11 Mar 2021
Revival of the seminar!
A general chat + a possible talk:
Jerzy Kocik
On a certain discrete matrix group
Wednesday, March 10, 2021
Sunday, December 6, 2020
Autumn 2020
Our seminar takes a break till the next semester (January). Thank you everybody for participating! Please use this space for sharing comments and interesting or relevant items. Use comments or send me a material to be posted.
Happy physical, spiritual, and mental transition to 2021!
From now on we shall use a permanent zoom address; see below.
Note that the link is also displayed in the right margin column.
Thursdays 2pm for seminar, any time for a chat:
Meeting ID: 923 4934 3807, Passcode: 426631
You may also join by Skype for Business.
Saturday, November 14, 2020
Autumn 2020
19 Nov and 3 Dec 2020
K. V. Shajesh
Casimir Effect
Thursdays 2pm for seminar, any time for a chat:
Meeting ID: 923 4934 3807, Passcode: 426631
You may also join by Skype for Business.
Wednesday, November 4, 2020
Autumn 2020
5 and 12 Nov 2020
Jerzy Kocik
Integrality implies super-integrality and hyper-integrality
Part 2: Disks as vectors in Minkowski space, inversions, and conclusion of the proof.
See Apolloniana for some background
Recording of Part 1
Recording of Part 2
Part 1: Here are two warm-up problems (related, but not central):
Suppose 4 integers do not have a common factor, gcd(a,b,c,d)=1, and satisfy quadratic equation $$(a+b+c+d)^2 = 2\, (a^2+b^2+c^2+d^2)$$ Show that:
1. Exactly two of them are odd (easy)
2. The sum of any two can be written as a sum of two squares (a challenge)
Examples of solutions to the quadratic equation: (2,3,6,23), (2,3,15,38), (3,6, 14 47), (0,1,4,9), (11,14,15,89),...
Part 1: Here are two warm-up problems (related, but not central):
Suppose 4 integers do not have a common factor, gcd(a,b,c,d)=1, and satisfy quadratic equation $$(a+b+c+d)^2 = 2\, (a^2+b^2+c^2+d^2)$$ Show that:
1. Exactly two of them are odd (easy)
2. The sum of any two can be written as a sum of two squares (a challenge)
Examples of solutions to the quadratic equation: (2,3,6,23), (2,3,15,38), (3,6, 14 47), (0,1,4,9), (11,14,15,89),...
Wednesday, October 28, 2020
Autumn 2020
29 Oct 2020
Don Redmond
Algebra via geometry
Here are Don's notes for the seminar. (Version of 29 Oct 20)
Wednesday, October 21, 2020
Autumn 2020
22 Oct 2020
Jerzy Kocik
Quaternions and Alice in Wonderland
16 October was an anniversary of the discovery of quaternions. In celebration, let's have a rather informal conversation if quaternions indeed motivated Lewis Carroll tow describe the infamous 6 o'clock mad tea-party. For your convenience some material:
- Mad Tea Party -- Chapter VII of Carroll's book (must read! Just a few pages)
- Devlin's blog describing the claim (here is the extracted text)
- Bayley's text of 2009 (the origin of the claim), 6 pages
- Helena Pycior 1984 (the ultimate origin?), 22 pages
- The whole Carroll's text (if you want to recall it): Adobe or here.
NEW:
- Kalpa is sharing a book "Quaternion Fourier Transforms for Signal and Image Processing". He comments: First two chapters are easy to follow. Applications start from Chapter 4
Monday, October 12, 2020
Autumn 2020
Anjala Babu
Finding good quantum codes using the Cartan form
Here is Anjala's paper in Phys. Rev. A
And here is a Wiki entry on the Cartan decomposition.
Wednesday, September 30, 2020
Autumn 2020
1 and 8 Oct 2020
How to solve quaternionic quadratic equations.
Part 1 and 2.
Wednesday, September 16, 2020
Autumn 2020
17 and 24 Sep 2020
Jerzy Kocik
Taking square roots in higher dimensions
-- spins, polarization, and a little metaphysics
[Recording of part 1] [Recording Part 2]
Borzu shared the link with this cool video on related toy
and this 3D-printable file . Check it out!
See also Copernicus Theorem at Wolfram, at Cut-the-knot, at Mathematics.
Cf. Tusi couple.
Wednesday, September 9, 2020
Autumn 2020
K.V. Shajesh
A comment on
"Delayed Choice and Indeterminate Past"
by Mohammad Sayeh
by Mohammad Sayeh
Shajesh suggeted:
- Julian Schwinger: Quantum Mechanics: Symbolism of atomic measurement (Edited by Bertold-Georg Englert)
- Englert, Schwinger, and Scully "Is spin coherence like Humpty-Dumpty? I. Simplified treatment"
Tuesday, September 1, 2020
Autumn 2020
Mohammad Sayeh
Delayed Choice and Indeterminate Past
[Recording]
Papers suggested by Mohammad:
Wednesday, August 26, 2020
Resuming the seminar
27 Aug 2020
ZOOM link https://zoom.us/j/97579809995
An informal gathering.
We may discuss anything,
including the following books
(graphic novels on math):
Don Redmond suggests yet another graphic novel:
Hiroshi Yuki, Mika Hisaka:
Math Girls Manga, Volume 1
https://www.amazon.com/dp/0983951349
ZOOM link https://zoom.us/j/97579809995
An informal gathering.
We may discuss anything,
including the following books
(graphic novels on math):
1. Andrew and Jennifer Granville, Robert J. Lewis:
Prime Suspects: The Anatomy of Integers
and Permutations
(2019) https://www.amazon.com/dp/
2. Sydney Padua:
The Thrilling Adventures of Lovelace and Babbage:
The (Mostly) True Story of the First Computer
(2015) https://www.amazon.
3. Apostolos Doxiadis & Christos Papadimitriou:
Logicomix: An epic search for truth
(2009) https://www.amazon.com/
Prime Suspects: The Anatomy of Integers
and Permutations
(2019) https://www.amazon.com/dp/
2. Sydney Padua:
The Thrilling Adventures of Lovelace and Babbage:
The (Mostly) True Story of the First Computer
(2015) https://www.amazon.
3. Apostolos Doxiadis & Christos Papadimitriou:
Logicomix: An epic search for truth
(2009) https://www.amazon.com/
Don Redmond suggests yet another graphic novel:
Hiroshi Yuki, Mika Hisaka:
Math Girls Manga, Volume 1
https://www.amazon.com/dp/0983951349
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