Penn Undergraduate Math Society
Welcome to PUMS! We are a student run organization dedicated to promoting mathematics on Penn's campus. We organize various events throughout the year to give students a taste of not only the theoretical aspect of math but also its various application in life. If you are interested in becoming part of the Penn math family, please join our listserv, where you'll receive notices of upcoming events and talks, math department happenings, and information from corporate recruiters. If you're interested in getting involved planning events with the PUMS board, please contact us.
Upcoming Events
Math Department Pizza Mixer
Monday, September 29, 2014 at 4:30 pm
4th floor math lounge, DRL
Come by the annual math department/PUMS pizza mixer for food, conversation, and mingling with faculty, grad students, and your fellow undergraduates.
Undergraduate Majors Fair
Thursday, October 16, 2014 from 10:30 am to 2:30 pm
Hall of Flags, Houston Hall
Faculty members and upperclassmen will be at the math department table to talk about the math undergraduate experience at Penn.
Past Talks
James Haglund
Wednesday, November 20, 2013 at 4:30 pm
Patricia Cahn
Friday, November 8, 2013 at 3:00 pm
DRL A5
TITLE: How to Recognize Wallpaper
ABSTRACT: There are exactly 17 types of wallpaper. More precisely, a wallpaper pattern is a pattern in the plane with two independent directions worth of translational symmetry. We say two patterns are the same if they have the same symmetries. By folding the pattern so that corresponding points are identified, we get a space called a quotient orbifold. Some familiar orbifolds include the torus, the Klein bottle, the Mobius strip, and the billiard table--that is, a rectangle with mirrors on its boundary. We'll use orbifolds to understand why there are only 17 different wallpaper patterns.
Clay Shonkwiler (University of Georgia)
Wednesday, October 30, 2013 at 4:30 pm
TITLE: Unlocking the geometry of polygon space by taking square roots
ABSTRACT: A polygon is a simple object: it consists of some number of points connected (in order) by line segments. Despite that simplicity, many real-world objects like robot arms, polymers, or images can be modeled by polygons. In applications it's usually not enough to handle just one polygon at a time, though: we don't only want to consider one rigid robot arm or one single polymer, we want to understand the possible motions of the robot arm or to say how likely this particular polymer's configuration is among all possible polymer configurations.
To get a handle on these questions, we need to understand the space of all possible polygons with a given number of edges and ideally find nice coordinates on this space so that we know how to move around. This turns out to be fairly easy in the case of a robot arm that doesn't form a loop, but surprisingly tricky in the case of "ring" polymers which do close up.
This talk will describe how to take the square root of a polygon and why this is an amazingly useful thing to do if you want to understand the geometry of polygon space. We will then apply that understanding to find optimal reconfigurations, to recognize contours, and to produce surprisingly mesmerizing GIFs.
Brett Frankel
Tuesday, October 22, 2014 at 4:30 pm
DRL 4C4
I will talk about quadratic forms in Z, a very old topic in algebraic number theory, and topographs, a relatively new tool for visualizing them due to Conway.
Past Events
Spring Faculty Dinner
Wednesday, April 23, 2014 at 8:00 pm
Pattaya, 4006 Chestnut St
Dinner with Professor Andreea Nicoara. RSVP at the Facebook event.
Pre-Putnam Pasta Party
Friday, December 6, 2013 at 9:00 pm
Harnwell College House, 14th floor lounge
If you're signed up to take the Putnam exam on December 7, come carb up with the Penn Undergrad Math Society the night before the six-hour exam! (Math competitions are serious business.) There will be good company, possibly a movie, and lots and lots of pasta. If you're not taking the Putnam, join us anyway! Facebook event here.
Fall Faculty Dinner
Friday, November 15, 2014 at 7:30 pm
Sotto, 151 S 24th St
Dinner with Patricia Cahn, Zachary Scherr, and Vedran Sohinger. RSVP at the Facebook event (must be a member of Math@Penn).