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Tbilisi Analysis & PDE Seminar

Past seminars

Past seminars


Seminar on March 8

Speaker: Prof. Dr. Pavel Exner,Doppler Institute for Mathematical Physics and Applied Mathematics;

https://gemma.ujf.cas.cz/~exner/personal.html

The title of the lecture: “Product formulae related to Zeno quantum dynamics”

Abstract: We present a new class of product formulae which involve a unitary group generated by a positive self-adjoint operator and a continuous projection-valued function. The problem is motivated by quantum description of decaying systems, in particular, the Zeno effect coming from frequently repeated measurements. Applied to it, the formula expresses the dynamics of such a system. An example of a permanent position ascertaining leading to the effective Dirichlet condition is given.

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Recorded talk N/A

Seminar on February 22

Speaker: Prof. Paata Ivanishvili,North Carolina State University (NC), USA;

https://sites.google.com/view/paata

The title of the lecture: “Rademacher type and Enflo Type Coincide”

Abstract: Pick any finite number of points in a Hilbert space. If they coincide with vertices of a parallelepiped then the sum of the squares of the lengths of its sides equals the sum of the squares of the lengths of the diagonals (parallelogram law). If the points are in a general position then we can define sides and diagonals by labeling these points via vertices of the discrete cube {0,1}n. In this case the sum of the squares of diagonals is bounded by the sum of the squares of its sides no matter how you label the points and what n you choose. In a general Banach space we do not have parallelogram law. Back in 1978 Enflo asked: in an arbitrary Banach space if the sum of the squares of diagonals is bounded by the sum of the squares of its sides for all parallelepipeds (up to a universal constant), does the same estimate hold for any finite number of points (not necessarily vertices of the parallelepiped)? In the joint work with Ramon van Handel and Sasha Volberg we positively resolve Enflo's problem. Banach spaces satisfying the inequality with parallelepipeds are called of type 2 (Rademacher type 2), and Banach spaces satisfying the inequality for all points are called of Enflo type 2. In particular, we show that Rademacher type and enflo type coincide.

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Recorded talk N/A

Seminar on February 8

Speaker: Prof. Michael Ruzhansky,Queen Mary University of London;

https://ruzhansky.org/

The title of the lecture: “Nonharmonic operator analysis”

Abstract: In this talk we will give a survey of our recent works on developing the nonharmonic symbolic calculus. This has applications to various questions for non-self-adjoint operators as well as for operators on manifolds with (or without) boundaries.

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Recorded talk N/A

Seminar on January 25

Speaker: Prof. Leonid Parnovski,Department of Mathematics, University College London, UK

http://www.homepages.ucl.ac.uk/~ucahlep/

The title of the lecture: “Floating mats and sloping beaches: spectral asymptotics of the Steklov problem on polygons”

Abstract: I will discuss asymptotic behaviour of the eigenvalues of the Steklov problem (aka Dirichlet-to-Neumann operator) on curvilinear polygons. The answer is completely unexpected and depends on the arithmetic properties of the angles of the polygon.

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Recorded talk N/A

Seminar on January 11

Speaker: Prof. Maria J. ESTEBAN, CEREMADE (CEntre de REcherche en MAthématiques de la DÉcision, French for Research Centre in Mathematics of Decision), Paris Dauphine University, 

https://www.ceremade.dauphine.fr/~esteban/MJEpage-engl.html

The title of the lecture: “Magnetic interpolations inequalities in dimensions 2 and 3”

Abstract: In this talk I will present some results concerning magnetic inequalities, similar to Gagliardo-Nirenberg inequalities, but involving magnetic operators. We will first consider the case of a general magnetic field where general results will be proved, but without much concrete information. Then, in the particular cases of constant or Aharonov-Bohm magnetic fields, we will be able to make those results more precise and get better estimates, or even complete information, about the best constants in the inequalities, or about the optimal extremals.

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Recorded talk N/A

Seminar on December 14

Speaker: Prof. Ari Laptev, Department of Mathematics, Imperial College London, http://wwwf.imperial.ac.uk/~alaptev/

The title of the lecture: “Magnetic rings”

Abstract: We study functional and spectral properties of perturbations of a magnetic second-order differential operator on a circle. This operator appears when considering the restriction to the unit circle of a two dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove some Hardy-type inequalities and sharp Keller-Lieb-Thirring inequalities.

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Recorded talk: https://youtu.be/DEs7IWzOyKs

Seminar on November 30

Speaker: Prof. Mikhail Sodin, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, https://en-exact-sciences.tau.ac.il/profile/sodin

The title of the lecture: “Fourier uniqueness and non-uniqueness pairs”

Abstract: Motivated by a remarkable discovery by Radchenko and Viazovska and by a recent work by Ramos and Sousa, we find conditions sufficient for a pair of discrete subsets of the real axis to be a uniqueness or a non-uniqueness pair for the Fourier transform. These conditions are not too far from each other. The uniqueness theorem can be upgraded to the frame bound and an interpolation formula, which in turn produce an abundance of Poisson-like formulas. This is a report on a joint work in progress with Aleksei Kulikov and Fedor Nazarov.

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Recorded talk: https://youtu.be/D9G3Sp8CkLQ

Seminar on November 16

Speaker: Prof. Kristian Seip, Norwegian University of Science and Technology, https://www.ntnu.edu/employees/kristian.seip

The title of the lecture: “Fourier interpolation with the zeros of the Riemann zeta function”

Abstract: Originating in work of Radchenko and Viazovska, a new kind of Fourier analytic duality, known as Fourier interpolation, has recently been developed. I will discuss the underlying general duality principle and present a new construction associated with the non-trivial zeros of the Riemann zeta function, obtained in joint work Andriy Bondarenko and Danylo Radchenko. I will emphasize how the latter construction fits into the theory of the Riemann zeta function.

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Recorded talk: Play recording (58 mins)







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გაწევრიანდი
ჩვენი სოციალური ქსელი
UG
კონტაქტი
მისამართი: 77ა, მ. კოსტავას ქუჩა, თბილისი, 0171, საქართველო ტელ: 2 55 22 22; info@ug.edu.ge, ug@ug.edu.ge
სასარგებლო ბმულები
ყველა უფლება დაცულია © 2018, საქართველოს უნივერსიტეტი