Video Lectures

Nearest neighbor search for general symmetric norms via embeddings into product spaces

February 13, 2017

Ilya Razenshteyn

I will show a new efficient approximate nearest neighbor search (ANN) algorithm over an arbitrary high-dimensional *symmetric* norm. Traditionally, the ANN problem in high dimensions has been studied over the $\ell_1$ and $\ell_2$ distances with a...

video lecture

Discrete harmonic analysis and applications to ergodic theory

February 08, 2017

Mariusz Mirek

Given $d, k\in\mathbb N$, let $P_j$ be an integer-valued polynomial of $k$ variables for every $1\le j \le d$. Suppose that $(X, \mathcal{B}, \mu)$ is a $\sigma$-finite measure space with a family of invertible commuting and measure preserving...

video lecture

Noncommutative algebraic varieties, their properties and geometric realizations II

February 08, 2017

Dmitry Orlov

Continuation of Friday, Feb 3 minicourse. We will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories (quasi) coherent sheaves on usual algebraic varieties and their...

video lecture

Optimization in dynamical systems

February 07, 2017

Amir Ali Ahmadi

In recent years, there has been a surge of exciting research activity at the interface of optimization (in particular polynomial, semidefinite, and sum of squares optimization) and the theory of dynamical systems. In this talk, we focus on two...

video lecture

Local systems and the Hofer-Zehnder capacity

February 06, 2017

Alexandru Oancea

The Hofer-Zehnder capacity of a symplectic manifold is one of the early symplectic invariants: it is a non-negative real number, possibly infinite. Finiteness of this capacity has strong consequences for Hamiltonian dynamics, and it is an old...

video lecture

Strongly Refuting Random CSPs below the spectral threshold

February 06, 2017

Prasad Raghavendra

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable...

video lecture

Noncommutative algebraic varieties, their properties and geometric realizations

February 03, 2017

Dmitry Orlov

We are will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories of (quasi)coherent sheaves on usual algebraic varieties and their enhancements. We are going to talk about...

video lecture

Relative quantum product and open WDVV equations

February 02, 2017

Sara Tukachinsky

The standard WDVV equations are PDEs in the potential function that generates Gromov-Witten invariants. These equations imply relations on the invariants, and sometimes allow computations thereof, as demonstrated by Kontsevich-Manin (1994). We prove...

video lecture

Noncommutative algebraic varieties, their properties and geometric realizations

February 01, 2017

Dmitry Orlov

video lecture

Sketching and embedding are equivalent for norms

January 31, 2017

Alex Andoni

Sketching for distance estimation is the problem where we need to design a possibly randomized function $F$ from a metric space to short strings, such that for any points $x,y$ from the metric space, the "sketches" $F(x)$ and $F(y)$ are sufficient...