הסמינר מתכנס בימי שלישי, בשעות 14:30-15:30, באולם -101

## השבוע

### Sloshing, Steklov and corners

The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.

## מפגשים בסמסטר אביב 2017

### המפגשים הבאים

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28 במרץ Some Fundamental Operator Relations in Convex Geometry and Classical Analysis Vitali Milman (Tel Aviv University)

The main goal of the talk is to show how some classical constructions in Geometry and Analysis appear (and in a unique way) from elementary and very simple properties. For example, the polarity relation and support functions are very important and well known constructions in Convex Geometry, but some elementary properties uniquely imply these constructions, and lead to their functional versions, say, in the class of log-concave functions. It turns out that they are uniquely defined also for this class, as well as for many other classes of functions. In this talk we will use these Geometric results as an introduction to the main topic which involves the analogous results in Analysis. We will start the Analysis part by characterizing the Fourier transform (on the Schwartz class in R^n) as, essentially, the only map which transforms the product to the convolution, and discuss a very surprising rigidity of the Chain Rule Operator equation (which characterizes the derivation operation). There will be more examples pointing to an exciting continuation of this direction in Analysis.

The results of the geometric part are mostly joint work with Shiri Artstein-Avidan, and of the second, Analysis part, are mostly joint work with Hermann Koenig.

The talk will be easily accessible for graduate students.

4 באפר Galois groups of local fields, Lie algebras and ramification Victor Abrashkin (U. of Durham)
25 באפר TBA Inna Entva-Aizenbud (BGU)
9 במאי TBA Jozsef Solymosi (UBC)
20 ביוני A fundamental group approach to the unit equation Ishai Dan-Cohen (BGU)

Over the course of the last 15 years or so, Minhyong Kim has developed a method for making effective use of the fundamental group to bound sets of solutions to hyperbolic equations; his method opens a new avenue in the quest for an effective version of the Mordell conjecture. But although Kim’s approach has led to the construction of explicit bounds in special cases, the problem of realizing the potential effectivity of his methods remains a difficult and beautiful open problem. In the case of the unit equation, this problem may be approached via motivic’’ methods. Using these methods we are able to describe an algorithm; its output upon halting is provably the set of integral points, while its halting depends on conjectures. This will be a colloquium-version of a talk that I gave at the algebraic geometry seminar here in November of 2015.

### המפגשים הקודמים

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21 במרץ Sloshing, Steklov and corners Yosif Polterovich (Université de Montréal)

The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.

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