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T.W.I.G.S.
The "What Is ...?" Graduate Seminar

Room 1634, Lederle Graduate Research Tower
University of Massachusetts, Amherst 		ComplexCubicUnitAction
The Seminar meets Wed 3:00-4:00 in 1634 LGRT.    
Driving Directions   and   Campus Maps
Overview of the Seminar as well as Unofficial mottos and sponsors of TWIGS
Maintained by Farshid Hajir.

NOTE Here are the schedules for Fall 2002, Spring 2003, Fall 2003, Spring 2004, Fall 2004, Spring 2005, Fall 2005, Spring 2006, Fall 2006. and Spring 2007.
Wednesday September 19 Farshid Hajir, UMass Amherst. "What is an elliptic curve?"
Abstract: An elliptic curve over a field F is a smooth curve of genus 1 over F equipped with a point on the curve defined over F. The set of points on the curve with coordinates in F forms an abelian group under a natural addition law. I'll describe the space of elliptic curves over the complex numbers and describe how this space can be viewed from analytic, geometric and arithmetic perspectives.
Wednesday Oct. 3 Evgeny Materov, UMass Amherst. "What is an amoeba?"
Abstract: Amoeba is a very fascinating notion in mathematics introduced by I.Gel''fand. It is defined as a logarithmic image of an algebraic set in the torus (C^*)^n. Now amoebas have a lot of applications from solving algebraic equations to mirror symmetry. Amoebas have their tentacles, spines and contours. In my talk I will review some basic results on amoebas (e.g., how to estimate the number of connected components in the complement to amoeba, define the "tropical" spine of amoeba analytically) and give illustrative examples.
Wednesday Oct. 10 Jenia Tevelev, UMass Amherst. "What is a non-archimidean amoeba?"
Abstract: Non-archimedean amoebas are to usual amoebas as p-adic numbers are to real numbers. These angular creatures live in tropics. Originally tropical geometry was introduced as an attempt to "dequantize" the real world by replacing multiplication with addition and addition with taking the minimum. But the thing that makes tropical geometry so entertaining and funny is the wealth of really amusing applications such as (just to name a few) count of Gromov-Witten invariants (Mihalkin), degenerations of Calabi-Yaus and mirror symmetry (Kontsevich-Soibelman, Gross-Siebert), honeycombs and Horn's problem (Speyer), compact moduli spaces (Hacking-Keel-Tevelev), statistics and computational biology (Pachter-Sturmfels), cluster algebras (Zelevinsky), dimers (Kenyon-Okounkov), algebraic dynamics (Einsiedler-Kapranov-Lind), etc. I will explain a little bit of this cool stuff.
Wednesday December 5 , UMass Amherst. "What is ...? STUMP THE CHUMP EDITION"
Abstract: Come and ask Farshid //any// math question you want!
Wednesday Dec. 12 , UMass Amherst. "What is Wedderburn's Theorem?"
Abstract: Every finite division ring is commutative. We'll give a beautiful proof, due to Ernst Witt.
The picture above was created by Paul Gunnells. It visualizes the natural action of the group of units of a complex cubic field on 3-space. Consult Paul for more details.

Last modified: Feb 2006 by Farshid Hajir