Emi L. Arima
earima @ math
MSB 2123

Euclid alone has looked on Beauty bare.
-Edna St. Vincent Millay




About me:
I'm a grad student in the Department of Mathematics at UC Davis. I did my undergrad at Bryn Mawr College in Bryn Mawr Pennsylvania. I received an A.B./M.A. in Math along with a concentration in International Economic Relations.

 Recent Talks:
Space curves and tangent planes
Graduate Student Topology & Geometry Conference 2009, University of Wisconsin - Madison
April 17, 2008

In 1980 Michael Freedman proved that for any simple, smooth, closed space curve with nonvanishing torsion, there are an even number of planes tangent to C at exactly three points. Throughout the 1980s several mathematicians including Banchoff, Gaffney and McCrory furthered Freedman's study of these triply tangent planes. The focus of my talk will be a paper of Ozawa published in 1985. Ozawa expands Freedman's work to consider simple smooth closed space curves with possibly vanishing torsion. A plane P is called a triple tangency of C if the total order of contact of P to C is three; thus a triple tangency can be one of three types depending on whether it is tangent to C at 3, 2 or 1 distinct points. The main concern of the paper is to find what relationships exist among the numbers of each type of triple tangency for a given space curve. I will present Ozawa's paper in the context of Freedman's work which preceded it. The presentation will include the results and a brief sketch of the proofs. In addition, I intend to address Freedman's related question: Does every generic smooth space curve have a triply tangent plane?

Ozawa, T: The Numbers of Triple Tangencies of Smooth Space Curves Topology, Vol. 24, No. 1 (1985), 1-13


Surgery and Dynamical Systems
Student Run Geometry/Topology Seminar, UC Davis
January 27, 2009

This talk is an introduction to the topological notion of surgery. I will give a brief explanation, with many pictures and even real-life examples, and draw a connection between surgery on surfaces and a 3-dimensional Lotka-Volterra model from dynamical systems.

Anoniou and Lambropoulou: Dynamical Systems and Topological Surgery arXiv:0812.2367 (2008)

 Teaching:
Fall 2009:
 Math B - Elementary Algebra
Office Hours:     T 1:30-2:30pm, F 2:00-3:00pm
Summer 2009:
 Math 12 - Precalculus
Office Hours:     MW 11:30-12:30pm

 Interests:
I just finished my fourth year here at UC Davis. I hale from the midwest and still claim the Chicago suburbs as my true home.

Academically speaking, my interests lie in low-dimensional topology. As an undergraduate I wrote a thesis based on the work of V.I. Arnold entitled "The Arnold Invariants of Plane Curves" under the guidance of Lisa Traynor (Bryn Mawr College). Currently I am working with Professor Abigail Thompson in geometric knot theory. Recently I have been interested the tritangent planes of smooth space curves (see the abstract above).

Beyond math, I have a few scattered hobbies. I have been running since high school and have completed 4 marathons to date. I am hoping that the 2009 California International Marathon will make five. I like to read and try awfully hard to read fiction, but what can I say - I'm just a sucker for history. However, by far my favorite pastime is keeping track of my 3 year old niece.