ICTS

Title: Dissipation and mixing: from turbulent flows to weak solutions Abstract: 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...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

​ ​ ​ ​ ​​ Title: Why We Explore? Abstract: 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...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

Title : Principles of Evolutionary Overdesign and Underperformance Abstract : 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...more

Title: The Evolutionary Enigma of Sex Abstract: 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...more

Title: Exact Solution Of Decaying Turbulence Abstract: 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...more

Duality has a long history in physics going back to the electromagnetic symmetry discovered by Dirac in 1931 and to the duality symmetry of the two-dimensional Ising model of statistical mechanics discovered by Kramers and Wannier in 1941. By now there are many extensions and generalizations of...more

Title : Statistical Mechanics of Mutilated Sheets and Shells Abstract : Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, a precursor of general relativity characterized by a dimensionless coupling...more

Title: A Century after Heisenberg: Discovering the World of Simultaneous Measurements of Noncommuting Observables. Abstract: One hundred years after Heisenberg’s Uncertainty Principle, the question of how to make simultaneous measurements of noncommuting observables lingers. I will survey one...more