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).
Related Articles
(Board) Game Night
Hey Nullset! You totally missed me, riiiight? =) Well missed me or not, here I am, and proud to announce the next (Board) Game Night. Are you excited? I’m excited. If you’re not, you’re silly. Start being excited. Anyways, the next (B)GN will be… drumroll please… When: Friday, October 4th at 9 pm Where: Fine […]
Undergraduate Colloquium
THE NASH PROBLEM FOR ARC SPACES Wednesday Oct 2nd Fine 214 6:00 pm Abstract: In a 1968 preprint, John Nash asked some very interesting questions about the family of all arcs on algebraic or analytic surfaces and hypersurfaces. I illustrate these questions using the examples of the surfaces (xy=z^n) and (x^2+y^3=z^4). I plan to end […]
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 […]