ICTS

In this talk, aimed at non-specialists, I’ll describe the geometric questions in the 19th century that led to the geometric theory of residual intersections, from oddities such as “How many conics in the plane are tangent to 5 given conics?” to central topics such as the Riemann-Roch theorem and...more

The quest for efficient algorithms is central both to theoretical computer science and to the practice of computing, but the metrics used in the two areas are different: theoreticians usually evaluate algorithms by their worst-case performance, whereas practitioners are more interested in empirical...more

The ergodic theory of Lyapunov exponents, initiated by the work of Furstenberg and Kesten at the dawn of the 1960s, has been a remarkably active field of mathematics over all these decades and, through the works of Oseledets, Pesin and many, many others, found extremely important applications in...more

Rigid disks falling under the effect of gravity, such as coins in water or confettis in air, may exhibit a large variety of paths: they may fall vertically, follow planar zigzags, tumble, etc. The selection of these paths depends on the disk’s inertia with respect to the surrounding fluid, on its...more

Solving the two-body problem in General Relativity has been crucial in observing gravitational waves from binary systems composed of black holes and neutron stars, and inferring their astrophysical and cosmological properties. I will review the theoretical groundwork that has enabled these major...more

I will give a pedagogical introduction to the modern theory of nuclear forces, Quantum Chromo Dynamics (QCD), a theory of quarks and gluons. I will also discuss the history and results from the collisions of heavy ions at ultra relativistic energies, which appears to have created a new phase of...more

Lecture 1 : Mathematics of Machine Learning: An introduction Date & Tim e: Tuesday, 12 February, 11:30 Abstract : Machine learning is the sub-field of computer science concerned with creating programs and machines that can improve from experience and interaction. It relies upon mathematical...more

How can physicists be so audacious as to declare all we see, hear and feel is from gravitational instability of quantum fluctuations in ultra-early universe fields encoded in energy-density phonons? Answer: the data reveals it, most precisely by our Planck cosmic microwave background (CMB) team...more

While the laws of quan tum mechanics have remained unchanged and have passed all tests for the last eighty-five years, new discoveries about the exotic states that they allow, “entanglement”, and ideas from quantum information theory, have greatly changed our perspective, and some believe that a “...more

A hundred years ago, Einstein wondered about a good description of the spectrum of disordered systems in the emerging quantum theory. Although a full mathematical answer is still missing, a lot of progress has been made to describe chaotic behavior of waves in quantum mechanics Download Postermore