Associate Professor of Mathematics
Burton Hall 314
Email: jtymoczko AT smith dot edu
Office hours: (Tentative pending results of class poll!) Monday approximately noon-1pm, many Tuesdays 11-11:45, Wednesday and Friday 2:30-3:30, and by appointment. I also hold email office hours Sunday, Tuesday, and Thursday from 8-9pm.
I attend the Valley Geometry Seminar and the Representation Theory seminar regularly.
- In April, I'll speak at a conference on equivariant Schubert calculus in Ottawa.
- In April, I'm also organizing a Discrete Math Day conference here at Smith.
- In May, I'll speak at a conference on geometric representation theory at the University of Michigan.
- In May, I may go to an approximation theory conference in San Antonio (tentative).
Research Interests and Activities
My research is in algebraic geometry where it intersects combinatorics and representation theory. I use combinatorial or algebraic tools to answer geometric questions, and vice versa. I am supported by a National Science Foundation grant and was an Alfred P. Sloan fellow.
A geometer studies objects like circles, spheres, doughnuts, inner tubes, and 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 the zero set of seventeen polynomials in forty variables. What dimension is it? Does it have holes? How many pieces does it have? An algebraic geometer uses the algebra of polynomials to answer questions like these about the object.
Technical details are on my research page.