| Talk_id | Date | Speaker | Title |
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13343
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Tuesday 5/22
1:00 PM
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From Picard groups of hyperelliptic curves to class groups of quadratic fields
- From Picard groups of hyperelliptic curves to class groups of quadratic fields
- 05/22/2018
- 1:00 PM - 2:00 PM
- C304 Wells Hall
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Let C be a hyperelliptic curve defined over Q, whose
Weierstrass points are defined over extensions of Q of degree at most
three, and at least one of them is rational. Generalizing a result of
R. Soleng (in the case of elliptic curves), we prove that any line
bundle of degree 0 on C which is not torsion can be specialized into
ideal classes of imaginary quadratic fields whose order can be made
arbitrarily large. This gives a positive answer, for such curves, to a
question by Agboola and Pappas.
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13344
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Monday 6/11
4:10 PM
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Xinliang An, University of Toronto / National University of Singapore
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How to Make a Black Hole
- How to Make a Black Hole
- 06/11/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Xinliang An, University of Toronto / National University of Singapore
Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being. In this talk, with tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis and dynamical systems, we will prove that, through a nonlinear focusing effect, initially low-amplitude and diffused gravitational waves can give birth to a black hole region in our universe. This result extends the 1965 Penrose’s singularity theorem and it also proves a conjecture of Ashtekar on black-hole thermodynamics. Open problems and new directions will also be discussed.
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13347
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Wednesday 7/18
11:00 AM
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Christian Sadel, Pontificia Universidad Católica de Chile
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One-Channel Operators, a General Radial Transfer Matrix Approach and Absolutely Continuous Spectrum
- One-Channel Operators, a General Radial Transfer Matrix Approach and Absolutely Continuous Spectrum
- 07/18/2018
- 11:00 AM - 12:00 PM
- C304 Wells Hall
- Christian Sadel, Pontificia Universidad Católica de Chile
First I will introduce one-channel operators and their spectral theory analyses through transfer matrices solving the eigenvalue equation.
Then, inspired from the specific form of these transfer matrices, we will define sets of transfer matrices for any discrete Hermitian operator with locally finite hopping by considering quasi-spherical partitions.
A generalization of some spectral averaging formula for Jacobi operators is given and criteria for the existence and pureness of absolutely continuous spectrum are derived.
As applications we will mention certain cases of random operators with absolutely continuous spectrum (Anderson model on anti trees and partial anti-trees; random decaying shell-matrix potential).
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