# Techmath - Math Seminars in Israel[ Submit event ]

*Abstract:*

For every irreducible reductive dual pair (G, G’) in Sp(W), R. Howe proved the existence of an isomorphism between the spaces R(G) and R(G’), where R(G) is the set of infinitesimal equivalence classes of irreducible admissible representations of \tilde{G} which can be realized as a quotient of the metaplectic representation. As proved by Harish-Chandra, all the representations appearing in the correspondence have a character, and this character parametrize entirely the representation. In particular, one way to study the Howe’s duality is to understand the transfer of the characters. In 2000, T. Przebinda introduced the Cauchy-Harish-Chandra integral and conjectured that the correspondence of characters should be obtained via this map. In my talk, after recalling in detail Harish-Chandra’s character theory and Howe’s duality theorem, I am going to introduce carefully the Cauchy-Harish-Chandra integral and explain at the end in which cases the conjecture had been proved, and in particular say few words about my last paper on the transfer of characters of discrete series representations of the unitary groups in the equal rank case.

Link to the zoom meeting: https://technion.zoom.us/j/95771480969

*Abstract:*

A common observation in data-driven applications is that data has a low intrinsic dimension, at least locally.Thus, when one wishes to work with data that is not governed by a clear set of equations, but still wishes to perform statistical or other scientific analysis, an optional model is the assumption of an underlying manifold from which the data was sampled.This manifold, however, is not given explicitly but we can obtain samples of it (i.e., the individual data points).In this talk, we will consider the mathematical problem of estimating manifolds from a finite set of samples, possibly recorded with noise.Using a Manifold Moving Least-Squares approach we provide an approximant manifold with high approximation order in both the Hausdorf sense as well as in the Riemannian metric (i.e., a nearly isometry).In the case of bounded noise, we present an algorithm that is guaranteed to converge in probability when the number of samples tends to infinity.The motivation for this work is based on the analysis of the evolution of shapes through time (e.g., handwriting or primates' teeth) and we will show how this framework can be utilized to answer scientific questions in paleontology and archaeology.

*Announcement:*

The 'What Is' seminar returns!

The next 'What Is' talk will be given by Eran Igra on:The Schwarzian Derivative.

The 'What is' seminar is by grad students, for grad students. All talks will be at an introductory level. Bring your own pizza and beer.

*Abstract:*

Join Zoom Meeting https://us04web.zoom.us/j/2331841631?pwd=dlUxeXFmVlY4REFEdHBUZTkzM0hDQT09

Meeting ID: 233 184 1631

Passcode: 4NGauG

**Advisor: **Prof. Agnon Yehuda

**Abstract: **The irrotational ow of an incompressible homogeneous inviscid uid is a three dimensional problem. Mild-slope type equations reduce the three- dimensional ow problem description to a two-dimensional one by assuming a vertical structure to the velocity components. The mild-slope assumption states that the change in the water depth over a wavelength is small. In the classi- cal mild slope equations the vertical prole is constructed based on a uniform depth approximation. The dierent versions dier in the parameter utilized to formulate the equation and the order of expansion of the small parameter. A new long-wave limit equation is derived for which the vertical prole is constructed based on a constant bottom slope approximation. This increases the order of the bottom derivatives in the equation while maintaining the same order and structure. The vertical prole is developed by use of a polar coordinate system as opposed to a Cartesian coordinate and leads to an improved dispersion relation as well. The equation is simulated numerically for several benchmark problems with known analytical solutions. The results of the polar-cartesian mild slope equa- tion simulations are compared to the extended shallow water equation which shares a similar dispersion relation and expansion order. 1

*Announcement:*

A Workshop on Geometry and Optimization, in memory of Professor Victor Zalgaller, is scheduled to take place **on December 9, 2020**, via Zoom, in the Department of Mathematics of the Technion -- Israel Institute of Technology, under the auspices of the Center for Mathematical Sciences.

Organizing Committee: Michael Khanevsky, Simeon Reich and Alex Zaslavski

**The list of confirmed speakers:**

**Mark Agranovsky**, Bar-Ilan University,*On integrable domains and hypersurfaces***Misha Gromov**, IHES and New York University,*TBA***Bo'az Klartag**, Weizmann Institute of Science,*Steiner point and the problem of chasing convex bodies***Russell Luke,**Universitaet Goettingen,*TBA***Roman Polyak**, the Technion - IIT,*Nonlinear Equilibrium vs. LP for Optimal Allocation of Limited Resources***Vladimir Shikhman**, TU Chemnitz,*On nondegenerate M-stationary points for sparsity constrained nonlinear optimization***Alexander Solynin**, Texas Tech University,*When Analysis needs Geometry: How I worked with V.A. Zalgaller***Oliver Stein**, Karlsruhe Institute of Technology, "*A general branch-and-bound framework for global multiobjective optimization*"

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