Author Archives: Blair Wang

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.

Undergraduate Colloquium, Wednesday, 3/26

When: 5:30 pm – 6:30 pm, March 26th
Where: Fine 214
Who: Prof. Klainerman, who specializes in PDE and analysis
What:  Title: Are black holes real
Blackholes are precise mathematical solutions of the Einstein field equations of General Relativity. Some of the most exciting astrophysical objects in the Universe have been identified as corresponding to these mathematical Black Holes, but since no signals can escape their extreme gravitational pull, can one be sure that the right identification has been made?
I will show how this crucial issue of reality of Black Holes can be addressed by nothing more than pen and paper, those perennial tools of the mathematician. I will discuss three fundamental mathematical problems concerning Black Holes, intimately connected to the issue of their reality: rigidity, stability and collapse.

Undergraduate Colloquium, Monday Mar 3rd

When: 4.30 pm – 5.30 pm, March 3 (coming Monday)
Where: Fine 322
Who: Prof. Robert Gunning, who has been teaching advanced 215/217 sequence for the past two years. His research focuses on analysis 
What: here are the title and abstracts
 
Topic: What is a Riemann surface

The graph of a curve is a familiar construction in the real plane; the analogous construction for complex valued functions of a complex variable is a “curve” that is a 2-dimensional set in a 4-dimensional space. Such curves, aside from a few singularities, locally look just like pieces of the complex plane, so it is possible to carry out complex analysis on such “curves”, just as for the complex plane; but the global geometry introduces a rich and fascinating structure on these sets, called Riemann surfaces (following the work of B. Riemann).

Math Colloquium, Friday Feb. 21

We arranged with Prof. Conway a rescheduling of his colloquium! 
 
When: 4 pm – 5 pm, February 21 (coming Friday)
Where: Fine 224
Who: I don’t think I need to say more about Prof. Conway, but if you are interested in more details, please check wikipedia page here:
What: here are the title and abstracts
Two Subtle Theorems about Equilateral Triangles

In 1899 Frank Morley noticed that the points of intersection of the adjacent angle trisectors form an equilateral triangle. Since then, proofs of various levels of complexity have been given, and in this colloquium Professor Conway will present a surprisingly simple proof discovered by himself. In addition, Professor Conway will introduce a new theorem of himself on equilateral triangles and the subtle mathematics behind it.

Math Colloquium

When: 5 pm – 6 pm, February 17 (coming Monday)
Where: Fine 314
Who: Prof. Paul Yang, whose interest lies in differential geometry and geometric analysis
What: here are the title and abstracts
 
The isoperimetric problem on the Heisenberg

Abstract:

I will explain the geometry of a contact form in dimension three. The basic problem is to find the isoperimetric profile in the Heisenberg group. This variational problem is approached via a mean curvature equation. However this equation is not an elliptc equation in this low dimension, hence the problem remains largely open due to regularity issues.