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
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.
We study the strategic advantages of following rules of thumb that bundle different games together (called rule rationality) when this may be observed by one’s opponent. We present a model in which the strategic environment determines which kind of rule rationality is adopted by the players. We apply the model to characterize the induced rules and outcomes in various interesting environments. Finally, we show the close relations between act rationality and “Stackelberg stability” (no player can earn from playing first). Refreshments available at 3:30 p.m.
Peretz (2013) showed that, perhaps surprisingly, players whose recall is bounded can correlate in a long repeated game against a player of greater recall capacity. We show that correlation is already impossible against an opponent whose recall capacity is only linearly larger. This result closes a gap in the characterisation of min-max levels, and hence also equilibrium payoffs, of repeated games with bounded recall.
This paper characterizes the ordinal utilities over the bounded infinite streams of payoffs that satisfy the time-value of money principle and an additivity property, and those that in addition are impatient. Building on this characterization, the paper introduces the concept of optimization that is robust to small imprecision in the specification of the preference, and proves that the set of feasible streams of payoffs of a finite Markov Decision Process admits such a robust optimization.
A sound legal infrastructure is critical to the development of the Israeli economy. In its absence, business people and private persons alike face difficulties in planning their actions. All too often they are obliged to turn to the courts of law. However, in the absence of a proper infrastructure, those do not themselves have the necessary tools to resolve the disputes. The matters at issue are not marginal. They have long-lasting consequences for the economy. The number of publicly-traded companies listed in Tel-Aviv Stock Exchange sank from 657 in 2008 to 461 in March 2016.