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:

                                          Link to Zoom (click here)

Meeting ID: 923 4934 3807,   Passcode: 426631
You may also join by Skype for Business.

Autumn 2020

19 Nov and 3 Dec 2020

K. V. Shajesh

Casimir Effect

Recording of Part 1 

Recording of Part 2

Thursdays 2pm for seminar, any time for a chat:

                                          Link to Zoom (click here)

Meeting ID: 923 4934 3807,   Passcode: 426631

You may also join by Skype for Business.

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),...

Autumn 2020

29 Oct 2020

Don Redmond

Algebra via geometry

[recording]

Here are Don's notes for the seminar. (Version of 29 Oct 20)

Autumn 2020

22 Oct 2020

Jerzy Kocik

Quaternions and Alice in Wonderland

[recording]

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  

Autumn 2020

15 Oct 2020 

Anjala Babu
Finding good quantum codes using the Cartan form

[Recording]

Here is Anjala's paper  in Phys. Rev. A 

Here is the same text in Arxiv.  [pdf]

And here is a Wiki entry on the Cartan decomposition.

Autumn 2020

1 and 8 Oct 2020

Kalpa Madhava 

How to solve quaternionic quadratic equations.

Part 1 and 2.

• Recording of part 1.
• Recording of part 2.
• A few comments from Kalpa

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.

 

Autumn 2020

10 Sep 2020

K.V. Shajesh 

A comment on 

"Delayed Choice and Indeterminate Past"
by Mohammad Sayeh

[Recording]

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"

Autumn 2020

3 Sep 2020

Mohammad Sayeh

Delayed Choice and Indeterminate Past

[Recording]

 

Papers suggested by Mohammad:

Delayed choice 2015

Quantum erasure 2012 

Photon Delayed Choice 2006

Intermediate past 2013

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):

1.  Andrew and Jennifer Granville, Robert J. Lewis:
     Prime Suspects: The Anatomy of Integers
     and Permutations       
     (2019)  https://www.amazon.com/dp/0691149151


2.   Sydney Padua: 
      The Thrilling Adventures of Lovelace and Babbage:
      The (Mostly) True Story of the First Computer 
      (2015)   https://www.amazon.com/dp/0307908275/ 

3.    Apostolos Doxiadis & Christos Papadimitriou:
       Logicomix: An epic search for truth 
       (2009) https://www.amazon.com/gp/product/B0117S8JSS 

Don Redmond suggests yet another graphic novel:

       Hiroshi Yuki, Mika Hisaka:
       Math Girls Manga, Volume 1
       https://www.amazon.com/dp/0983951349

Mathematical Summer conversations 12

13 Aug 2020

John Joseph Marchetta 

Understanding non-intuitive repulsive forces from quantum vacuum


Recording