Video Lectures

I will discuss recent work with Harald Helfgott in which we establish roughly speaking that the graph connecting nn to n±pn±p with pp a prime dividing nn is almost "locally Ramanujan". As a result we obtain improvements of results of Tao and Tao...

The talk introduces the Kazhdan-Lusztig equivalence between the Kazhdan-Lusztig category of representations of affine algebra and category of modules over the quantum group.

I will report on a joint work in progress with K. Coulembier and V. Ostrik. We show that a symmetric tensor category in characteristic p>0 admits a fiber functor to the Verlinde category (semisimplification of Rep(Z/p)) if and only if it has...

Dr. Monica Vazirani is a professor at UC Davis.  She received her PhD from UC Berkeley in 1999, after which she had an NSF postdoc she spent at UC San Diego and UC Berkeley, as well as postdoctoral positions at MSRI and Caltech.  Dr. Vazirani's...

Algorithms make predictions about people constantly.  The spread of such prediction systems has raised concerns that algorithms may exhibit unfair discrimination, especially against individuals from minority groups.  While it's easy to speculate on...

I will discuss joint work with Olga Plamenevskaya studying symplectic fillings of links of certain complex surface singularities, and comparing symplectic fillings with complex smoothings. We develop characterizations of the symplectic fillings...

One of Alan Turing's most influential papers is his 1950 Computing machinery and intelligence, in which he introduces the famous "Turing test" for probing the nature of intelligence by evaluating the abilities of machines to behave as humans. In this...

A group is said to have bounded generation (BG) if it is a finite product of cyclic subgroups. We will survey the known examples of groups with (BG) and their properties. We will then report on a recent result (joint with P. Corvaja, J. Ren and U...

Powerful extragalactic radio sources hosted in galaxies come in all shapes, sizes, powers, and presumably ages.  What might a young or nascent powerful radio source look like?  The class of compact powerful extragalactic radio sources are defined to...

A new class of phase transitions has been recently studied in quantum many-body systems that are subject to measurements but not otherwise open to any external decoherence.  This phase transition arises from a competition between scrambling dynamics...