User:Vipul: Difference between revisions

Revision as of 18:35, 6 August 2026

I am Vipul Naik. I completed my B.Sc. (Hons) Math at Chennai Mathematical Institute and in Fall 2007, I began the Doctoral Program in Mathematics at the University of Chicago. I completed the program in December 2013. This wiki (on Group Properties) is my brainchild, and so far, I have been the principal contributor.

You can learn more about me at my personal website, vipulnaik.com.

Math formula tests:

$9^{\sqrt{7 + 2}} = 729$
$2^{7} - 1 = 127$
$2^{8 - 1} = 128$
$5^{1 + 2} = 125$
$\sqrt{7 + 2}!! + 4 = 724$

Notes for stuff I plan to expand

I'm putting notes here for stuff that I sort-of worked out but didn't want to start editing on the wiki.

APS theory

[Private Claude conversation](https://claude.ai/chat/5739d4ee-5781-42ba-85bc-6c133865184f)

=Wrapping up the finitely displaced, contrasaturated, etc. stuff

Contrasaturated of bounded defect, and rename existing result to point to that
Shortfall lemma that allows for converse given padding-saturation
Memberwise complemented normal sub-IAPS that combined with contrasaturated of bounded defect allows us to infer finite displacement

Asymptotics

Asymptotics, log log |G_n|, log log (#conjugacy classes(G_n)), relative to log n (Fekete), connect to Math Overflow problem on conjugacy classes and double logs. Lots of useful material in chat with Claude.

Automorphism APSes

Automorphism of polynomial rings, free groups, etc. Some useful material in chat with Claude.

Tight fit concept for APSes

For instance, generation by Levi subgroups. Search for tight fit in chat with Claude.

@@ Line 1: / Line 1: @@
-I am Vipul Naik. I have completed my B.Sc. (Hons) Math at [http://www.cmi.ac.in Chennai Mathematical Institute] and in Fall 2007, I began the Doctoral Program in Mathematics at the [http://www.math.uchicago.edu University of Chicago]. I completed the program in December 2013. This wiki (on Group Properties) is my brainchild, and so far, I have been the principal contributor.
+I am Vipul Naik. I completed my B.Sc. (Hons) Math at [http://www.cmi.ac.in Chennai Mathematical Institute] and in Fall 2007, I began the Doctoral Program in Mathematics at the [http://www.math.uchicago.edu University of Chicago]. I completed the program in December 2013. This wiki (on Group Properties) is my brainchild, and so far, I have been the principal contributor.
 You can learn more about me at my personal website, [http://www.vipulnaik.com vipulnaik.com].
@@ Line 10: / Line 10: @@
 * <math>5^{1 + 2} = 125</math>
 * <math>\sqrt{7 + 2}!! + 4 = 724</math>
+==Notes for stuff I plan to expand==
+I'm putting notes here for stuff that I sort-of worked out but didn't want to start editing on the wiki.
+===APS theory===
+[Private Claude conversation](https://claude.ai/chat/5739d4ee-5781-42ba-85bc-6c133865184f)
+====Wrapping up the finitely displaced, contrasaturated, etc. stuff===
+* Contrasaturated of bounded defect, and rename existing result to point to that
+* Shortfall lemma that allows for converse given padding-saturation
+* Memberwise complemented normal sub-IAPS that combined with contrasaturated of bounded defect allows us to infer finite displacement
+===Asymptotics===
+Asymptotics, log log |G_n|, log log (#conjugacy classes(G_n)), relative to log n (Fekete), connect to [https://mathoverflow.net/questions/92120/double-log-ratio-of-number-of-conjugacy-classes-to-order-of-group-in-infinite-si Math Overflow problem on conjugacy classes and double logs]. Lots of useful material in chat with Claude.
+===Automorphism APSes===
+Automorphism of polynomial rings, free groups, etc. Some useful material in chat with Claude.
+===Tight fit concept for APSes===
+For instance, generation by Levi subgroups. Search for tight fit in chat with Claude.