Principia: The Princeton Undergraduate Mathematics Journal

Principia is officially accepting submissions! Visit our brand new website at www.pumj.org to view submission guidelines.

We are also looking for advertisers! More information can be found here:

http://www.pumj.org/advertising

Principia announcement on webpage of Princeton’s Office of Undergraduate Research:

https://undergraduateresearch.princeton.edu/news/principia-now-accepting-submissions-spring-issue

Grad school info session, Friday, May 9

What: info session on applying to graduate schools.
Where: Fine common room
When: Friday 5/9, 3:30pm (a.k.a. tea time!)
Seniors: If you can make it, please let me know! We will are mainly be sharing our experiences with the application process.
Non-seniors: If you’re interested at all in applying to graduate school, you should come and learn from our experiences. Bring questions!

 

Undergraduate Colloquium, Wednesday, May 7th

We will be having a colloquium this coming Wednesday at 5 pm in Fine 214. The speaker will be Prof. Gang Tian who specializes in geometric analysis. Check out his profile/wikipedia page here: http://en.wikipedia.org/wiki/Gang_Tian
The title of the talk will be “Conic spherical metrics”. Here is the abstract:
 I will discuss the problem of constructing spherical structures on 2-sphere with prescribed conic angles and its connection to geometric stability. In the end, I will briefly discuss higher dimensional analogue of this problem.
Hope to see you there!

Undergraduate Colloquium, Monday, April 28

The next colloquium will be this coming Monday, 4/28, given by Prof. Yakov Sinai. It will be at 5pm in Fine 322. He will be talking about deterministic chaos and here is the abstract:

Deterministic chaos is a property of deterministic dynamics. I shall explain main properties of chaotic dynamics and give some example of chaotic dynamical systems.

Prof. Sinai is known for his work in dynamic systems. As many of you may have heard, he received the Abel Prize, which is often described as the mathematician’s Nobel Prize, not long ago. Check out his wikipedia page if you are interested!http://en.wikipedia.org/wiki/Yakov_Sinai

Undergraduate Colloquium, Wednesday April 23

When: 4:30 pm – 5:30 pm, April 23
Where: Fine 214
Who: Prof. Schapire, who is a professor in the department of Computer Science and specializes in theoretical and applied machine learning.
What:  
Title: How to Play Repeated Games
Abstract:

This talk will describe a simple, general algorithm for learning to play any matrix game against an unknown adversary.  The algorithm can be shown never to perform much worse than the best fixed strategy, even if selected in hindsight.  Moreover, because of the algorithm's moderate resource requirements, it can be used even when working with extremely large game matrices.  Taken together, these properties make the algorithm a good fit for a range of machine-learning applications, some of which will be discussed, for instance, to the problem of learning to imitate the behavior of an "expert" while attempting simultaneously to improve on the expert's performance.

Undergraduate Colloquium, Wednesday April 9th

When: 5:00 pm – 6:00 pm, April 9th (coming Wednesday)
Where: Fine 214
Who: Prof. Adam Levine, who specializes in low-dimensional topology (and he only joined Princeton this academic year!) You can check out some details here:https://www.math.princeton.edu/news/home-page/mathematics-department-welcomes-new-faculty

What:
Title: Knot Concordance
Abstract: Concordance is the study of which knots in three-dimensional space can be realized as the boundaries of embedded disks in four dimensions, a question that was first introduced by Princeton’s Ralph Fox and John Milnor in the 1950s. This question is closely tied to many of the strange features of four-dimensional topology and is the subject of much current research. I’ll provide an overview of this subject and an introduction to some of the modern tools that have led to breakthroughs in our understanding.

Undergraduate Colloquium, Wednesday April 2nd

When: 5:45 pm – 6:45 pm, April 2nd (coming Wednesday)
Where: Fine 314
Who: Prof. Ken Ono, a professor from Emory University who specializes in number theory. You can check him out here: http://en.wikipedia.org/wiki/Ken_Ono
What: Title: Cool theorems proved by undergraduates

Abstract. I will explain some cool theorems in number theory that undergraduates
have proven in the last few years. This will include work on the distribution of
primes, number fields, and extensions if works by Euler-Jacobi-Nekrasov-Okounkov-Serre. Let me explain.