# Pi Mu Epsilon Conference

# April 11-12 2014

Peter Engel Science Center

Saint John's University

## Invited Speaker: Dr. Hal Schenck (Univ of Illinois at Urbana-Champaign)

**The Mathematics of Google**

8 pm Friday, 11 April in Pellegrene Auditorium

How does Google sort through the roughly thirteen billion webpages

to find relevant sites? It turns out that the answer involves the

mathematics of linear algebra, which, roughly speaking, involves

solving systems of linear equations. Such systems are ubiquitous

in science and engineering. In this whirlwind talk, we'll learn

about Gaussian elimination, linear transformations and change of

basis, eigenvalues and eigenvectors. All of this leads to the

crown jewel: the page rank algorithm developed by Page and Brin

(while they were graduate students at Stanford!). If you have

not yet had a class in linear algebra, fear not--all the tools

needed will be developed in the talk**Warning: Higher Dimensions Alter Reality**11:30 am, Saturday 12 April in Pellegrene Auditorium

This talk will give an overview of the spectacular success of

algebraic methods in studying problems in discrete geometry and

combinatorics. First we'll discuss the face vector (number of

vertices, edges, etc.) of a convex polytope and recall Euler's

famous formula for polytopes of dimension 3. Then we'll discuss

graded rings, focusing on polynomial rings and quotients.

Associated to a simplicial polytope P (every face is "like" a

triangle) is a graded ring called the Stanley-Reisner ring, which

"remembers" everything about P, and gives a beautiful dictionary.

We'll sketch Stanley's solution to a famous conjecture using this

machinery. No prior knowledge of any of the terms above will be

assumed (or needed!) Take home bonus: the coolest counterexample

in all mathematics.

**Upcoming Conference Speakers**

- 2014 Hal Schenck
- 2015 Ami Radunskaya

**Former Conference Speakers**

- 2013 Annalisa Crannell (Videos: Friday's Lecture, Saturday's Lecture)
- 2012 Kenneth Millett
- 2011 William Dunham
- 2010 Claudia Neuhauser
- 2009 Joe Gallian
- 2008 (Conference cancelled due to weather)
- 2007 Carlos Castillo-Chavez
- 2006 Edward Burger
- 2005 Jennifer Quinn
- 2004 Frank Farris
- 2003 Colin Adams
- 2002 David Bressoud
- 2001 Underwood Dudley
- 2000 Sam Patterson
- 1999 Robert L. Devaney
- 1998 Richard Guy
- 1997 Ron Graham
- 1996 Frank Morgan
- 1995 Carl Pomerance
- 1994 Philip Straffin
- 1993 Thomas Banchoff
- 1992 Judith Grabiner
- 1991 Raymond Smullyan
- 1990 Joan Hutchinson
- 1989 Richard Askey
- 1988 Sherman Stein
- 1987 Reuben Hersh
- 1986 Peter Hilton
- 1985 I.N. Herstein
- 1984 Ruth Struik
- 1983 Joan Fisher Box, George Box
- 1982 Alfred Willcox (in conjunction with the North Central Section Meeting)
- 1981 Doris Schattschneider, Leonard Gillman, Don Koehler
- 1980 Mary Ellen Rudin
- 1979 Paul Halmos

**Lectures will be geared toward a general audience**

*Funding for travel to SJU Pi Mu Epsilon conference is provided by NSF grant DMS‐0846477 through the MAA Regional Undergraduate Mathematics Conferences program,http://**www.maa.org/RUMC*