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Upcoming Seminars

WednesdayNov 22, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Alexander Elashvili Title:About Index of Lie AlgebrasAbstract:opens in new windowin html    pdfopens in new window
In my talk I plan to give overview of results about of index of biparaboic subalgebras of classical Lie algebras and formulate conjecture about asymptotic biheviar of lieandric numbers.
WednesdayNov 22, 201716:15
Special Guest LectureRoom 155
Speaker:Dalia TerhesiuTitle:The pressure function for infinite equilibrium Abstract:opens in new windowin html    pdfopens in new window

 Assume that $(X,f)$ is a dynamical system and $\phi$ is a real non negative potential such that the corresponding $f$-invariant measure $\mu_\phi$ measure is infinite.  Under assumptions of good inducing schemes, we give conditions under which the pressure of $f$ for a perturbed potential $\phi+s\psi$ relates to the pressure of the induced system term.
This extends some of Sarig's results to the setting of infinite "equilibrium states".
In addition, limit properties of the family of measures $\mu_{\phi+s\psi}$ as $s\to 0$ are studied and statistical properties (e.g. correlation coefficients) under the limit measure are derived. I will discuss several examples.
This is based on joint work with H. Bruin and M. Todd.

ThursdayNov 23, 201712:15
Vision and Robotics SeminarRoom 1
Speaker:Aviv GabbayTitle:Seeing Through Noise: Visually Driven Speaker Separation and EnhancementAbstract:opens in new windowin html    pdfopens in new window

Isolating the voice of a specific person while filtering out other voices or background noises is challenging when video is shot in noisy environments, using a single microphone. For example, video conferences from home or office are disturbed by other voices, TV reporting from city streets is mixed with traffic noise, etc. We propose audio-visual methods to isolate the voice of a single speaker and eliminate unrelated sounds. Face motions captured in the video are used to estimate the speaker's voice, which is applied as a filter on the input audio. This approach avoids using mixtures of sounds in the learning process, as the number of such possible mixtures is huge, and would inevitably bias the trained model.

In the first part of this talk, I will describe a few techniques to predict speech signals by a silent video of a speaking person. In the second part of the talk, I will propose a method to separate overlapping speech of several people speaking simultaneously (known as the cocktail-party problem), based on the speech predictions generated by video-to-speech system.

ThursdayNov 23, 201714:10
Geometric Functional Analysis and Probability SeminarRoom 155
Speaker:Naomi Feldheim Title:Persistence of Gaussian Stationary ProcessesAbstract:opens in new windowin html    pdfopens in new window

Consider a real Gaussian stationary process, either on Z or on R.
What is the probability that it remains positive on [0,N] for large N?

The relation between this probability, known as the persistence probability, and the covariance kernel of the process has been investigated since the 1950s with motivations stemming from probability, engineering and mathematical physics. Nonetheless, until recently, good estimates were known only for particular cases, or when the covariance kernel is either non-negative or summable.

In the first hour of the talk we will discuss new spectral methods which greatly simplify the analysis of persistence. We will then describe its qualitative behavior in a very general setting.

In the second hour, we will describe (very) recent progress. In particular we will show the proof of the "spectral gap conjecture'', which states: if the spectral measure vanishes on an interval containing 0 then the persistence is less then e^{-cN^2}, and this bound is tight if the measure is non-singular and compactly supported. 
Time permitting, we will also discuss "tiny persistence'' phenomena (of the order of e^{-e^{cN}}).

Based on joint works with Ohad Feldheim, Benjamin Jaye, Fedor Nazarov and Shahaf Nitzan.

MondayNov 27, 201714:30
Foundations of Computer Science SeminarRoom 155
Speaker:Yakov Babichenko Title:Informational Bounds on Approximate Nash EquilibriaAbstract:opens in new windowin html    pdfopens in new window

The talk will discuss informational lower bounds of approximate Nash equilibrium in two complexity models: Query Complexity and Communication Complexity.
For both models we prove exponential (in the number of players) lower bound on the complexity of computing ε -Nash equilibrium, for constant value of approximation ε .

TuesdayNov 28, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Yuanqing Cai Title:Weyl group multiple Dirichlet seriesAbstract:opens in new windowin html    pdfopens in new window

Weyl group multiple Dirichlet series are Dirichlet series in r complex variables which initially converge on a cone in C^r, possess analytic continuation to a meromorphic function on the whole complex space, and satisfy functional equations whose action on C^r is isomorphic to the Weyl group of a reduced root system. I will review different constructions of such series and discuss the relations between them.

WednesdayNov 29, 201711:15
Machine Learning and Statistics SeminarRoom 1
Speaker:Roy Lederman Title:Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)Abstract:opens in new windowin html    pdfopens in new window

Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. "hyper-molecules", the first mathematical formulation of truly continuously heterogeneous molecules, 2. The optimal representation of objects that are highly concentrated in both the spatial domain and the frequency domain using high-dimensional prolate spheroidal functions, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.

TuesdayDec 05, 201711:15
Mathematical Analysis and Applications SeminarRoom 1
Speaker:Victor Ivrii Title:Spectral asymptotic for Steklov’s problem in domains with edges (work in progress)Abstract:opens in new windowin html    pdfopens in new window
We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacle for deriving the second term
TuesdayDec 12, 201716:15
Seminar in Geometry and TopologyRoom 155
Speaker:Ary ShavivTitle:Tempered Manifolds and Schwartz Functions on ThemAbstract:opens in new windowin html    pdfopens in new window

Schwartz functions are classically defined as smooth functions such that they, and all their (partial) derivatives, decay at infinity faster than the inverse of any polynomial. This was formulated on $\mathbb{R}^n$ by Laurent Schwartz, and later on Nash manifolds  (smooth semi-algebraic varieties) by Fokko du Cloux and by Rami Aizenbud and Dima Gourevitch. In a joint work with Boaz Elazar we have extended the theory of Schwartz functions to the category of (possibly singular) real algebraic varieties. The basic idea is to define Schwartz functions on a (closed) algebraic subset of $\mathbb{R}^n$ as restrictions of Schwartz functions on $\mathbb{R}^n$.

Both in the Nash and the algebraic categories there exists a very useful characterization of Schwartz functions on open subsets, in terms of Schwartz functions on the embedding space: loosely speaking, Schwartz functions on an open subset are exactly restrictions of Schwartz functions on the embedding space, which are zero "to infinite order" on the complement to this open subset. This characterization suggests a very intuitive way to attach a space of Schwartz functions to an arbitrary (not necessarily semi-algebraic) open subset of $\mathbb{R}^n$.

In this talk, I will explain this construction, and more generally the construction of the category of tempered smooth manifolds. This category is in a sense the "largest" category whose objects "look" locally like open subsets of $\mathbb{R}^n$ (for some $n$), and on which Schwartz functions may be defined. In the development of this theory some classical results of Whitney are used, mainly Whitney type partition of unity (this will also be explained in the talk). As time permits, I will show some properties of Schwartz functions, and describe some possible applications. This is a work in progress.

TuesdayDec 26, 201711:15
Algebraic Geometry and Representation Theory SeminarRoom 155
Speaker:Eyal Subag Title:Algebraic Families of Harish-Chandra Modules and their ApplicationAbstract:opens in new windowin html    pdfopens in new window

I shall review the framework of algebraic families of Harish-Chandra modules, introduced recently, by Bernstein, Higson, and the speaker. Then, I shall describe three of their applications.

The first is contraction of representations of Lie groups. Contractions are certain deformations of representations with applications in mathematical physics.

The second is the Mackey bijection, this is a (partially conjectural) bijection between the admissible dual of a real reductive group and the admissible dual of its Cartan motion group.

The third is the hidden symmetry of the hydrogen atom as an algebraic family of Harish-Chandra modules.