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Andres Caicedo
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Andres Caicedo

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The thesis of Madame Sinh

The thesis of Hoàng Xuân Sính [1], one of Grothendieck's PhD students, dealt with what we call today 2-groups, called by her gr-categories. Her thesis is somewhat legendary, being a source of many results, but essentially unavailable to consult. But today I found someone has put it online! (It is hand-written :-)

http://w5.mathematik.uni-stuttgart.de/fachbereich/Kuenzer/Kuenzer/sinh.html

She received the Ordre des Palmes Académiques [2] for her contribution to the development and scientific cooperation between France and Vietnam.

[1] https://vi.wikipedia.org/wiki/Ho%C3%A0ng_Xu%C3%A2n_S%C3%ADnh (in Vietnamese!)
[2] http://comments.gmane.org/gmane.science.mathematics.categories/2227
Thesis of Hoàng Xuân Sính "Gr-catégories" Scans (pdf) Chapter I · Chapter II · Chapter III (part a) · Chapter III (part b). "Gr-catégories strictes", Acta Mathematica Vietnamica 3 (2), p. 47-59, 1978, scans (pdf). "Catégories de Picard restreintes", Acta Mathematica Vietnamica 7 (1), p.
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Celebrating Mathematical Reviews 75th Anniversary: Even before the first issue of MR appeared, there were more than 700 subscribers and 350 reviewers. #MR75
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QR method and eigenvalues

to illustrate the course of numerical analysis I currently give to my students, and I made (using scilab software) short animations like the gif below . The magnitude of matrix coefficients is represented by a color (black/deep blue for low values, red/white for hight ones) For a symmetric matrix the process tends quickly  to a diagonal matrix with values sorted in decreasing order on its diagonal which are the eigenvalues of A . The method also works for non-symmetric matrix but the process converge to a upper-triangular matrix , you can see it in my previous gif :

https://plus.google.com/+philipperoux/posts/cuXqSgp4CuA


#mathematics      #eigenvalue #matrix #scilab  

See also :
http://en.wikipedia.org/wiki/QR_algorithm
http://en.wikipedia.org/wiki/QR_decomposition
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Diophantine Equations

Tuesday, September 15, 2015 to Saturday, September 19, 2015

LMS-CMI Research School

Baskerville Hall
Hay-on-Wye, UK

Organizers: Tim Dokchitser (Bristol), Vladimir Dokchitser (Warwick)

The course will give an overview of the existing methods for investigating integer and rational solutions to Diophantine equations. It will include both the algebraic, analytic and model theory aspects of the subject. The course will take the format of three 6-hour mini-courses, supported by exercise classes.

1. Rational Points
A. Rational points on curves (Michael Stoll, Bremen)
B. Higher-dimensional varieties (Alexei Skorobogatov, Imperial)

2. Integral Points
A. Basic methods and solubility (Jennifer Park, McGill)
B. Analytic methods, (Trevor Wooley, Bristol)

3. Elliptic and modular curves
A. Elliptic curves (Tim Dokchitser, Bristol and Vladimir Dokchitser, Warwick)
B. Modularity (Andrew Granville, Montreal/UCL)
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(Via Noah Schweber on the FOM list)

First Announcement
2nd Workshop on Vaught's Conjecture
June 1-5, 2015 at the University of California - Berkeley
https://math.berkeley.edu/~schweber/vcc15/

Organized by:
 - Julia Knight (University of Notre Dame, Julia.F.Knight.1@nd.edu)
 - Antonio Montalbán (UC Berkeley, antonio@math.berkeley.edu)
 - Thomas Scanlon (UC Berkeley, scanlon@math.berkeley.edu)
 - Noah Schweber (UC Berkeley, schweber@math.berkeley.edu)

******

A workshop on the mathematics surrounding Vaught's Conjecture (on the number of isomorphism types of countable models of a countable complete first order theory) will be held at the University of California at Berkeley from June 1 to June 6, 2015. The first workshop on Vaught's Conjecture was held at the University of Notre Dame, in May of 2005. This workshop resulted in a number of new ideas and collaborations, some of which were published in a special issue of the Notre Dame Journal of Formal Logic. We hope that this second workshop will build on the success of the first. 


There will be tutorials by Uri Andrews, Su Gao, and Chris Laskowski; the invited speakers currently include:

Nate Ackerman
John Baldwin
Howard Becker
Samuel Coskey
Cameron Freer
Sy Friedman
Robin Knight
Paul Larson
David Marker
Ludomir Newelski
Richard Rast
Gerald Sacks
Slawomir Solecki
Ioannis Souldatos
A workshop on Vaught's Conjecture will be held at the University of California - Berkeley on June 1-5 of 2015, with support from the David and Lucile Packard Foundation. Organizers Julia Knight (Julia.F.Knight.1@nd.edu), Antonio Montalbán (antonio@math.uchicago.edu), Thomas Scanlon ...
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I hope they figure it out!
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I finally finished LaTeXing Lester Hill's paper (from the 1920s?) when he discovered error-correcting codes (which he called error-detecting codes, since he did not realize when they were). Essentially, he discovered (about 20 years before Hamming and Golay) cyclic MDS codes without knowing it, and never published his notes. 
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Binomial Coefficients and Villainy. Yesterday in his talk on elliptic genera [1] at "Flavors of Cohomology" [2] +Carl McTague had occasion to reference Moriarty's work on binomial coefficients

   http://www.mctague.org/carl/blog/2014/12/02/moriarty/

"His career has been an extraordinary one. He is a man of good birth and excellent education. Endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the binomial theorem, which has had a European vogue. On the strength of it he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him. But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his blood, which, instead of being modified, was increased and rendered infinitely more dangerous by his extraordinary mental powers. Dark rumours gathered round him in the university town, and eventually he was compelled to resign his chair and to come down to London, where he set up as an army coach."

[1] http://ncatlab.org/nlab/show/elliptic+genus
[2] http://www.mathematics.pitt.edu/node/1499
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Chandan Dalawat originally shared:
 
Elisenda Grigsby is the inaugural recipient of the AWM-Joan and Joseph Birman Research Prize in Topology and Geometry.
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QR method and eigenvalues
I'm currently working on a course of numerical analysis for my students, and I've realized (using scilab software) a short animation to help them understanding how the QR method works . The QR method is a fast algorithm for computing matrix eigenvalues . It is based on the QR decomposition of a matrix A : a factorization A=Q*R where R is upper-triangular and Q is orthogonal. The QR decomposition can be obtained from Gram-Schmidt process applied to column vectors of A. Then the QR method can be implemented in a very simple way :
compute QR decomposition of A
replace A by R*Q
repeat until R be sufficiently
close to a upper-triangular matrix
In the gif below you can visualize the behavior of matrix coefficients : the absolute value of each cell is represented by a color (black/deep blue for low values, red/white for hight ones) and you can see that quickly the matrix tends to be upper-triangular with values sorted in decreasing order on its diagonal which are the eigenvalues of A . The explanation is that at each step of the algorithm , the new matrix A is similar to the old one, because R*Q=Q'*A*Q, so they have the same spectrum which corresponds to diagonal values for a triangular matrix. Note also that  the sequence of Q matrix tends to a diagonal matrix  with +1 or -1 diagonal values, The error value is the norm || Id(i,j) - |Q(i,j)|  ||  is close to the relative error on eigenvalues, and is a good stopping criteria for the algorithm's loop.

#mathematics #eigenvalue #matrix     #scilab

See also :
http://en.wikipedia.org/wiki/QR_algorithm
http://en.wikipedia.org/wiki/QR_decomposition
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I will be taking a leave from BSU this coming academic year, and moving to Ann Arbor, to work as an Associate Editor at MathReviews.
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+Robert Lubarsky  Hi Bob. It should be fine. Reply to one of the automated emails informing you of the lateness, and indicate a realistic deadline now that the term is almost over. They should get back to you in case the new deadline can work. If not, well, these things happen.
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Summer school for graduate students in set theory at UC Irvine (July 6 - 17, 2015).  The theme is forcing and large cardinals, the instructors are Brent Cody (VCU), Monroe Eskew (VCU), and Spencer Unger (UCLA).
 https://gssst2015.wordpress.com/ 

Masters or PhD students with the appropriate background (or their advisors), please contact Sean Cox (details at the link above).  US citizens and permanent residents are fully covered. 
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kinda tempted to go....
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Jíři Matoušek died earlier this week, after a long illness.  Jirka was an inspirational researcher in discrete and computational geometry and topology, with seminal results on many different topics, including geometric range searching, discrepancy theory, derandomization, linear programming, metric embeddings, and algorithmic topology. He was also the author of several beautifully written textbooks and monographs.

János Pach reports that Jirka continued to work on his newest book through the last day of his life.

He will be sorely missed.
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