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
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.
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.
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).
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.
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.
Abstract: Communication complexity studies the amount of communication that needs to be exchanged by parties to solve a problem on a distributed
input. In this talk I will introduce communication complexity, and
discuss several basic results and applications. No prior background
will be assumed.
This coming week we are pleased to have Professor Christine Taylor at the colloquium. Professor Taylor whose interests include mathematical biology will be talking about links between game theory and evolutionary biology. Please note that the talk will be on Monday, in Fine 314.
Refreshments will be served. Hope to see you there!
MONDAY Nov.11th 6:00 pm Fine 314
The basic ingredients of Darwinian evolution, selection and mutation, are
very well described by simple mathematical models. In 1973, John Maynard
Smith linked game theory with evolutionary processes through the concept of
evolutionarily stable strategy. Since then, cooperation has become the
third fundamental pillar of evolution. I will discuss, with examples from
evolutionary biology and ecology, the roles played by replicator equations
(deterministic and stochastic) and cooperative dilemma games in our
understanding of evolution.