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Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

A motivating problem in number theory and algebraic geometry is to find
all integer-valued solutions of a polynomial equation. For example,
Fermat's Last Theorem asks for all integer solutions to x^n + y^n = z^n,
for n >= 3. This kind of problem is easy
to state, but notoriously difficult to solve. I'll explain a p-adic
method for attacking Diophantine equations, namely, p-adic integration
and the Chabauty--Coleman method. Then I'll talk about some recent
joint work on the topic.

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

The talk will include a crash course on infinite dimensional
topology, with applications to various topological properties of the
space of congruence classes of convex bodies in the Euclidean space.

Series: Research Horizons Seminar