# Special Mathematics Seminar

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Contact:

Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 237 in Sci. Bldg. A

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Schedule : Thursday January 24, 2019 (18:30 - 20.00) in room 207 of the Science Building A

Speaker : *Rafael Tiedra*

Title: Ruled strips with asymptotically diverging twisting

**Abstract : **
We consider the Dirichlet Laplacian in a two-dimensional strip composed of segments translated along a straight line with respect to a rotation angle with velocity diverging at infinity. We show that this model exhibits a "raise of dimension" at infinity leading to an essential spectrum determined by an asymptotic three-dimensional tube of annular cross section. If the cross section of the asymptotic tube is a disc, we also prove the existence of discrete eigenvalues below the essential spectrum. Joint work with David Krejcirik (Prague).

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Schedule : Thursday July 12, 2018 (18:30 - 20.00) in room 207 of the Science Building A

Speaker : *Francesco Buscemi* (Nagoya University)

Title: The Information-Disturbance Trade-Off in Quantum Theory

**Abstract : **
Heisenberg's "uncertainty relations" (HURs) are among those few ideas of modern science that found their way into common language. They are also among the most debated results since the inception of quantum theory. The reason for this is not to be found in their mathematical derivation, which is absolutely transparent, but rather in their interpretation. In this talk I will review HURs, the idea behind HURs, some problems with the original idea, and how a modern, information-theoretic approach can help in clarifying the whole matter. At the end of my talk, we will come to appreciate why uncertainty relations are so important to our understanding of nature and, at the same time, so problematic to be, 90 years since their first appearance, still at the center of heated scientific discussions.

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Schedule : Thursday June 28, 2018 (18:30 - 20.00) in room 207 of the Science Building A

Speaker : *Jeremy Faupin* (University of Lorraine, France)

Title: Scattering theory for dissipative quantum systems

**Abstract : **
In this talk, we will consider an abstract pseudo-hamiltonian given by a dissipative operator of the form H = H_V - i C*C, where H_V = H_0 + V is self-adjoint and C is a bounded operator. Such operators are frequently used to study scattering theory for dissipative quantum systems. We will recall conditions implying existence of the wave operators associated to H and H_0, and we will see that they are asymptotically complete if and only if H does not have spectral singularities on the real axis. For Schroedinger operators, the spectral singularities correspond to real resonances.
This is joint work with Juerg Froehlich.

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