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)
Abstract:
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
Program:
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
Manchester Building (Hall 2), Hebrew University Jerusalem
Additive combinatorics enable one to characterize subsets S of elements in a group such that S+S has small cardinality. We are interested in linear analogues of these results, namely characterizing subspaces S in some algebras (mostly extension fields) such that the linear span of the set S^2 of products st, for s,t in S, has small dimension. We shall present a linear analogue of a theorem of Vosper which says that under the right conditions, a sufficiently small dimension for S^2 implies that S has a basis of elements in geometric progression.
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
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.
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.
