Video Lectures

Math in the Real World: More Than Just a Numbers Game

May 11, 2016

Sandi Peterson and Kathy Wengel

Mathematics has a vital role in shaping a product’s life, from research & development to manufacturing, and from marketing to supply chain. In this public lecture, Institute Trustee Sandi Peterson and Kathy Wengel, both Princeton alumnae, will...

video lecture

2016 Women in Mathematics

May 09, 2016

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

video lecture

Celebrating Emmy Noether

May 06, 2016

Georgia Benkart

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...

video lecture

Emmy Noether: breathtaking mathematics

May 06, 2016

Georgia Benkart

video lecture

Symmetry and conservation laws: Noether's contribution to physics

May 06, 2016

Karen Uhlenbeck

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...

video lecture

Rational curves on elliptic surfaces

May 05, 2016

Douglas Ulmer

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...

video lecture

The minimum modulus problem for covering systems

May 04, 2016

Bob Hough

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...

video lecture

NonLERFness of groups of certain mixed 3-manifolds and arithmetic hyperbolic $n$-manifolds

May 03, 2016

Hongbin Sun

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...

video lecture

Fourier tails for Boolean functions and their applications

May 03, 2016

Avishay Tal

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...

video lecture

Who Lost the Middle East?

April 29, 2016

Richard Murphy

What brought about the current chaos in the Middle East? Did the machinations of the Cold War exhaust the region leaving it unable to develop new relationships between governor and governed? As Americans, how much should we criticize our role or...