M. Sayeh: time

21 March 2019

Mohammad Sayeh
Time and the hazardous F-word

This will be a non-mathematics seminar on time, freedom, and related issues.  I understand we need to review I. Kant, Bergson, etc. before the meeting. 

From http://www.math.is.tohoku.ac.jp/english/about/laboratories.html 

28 Feb 2019
7 Mar 2019

Don Redmond 

Evaluating the Riemann zeta function

Here are Don's notes that he kindly shares with us (+ his description):

There is some notes on a version of Euler's early attempts (Euler and the Basel Problem). Then there is the set of notes on the actual evaluation of zeta(2n). Finally, there are some notes on generating functions, which I am sending along because they include the details on some of the properties of Bernoulli numbers.

eulerbasel.doc       zeta(2n).doc       gen fct.doc

You need to download the files before opening to see the equations. 

14 and 21 Feb 2019

Jerzy Kocik

Taming 1 - 2 +3 - 4 + 5 -  ... 
   and other Dirichlet series


Cf: Shanks transformation.  -- No, not the same...

7 Feb 2019

This week the seminar is cancelled due to external circumstances...

Kalpa: Josephus

31 January

Kalpa Madhava
Josephus Problem

Mohammad: Time

29 Nov 2018

Mohammad Sayeh
Time and Freedom

Cancelled due to external factors....

Lakshika: quadratic forms

Pythagorean triples, Wikipedia

1 and 8 Nov 2018

Lakshika Gunawardana 
Quadratic forms and representations
Part 1 1nd 2



Here are some universal forms from Lakshika (click to display).

(Recall that the quadruple in bold letters turned out to be false)




And here is the Plimpton 322 with Pythagorean triples.  Written about 1800 BCE.

John: sequential covering designs

18 and 25 October

John McSorley
What is a sequential covering design?  Come and find out...

Part 1 and 2

Quaternions: 175th anniversary

175th anniversary

of discovery^* of quaternions 

i² = j² = k² = -1

16 October 1843

Brougham Bridge, Dublin

William Rowan Hamilton

We celebrated appropriately the event by consuming a large amount of pizza prepared for us by Quatros

(Nomen-omen -- as noticed by Mohammad S.)

*) If you think "discovery" should be replaced by "invention" or else  -- please feel free to argue in the comments section.

After party...

Kalpa: rolling balls

From pages of J. Baez 

27 Sep and 4 , 11 Oct 2018

Kalpa Madhawa
Octonions and the rolling ball 

(Three parts)



Extra materials
Books suggested by Kalpa:

• Travian Dray:  The Geometry of the Octonions 
• John Hortan Convey:  On Quaternions and Octonions 

See also the paper and the video

• J. Baez and J. Huerta: G2 and the rolling balls 
• J. Baez: Lecture on Youtube

And here are suggestions from Terry-Ann:

• Youtube: on Octonions
• brief video of her stating that Octonions relate to particle physics, (without much explanation)

Shajesh: topological insulators

From Wikipedia

6 , 13, 20 September, 2018 

K.V. Shajesh  (Physics)  
Towards understanding topological insulators in a classical setting 

1. Lagrangian
2. Boundary conditions
3. Optical properties

2017

11 Oct  2017 
Mohammad Sayeh
The residue number system and applications

2017 SPRING 

4 May 2017
Jerzy Kocik
From circles to gears and back again 
-- on Stern-Brocot trees, Apollonian crowns, and related wonders 
(with Zeta function in the background).

27 Apr 2017
Shajesh Kuloth
Divergence theorem across delta-functions

13, 19 Apr 2017
Zeid Ghalyoun
A Primer on Eisenstein Series (two parts)

30 Mar, 6 Apr 2017
Mohammad Sayeh
Optimization with Collective Neurons 
(see also Hopfield's ealy work: 1982Hopfield ,  1984Hopfield, 1985Hopfield, 1986Hopfield .

23 Feb and 3, 8, 22 Mar 2017
Borzu Toloui
Game Theory and Quantum Mechanics: Deriving the Born Rule (4 parts)
Below are the links for the references once again. 

• Deutsch's original paper of 1999:  https://arxiv.org/pdf/quant-ph/9906015.pdf
• A more extensive study of the decision theoretic result and its philosophical implications: https://arxiv.org/pdf/quant-ph/0211104.pdf
• The constructor theory version of it that incorporates the result in the new approach to physics that is being developed: https://arxiv.org/pdf/1507.03287.pdf
• On the problem of testing physical theories, especially different versions of quantum theory: https://arxiv.org/pdf/1508.02048.pdf
• And finally, here are a set of video lectures by Deutsch on quantum mechanics and quantum computing: http://www.quiprocone.org/Protected/DD_lectures.htm
• On You Tube (lower quality):  https://www.youtube.com/playlist?list=PL4cl2VeMbE330GKLkYIE8UBrrYdp8L9mR

2, 9, 15 Feb 2017
John Mcsorley
Gentle introduction to Game Theory (3 parts)

26 Jan 2017
Jerzy Kocik
Chebyshev, Lucas and Fibonacci polynomials by matrices

19 Jan 2017
Just coffee and gossip