Previous Conferences & Workshops

This concerns recent work with P. Corvaja in which we relate the Hilbert Property for an algebraic variety (a kind of axiom linked with Hilbert Irreducibility, relevant e.g. for the Inverse Galois Problem) with the fundamental group of the variety...

https://www.ias.edu/math/wam/2016/schedule

By the mid 1920s, Emmy Noether had made fundamental contributions to commutative algebra and to the theory of invariants. Her crowning achievement from this period was "Noether's Theorem," establishing deep connections between conserved quantities...

A single result of Noether's is widely credited in physics papers as fundamental to the modern way of approaching physics. Two basic ideas are those of symmetry on the one side and the notion of quantities such as energy preserved under flows on the...

Given a non-isotrivial elliptic curve $E$ over $K = \mathbb F_q(t)$, there is always a finite extension $L$ of $K$ which is itself a rational function field such that $E(L)$ has large rank. The situation is completely different over complex function...

A distinct covering system of congruences is a finite collection of arithmetic progressions to distinct moduli \[ a_i \bmod m_i, 1 m_1 m_2 \cdots m_k \] whose union is the integers. Answering a question of Erdős, I have shown that the least...

I will show that the groups of mixed 3-manifolds containing arithmetic hyperbolic pieces and the groups of certain noncompact arithmetic hyperbolic $n$-manifolds ($n > 3$) are not LERF. The main ingredient is a study of the set of virtual fibered...

The discrete Fourier transform is a widely used tool in the analysis of Boolean functions. One can view the Fourier transform of a Boolean function $f:\{0,1\}^n \to \{0,1\}$ as a distribution over sets $S \subseteq [n]$. The Fourier-tail at level $k...

Around 1990, Joe Silverman wrote a series of three articles on the variation of canonical height in families of elliptic curves. I will discuss connections between these results and dynamical systems on $\mathbb P^1$ (and an associated Berkovich...