Manchester building, Hebrew University of Jerusalem, (Room 209)
There are by now several celebrated measure classification results to the effect that a measure is uniform provided it possesses sufficient "invariance" as quantified by stabilizer, entropy, or recurrence. In some applications, part of the challenge is to identify or construct measures to which these hypotheses apply.
Abstract: The motion planning problem of robotics leads to an interesting invariant of topological spaces, TC(X), depending on the homotopy type of X = the configuration space of the system. TC(X) is an integer reflecting the complexity of motion planning algorithms for all systems (robots) having X as their configuration space. Methods of algebraic topology allow to compute or to estimate TC(X) in many examples of practical interest. In the case when the space X is aspherical the number TC(X) depends only on the fundamental group of X. Read more about Michael Farber: "Robot motion planning and equivariant Bredon cohomology"
All talks will be given by Amnon Ta-Shma. 10:00-11:00 - The sampling problem and some equivalent formulations
11:30-12:30 - A basic "combinatorial" construction
14:00-14:45 - Algebraic constructions of randomness condensers
15:15-16:00 - Structured sampling
1. 10:00-11:00 - The sampling problem and some equivalent formulations. Abstract: We will first define Samplers, and the parameters that one usually tries to optimize: accuracy, confidence, query complexity
Real and complex Monge-Ampere equations play a central role in several
branches of geometry and analysis. We introduce a quaternionic version
of a Monge-Ampere equation which is an analogue of the famous Calabi
problem in the complex case. It is a non-linear elliptic equation of second
order on so called HyperKahler with Torsion (HKT) manifolds (the latter
manifolds were introduced by physicists in 1990's). While in full generality
it is still unsolved, we will describe its solution in a special case and some
How good is a forecaster? Assume for concreteness that every day the forecaster issues a forecast of the type "the chance of rain tomorrow is 30%." A simple test one may conduct is to calculate the proportion of rainy days out of those days that the forecast was 30%, and compare it to 30%; and do the same for all other forecasts. A forecaster is said to be _calibrated_ if, in the long run, the differences between the actual proportions of rainy days and the forecasts are small—no matter what the weather really was.
The National Health Insurance Law is operated through several economic mechanisms that are meant to implement its vision. In this lecture we will present the main flaws of some of these mechanisms and propose ways to fix them. The lecture will be in hebrew.
This paper analyzes the optimal assignment of objects which arrive sequentially to agents organized in a waiting list. Applications include the assignment of social housing and organs for transplants. We analyze the optimal design of probabilistic queuing disciplines, punishment schemes, the optimal timing of applications and information releases. We consider three efficiency criteria: the vector of values of agents in the queue, the probability of misallocation and the expected waste.
Topic: Endogenous Financial Networks: Efficient Modularity and Why Shareholders Prevent It (joint work with Jonathon Hazell) We consider systemic risk in financial networks, by examining the conflict of interest between debt- and equity-holders. Through trading, banks can diversify their idiosyncratic risks and avoid failures following small shocks. However, the resulting interdependencies can cause multiple failures after large shocks.
We study the simplest form of two-sided markets: one seller, one buyer and a single item for sale. It is well known that there is no fully-efficient mechanism for this problem that maintains a balanced budget. We characterize the quality of the most efficient mechanisms that are budget balanced, and design simple and robust mechanisms with these properties. We also show how minimal use of statistical data can yield good results. Finally, we demonstrate how solutions for this simple bilateral-trade problem can be used as a "black-box" for constructing mechanisms in more general environments.
I will present a new solution concept for multiplayer stochastic games, namely, acceptable strategy profiles. For each player \(i\) and state \(s\) in a stochastic game, let \(w_i(s)\) be a real number.
A common justification for boundedly rational expectations is that agents receive partial feedback about the equilibrium distribution. I formalize this idea in the context of the "Bayesian network" representation of boundedly rational expectations, presented in Spiegler (2015). According to this representation, the decision maker forms his beliefs as if he Öts a subjective causal model - captured by a directed acyclic graph (DAG) over the set of variables - to the objective distribution.