julianna tymoczko

Teaching in Fall 2009

Recent and upcoming events

• In February, I will visit Berkeley to work with my collaborator, Megumi Harada.
• In March, I will go to the American Institute of Mathematics (in Palo Alto) for a conference I am co-organizing with Bill Fulton and Rebecca Goldin, on localization techniques in equivariant cohomology.
• In March, I will also go to Smith College, to attend a memorial conference in honor of Mike Albertson, who had a profound influence on me, as well as on many other people (mathematicians and not).
• In April, I will go to Macalester College in St. Paul to speak at an AMS special session on combinatorial representation theory.

Seminars

• I organize the algebraic geometry seminar at the University of Iowa.
• I co-organize a professional development seminar for graduate students.

Research interests

My research is primarily in algebraic geometry at its intersection with combinatorics, representation theory, and algebraic groups. I tend to use combinatorial or algebraic tools to answer geometric questions, or vice versa. I am an Alfred P. Sloan Research Fellow and am also supported by a National Science Foundation grant.

A geometer studies geometric objects like circles, spheres, doughnuts, inner tubes, and many others too complicated to imagine. The most concise way to describe geometric objects is as the zero set of a collection of polynomials; for instance, the zero set of x²+y²=1 is the unit circle in the plane. Now imagine trying to find the zero set of seventeen polynomials in forty variables. What dimension is the geometric object? Does it have holes? How many pieces does it have? An algebraic geometer uses the algebra of polynomials to understand the geometry of the underlying object.

Copies of my preprints and a more technical discussion of my research may be found in the research section of this page.