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Series: SIAM Student Seminar

We develop a stochastic control system from a continuous-time
Principal-Agent model in which both the principal and the agent have
imperfect information and different beliefs about the project. We
attempt to optimize the agent’s utility function under the agent’s
belief. Via the corresponding Hamilton-Jacobi-Bellman equation we
prove that the value function is jointly continuous and satisfies the
Dynamic Programming Principle. These properties directly lead to the
conclusion that the value function is a viscosity solution of the HJB
equation. Uniqueness is then also established.

Series: Stochastics Seminar

Given a random word of size n whose letters are drawn independently

from an ordered alphabet of size m, the fluctuations of the shape of

the corresponding random RSK Young tableaux are investigated, when both

n and m converge together to infinity. If m does not grow too fast and

if the draws are uniform, the limiting shape is the same as the

limiting spectrum of the GUE. In the non-uniform case, a control of

both highest probabilities will ensure the convergence of the first row

of the tableau, i.e., of the length of the longest increasing

subsequence of the random word, towards the Tracy-Widom distribution.

Series: Analysis Seminar

We describe how time-frequency analysis is used to analyze boundedness
and Schatten class properties of pseudodifferential operators and
Fourier integral operators.

Wednesday, September 9, 2009 - 13:00 ,
Location: Skiles 114 ,
Amy Novick-Cohen ,
Technion ,
Organizer: John McCuan

Grain boundaries within polycrystalline materials are known to be governed by motion by mean curvature. However, when the polycrystalline specimen is thin, such as in thin films, then the effects of the exterior surfaces start to play an important role. We consider two particularly simple geometries, an axi-symmetric geometry, and a half loop geometry which is often employed in making measurements of the kinetic coefficient in the motion by mean curvature equation, obtaining corrective terms which arise due to the coupling of grain boundaries to the exterior surface. Joint work with Anna Rotman, Arkady Vilenkin & Olga Zelekman-Smirin

Series: Other Talks

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Series: ACO Student Seminar

In 1969, Gomory introduced the master group polyhedron for pure integer programs and derives the mixed integer cut (MIC) as a facet of a special family of these polyhedra. We study the MIC in this framework, characterizing both its facets and extreme points; next, we extend our results under mappings between group polyhedra; and finally, we conclude with related open problems. No prior knowledge of algebra or the group relaxation is assumed. Terminology will be introduced as needed. Joint work with Ellis Johnson.

Series: Research Horizons Seminar

Additive combinatorics is a relatively new field, with
many diverse and exciting research programmes. In this talk I will discuss
two of these programmes -- the continuing development of
sum-product inequalities, and the unfolding progress on
arithmetic progressions -- along with some new results proved by me and my
collaborators. Hopefully I will have time to mention some nice research
problems as well.

Series: PDE Seminar

Multicomponent reactive flows arise in many practical applicationssuch as combustion, atmospheric modelling, astrophysics, chemicalreactions, mathematical biology etc. The objective of this work isto develop a rigorous mathematical theory based on the principles ofcontinuum mechanics. Results on existence, stability, asymptotics as wellas singular limits will be discussed.

Series: Geometry Topology Seminar

Series: Combinatorics Seminar

Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application of LLL is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d \le 2^k/e other clauses then such a formula has a satisfying assignment. Recently, a randomized algorithm to efficiently construct a satisfying assignment was given by Moser. Subsequently Moser and Tardos gave a randomized algorithm to construct the structures guaranteed by the LLL in a very general algorithmic framework. We will address the main problem left open by Moser and Tardos of derandomizing their algorithm efficiently when the number of other events that any bad event depends on is possibly unbounded. An interesting special case of the open problem is the k-CNF problem when k = \omega(1), that is, when k is more than a constant.