Video Lectures

The goal of these lectures is to present the fundamentals of Simpson’s correspondence, generalizing classical Hodge theory, between complex local systems and semistable Higgs bundles with vanishing Chern classes on smooth projective varieties.

Tidal disruption events — where an unfortunate star is destroyed by a previously quiescent supermassive black hole — offer a unique probe of the low mass end of the supermassive black hole population. Recent observational advances have lead to the...

The fields of computer science and game theory both trace their roots to the first half of the 20th century, with the work of Turing, von Neumann, Nash, and others. The 21st century has seen many fruitful points of contact between these two fields...

The goal of these lectures is to present the fundamentals of Simpson’s correspondence, generalizing classical Hodge theory, between complex local systems and semistable Higgs bundles with vanishing Chern classes on smooth projective varieties.

Let q,Q be two integral quadratic forms in m less than n

variables. One can ask when q can be represented by Q - that is,

whether there exists an n×m-integer matrix T such that Q∘T=q.  Naturally, a necessary condition is that such a representation...

In the Calculus of Variations, convexity plays a seemingly irreplaceable role.

For vectorial problems, however, for good reasons a whole zoo of its generalizations was introduced. It ranges  from notions based on very classical

observation over...

In this talk we will construct (approximate) locally list decodable codes from high dimensional expanders (HDXs).

Last week we saw that locally list decoding is a powerful tool from coding theory. We also got a subspace-based construction of...

The interstellar medium (ISM) is a turbulent, multi-phase, magnetic environment. It is home to vastly different gas phases, from cold, dense clouds to hot, tenuous plasma. Magnetic fields thread this interstellar environment, helping to sculpt...

One of the primary goals of the mathematical analysis of algorithms is to provide guidance about which algorithm is the “best” for solving a given computational problem. Worst-case analysis summarizes the performance profile of an algorithm by its...