can be things for which you have some knowledge and would like to better understand by giving a talk, or things that you would like to learn from a peer. For speakers, your talks can be very general e.g. an overview of Fermat's last theorem, or very specific e.g. the proof of the Pólya-Vinogradov bound. We only ask that you keep in mind that everyone in the audience has different backgrounds.
Analytic Number Theory
What is…
… the prime number theorem?
… Pólya-Vinogradov?
… a Dirichlet L-function?
… the L-function of ___?
… the circle method?
… the Burgess bound?
Algebraic Number Theory
What is…
… Fermat’s Last Theorem?
… a regular prime?
… a Dirichlet L-function?
… the L-function of ___?
… a Galois Representation?
… the p-adic cyclotomic character?
… the p-adic Mandlebrot set?
… class field theory?
… the Langlands Program?
Arithmetic Geometry
What is…
… a motive?
… a toric variety?
… a Shimura Variety?
… a Dessin d'Enfant?
… étale cohomology?
… the Weil Conjecture(s)?
Other
What is…
… an orbifold?
... a Germain prime?
... the method of infinite descent?