When: 4:30 pm – 5:30 pm, April 23
Who: Prof. Schapire, who is a professor in the department of Computer Science and specializes in theoretical and applied machine learning.
Title: How to Play Repeated Games
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.
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
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.
Check out the slides of yesterday’s awesome colloquium on “Cool theorems proved by undergraduates” by Prof. Ken Ono from Emory University! :D
When: 5:45 pm – 6:45 pm, April 2nd (coming Wednesday)
Where: Fine 314
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.
Come Meet Professor Dunham, visiting professor and author of Journey Through Genius, this Thursday at 6 in the Butler Private Dining Room!
Sign up for “Meet Your Professor Dinner” here: https://wass.princeton.edu/pages/viewcalendar.page.php?makeapp=1&cal_id=1720
William Dunham is visiting Princeton this semester and teaching a Freshman Seminar titled “The Great Theorems of Mathematics.” He is a historian of mathematics who has spoken at scores of institutions — e.g., Harvard, Penn, Swarthmore — and written multiple books on the subject — e.g., Journey Through Genius(1990), Euler: The Master of Us All (1999), and The Calculus Gallery (2005). Except for the weather, he’s very much enjoying his term at Princeton, where he’s addressed the Mathematics Colloquium and given the 2014 Pi Day talk to the Math Club. And he’s thrilled to be part of this “Meet Your Professor” dinner.
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.
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).