Title: Algebraic Geometry in an arbitrary variety of algebras and Algebraic Logic
Abstract: I will speak about a system of notions which lead to interesting new problems for groups and algebras as well as to reinterpretation of some old ones.
Title: Character values on compact simple Lie groups
Abstract: This work is part of a joint project with Aner and others to find upper bounds for values of irreducible characters in two related settings: compact simple Lie groups and finite groups of Lie type. I will discuss the first case, presenting bounds of the form
$$|\chi(g)| = O(\chi(1)^\alpha),$$
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"
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
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.