ICTS

It seems likely that our universe contains a stochastic background of gravitational waves (GW), in some ways similar to the electromagnetic cosmic background radiation. In some frequency bands, this background is probably dominated by GW emission from "astrophysical" sources such as unresolved...more

When electrons are confined to two dimensions and exposed to a strong magnetic field, they give rise to an astonishing new world — one that defies our everyday intuition. In this realm, electrons capture quanta of magnetic field to transform into exotic particles known as composite fermions. These...more

In the original Matrix movie, the bulk of the human population lives not in the real world but inside a computer simulation called the Matrix. They are unable to detect this situation, except for the fact that certain agents can transcend the normal rules of physics. In this talk, I will explain...more

There is a well-known discrepancy in mathematical fluid mechanics between phenomena that we can observe and phenomena on which we have theorems. The challenge for the mathematician is then to formulate an existence theory of solutions to the equations of hydrodynamics which is able to reflect...more

Ideas of quantum field theory have completely changed the mathematical landscape of geometry and topology over the last 40 years. This has included new definitions (such as quantum field theoretic invariants of manifolds) and new problems (mirror symmetry) as well as modes for thinking about...more

Humanity faces real and present problems. Our resources to address these problems are limited. It’s easy to think, then, that we should devote ourselves to our most promising solutions. It’s easy, but it’s wrong. The great paradox of scientific research is that pure exploration – research into deep...more

The Atiyah Singer theorem is one of the great theorems of 20th century mathematics. It is a theorem which is at the interface of three different areas of Mathematics: Differential Equations, Differential Geometry and Topology. In this talk I will essentially describe the theorem and make some...more

For over a century, most biologists have been convinced that all aspects of biodiversity have been driven entirely by natural selection, with stochastic forces and mutation bias playing a minimal role. However, this is not the case at the molecular and cellular levels, where diverse traits scale...more

Understanding the selective forces maintaining sexual reproduction has been a long-standing question in evolutionary biology. The near universality of sex, in the face of its many costs, has been touted as one of the biggest open questions in the field, earning such labels as “mystery,” “enigma,”...more

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\mathbb C^d$ with random steps parametrized by $N...more