Video Lectures

Fun with finite covers of 3-manifolds: connections between topology, geometry, and arithmetic

November 23, 2015

Following the revolutionary work of Thurston and Perelman, the topology of 3-manifolds is deeply intertwined with their geometry. In particular, hyperbolic geometry, the non-Euclidean geometry of constant negative curvature, plays a central role. In...

video lecture

Advances on Ramsey numbers

November 23, 2015

Jacob Fox

Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that "Every very large system contains a large well-organized subsystem." Ramsey numbers capture how very large...

video lecture

Geometric deformations of orthogonal and symplectic Galois representations

November 19, 2015

Jeremy Booher

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we would like to know if there exists a lift to characteristic zero with nice properties. In particular, we would like it to be geometric...

video lecture

Cohomology for computer science II

November 17, 2015

Alex Lubotzky

We will start with presenting the basic notions of (co)homomology of simplical complexes (which requires only basic linear algebra over the field of order 2) and then we will indicate its relevance for several topics in computer science and...

video lecture

The complex geometry of Teichmüller spaces and bounded symmetric domains I & II

November 17, 2015

Stergios Antonakoudis

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Welcome and Introduction

November 17, 2015

https://www.ias.edu/gr100 Albert Einstein’s general theory of relativity, a pillar of modern physics formulated 100 years ago, will be celebrated by the Institute for Advanced Study and Princeton University in a two-day conference, General...

video lecture

Cohomology for computer science

November 17, 2015

Alex Lubotzky

video lecture

The $\mathrm{SL}(2,\mathbb R)$ action on moduli space

November 16, 2015

Alex Eskin

There is a natural action of the group $\mathrm{SL}(2,\mathbb R)$ of $2 \times 2$ matrices on the unit tangent bundle of the moduli space of compact Riemann surfaces. This action can be visualized using flat geometry models, which allows one to make...

video lecture

How quaternion algebras over number fields are useful for creating compiler for a quantum computer?

November 16, 2015

Vadym Kliuchnikov

Solving the following problem is crucial when compiling for a quantum computer: given a finite set $G$ of elements of $SU(2)$, target element $U$ from $SU(2)$ and real number $\epsilon$ find $g_1,\dotsc, g_N$ from $G$ such that $\| g_1 \dotsm g_N -...

video lecture

THE ART OF DINING: Downton Abbey

November 13, 2015

Francine Segan

Join returning speaker Francine Segan and discover the elaborate etiquette, enchanting entertainments, and dishes Mrs. Patmore would have been proud to send to the table. Vivid descriptions of Lord Grantham-esque dinner parties, cotillions, and...