SPRING 2021

 

 15 Apr 2021 

  K. V. Shajesh

  Direction of friction on
  wheels of a car

[Video]

SPRING 2021

[1 April seminar is cancelled]

8 April 2021

Borzu Toloui

The Descriptor Picture of Quantum Mechanics

(Part 3 -- conclusions)

Video 3  (starts at 20th minute)

[2 pm, zoom link at the top]

Borzu suggests these papers for further insights:

• https://arxiv.org/pdf/quant-ph/9906007.pdf
• https://arxiv.org/pdf/quant-ph/0104033.pdf
• https://arxiv.org/pdf/2012.11189.pdf
• https://arxiv.org/pdf/2001.09646.pdf
• https://arxiv.org/pdf/quant-ph/0609085.pdf
• https://arxiv.org/pdf/1109.6223.pdf

SPRING 2021

18 and 25 March 2021

Borzu Toloui

The Descriptor Picture of Quantum Mechanics
(Part1 and Part 2)

[Video 1]  [Video 2]

Here is the link to a relevant paper: 

https://arxiv.org/pdf/2012.11189.pdf

[For basics on quantum computing see Lomonaco's "Roseta Stone"]

Spring 2021

 11 Mar 2021

 Revival of the seminar! 

  A general chat + a possible talk:

 Jerzy Kocik

 On a certain discrete matrix group

  

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.