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.

 Upcoming Talks:
Space curves and tangent planes
Student Run Geometry/Topology Seminar, UC Davis
September 30, 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

 Teaching:
Fall 2008:
Math 21A - Professor Kapovich
Office Hours: Monday, Thursday 3-4pm
I am the lead TA for Kapovich's 21A class. Students should email me with any questions regarding MyMathLab.

Math 215 - Professor Hass
Office Hours: Tuesday 2-3pm and Friday 10-11am

 Interests:
I am starting 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 the realm of 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 low-dimensional topology. 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 3 marathons to date. I am hoping that the 2008 Chicago Marathon will make four. I like to read and try awfully hard to read fiction, but what can I say - I'm just a sucker for history and biographies. However, by far my favorite pastime is keeping track of my now 2 year old neice.