Q:

How can I avoid widows and orphans after displayed equations? 

Edit:  The original title of this question was "How can I avoid widows and orphans with the geometry package?"   However, as egreg pointed out, the geometry package was not the cause of the problem.   So, I have corrected the title. 
I am writing my dissertation.   My university specifies the page margins and absolutely forbids widows and orphans.   To avoid the latter, I have set both clubpenalty and widowpenalty to 10000.   I am using the geometry package to set the margins.   As the following example shows (or, at least, does when I run pdfLaTeX), this can create widows and orphans.   I've tried using geometry with various options, such as including or ignoring this or that.   How can I keep to the required margins without creating widows and orphans? 
\documentclass{article}
\usepackage[lmargin=1.5in,rmargin=1.0in,tmargin=1.0in,bmargin=1in]{geometry}
\usepackage{lipsum}

\widowpenalty = 10000
\clubpenalty = 10000

\begin{document}

\lipsum

This text is boring and repetitive. 

This text is boring and repetitive. 

This text is boring and repetitive.   However, it is easy to see that
\[x^n + y^n = z^n\]
has no solutions for $n \geq 3$.  This text is boring and repetitive.   This text is boring and repetitive. 

This text is boring and repetitive. 

This text is boring and repetitive. 

\end{document}

A:

The geometry package has nothing to do with widows and orphans.  In your example a widow is created because of the display.  Some remedy can be applied, but only when the text of your document is in final form. 
For example, adding a line to an "almost full" long paragraph may avoid an orphan or a widow
Some long paragraph that ends almost flush right.\looseness=1

or conversely trying to shorten a long paragraph that doesn't quite fill the last line
Some long paragraph that doesn't fill the last line.\looseness=-1

Other known tricks are adding some words to a paragraph, or cutting some. 
The correct parameter to set for "avoiding" orphans is
\makeatletter
\@clubpenalty=10000
\makeatother
\clubpenalty=10000 % initial value

because LaTeX uses \@clubpenalty to reinstate \clubpenalty after it has changed it to 10000 in some occasions. 
A final comment: your institution forbids club and widow lines, but forces you to use a page format that's simply awful and unreadable. :( 

A:

The displayed equation is not counted as part of the paragraph in the context of widows and orphans.  You can forbid a page break after the displayed equation by setting
\postdisplaypenalty=10000

