Members’ Colloquium

The SAT (Boolean Satisfiability) problem asks whether a given logical formula on n Boolean variables has an assignment of true/false values to its variables that makes the formula true.  The P vs NP question is equivalent to asking whether SAT has a...

I'll give a brief introduction to o-minimality and how it can be used to prove asymptotic estimates for the number of rational points in definable sets. I'll then show how problems from various areas of mathematics can be reformulated as questions...

In 1947 John Von Neumann and Herman Goldstine, while developing the IAS computing machines, wrote a seminal paper on numerical errors in matrix computations. They suggested modeling the "computing noise" (coming from rounding errors, transcendental...

Consider a point mass traveling in a polygon. It travels in a straight line, with constant speed, until it hits a side, at which point it obeys the rules of elastic collision. What can we say about this? When all the angles of the polygon are...

The field of unlikely Intersections presents a robust paradigm for problems in which several subjects intermingle: arithmetic, o-minimality, and hodge theory. The goal of this talk will be to introduce some of those connections. My aim is to...

Persistence modules and their associated barcodes were intensively studied since the early 2000s with a view towards applied mathematics. Recently they have also found numerous applications in pure mathematics. We will discuss a few examples from...

Selmer groups are a cohomological tool used to reduce the task of finding solutions of certain diophantine equations to easier field and modular arithmetic. I'll explain how this works in down to earth terms and give some concrete applications...

Hel Braun (IAS member 1947-1948) was a mathematician who introduced approaches that continue to impact research today.  Braun's research contributions lie in three areas: classical number theory problems about integers, modular and automorphic forms...

Originally introduced as analogs of symmetric spaces for  groups over non-archimedian fields buildings have proven useful in various areas by now. In this talk I will introduce (Bruhat-Tits) buildings,  combinatorial toolkits to study them and their...

Erd\H{o}s unit distance problem asks the following: Let P

be a set of n distinct points in the plane, and let U(P)

denote the number of pairs of points in P that are at distance 1. How large can U(P) be? In 1946, Erd\H{o}s showed that for P=[n‾√]×[n‾√...