Zeyu Shen
"G-Ttheory of simplicial toric varieties" (May 2025)
Zeyu Shen's thesis relates the G-theory of a
(simplicial) toric variety X to the Chow groups of X.
The G-theory of a variety X is the K-theory of the category of
coherent sheaves on X. His primary results are published in
Communications in Algebra
Here are my previous students.
Masoud Zargar
"Voevodsky Motives, Stable Homotopy Theory, and Integration"
(June 2018, Princeton Univ.),
co-advisors Denis-Charles Cisinski, Peter Ozsvath and Charles Weibel.
Glen Wilson
"Motivic stable stems over finite fields" (May 2016)
Jaret Flores
"Homological algebra of commutative monoids" (January 2015)
Knight Fu
"Slice filtration and torsion theory in motivic cohomology"
(May 2014)
Carlo Mazza
"Schur functors and motives" (December 2003)
Jason Andrew Jones
"Reconstruction of quantum coordinate algebras" (December 1995)
Jean Rynes
"Nonsingular Affine k*-Surfaces" (May 1988)
Masoud Zargar's thesis concerned motivic stable homotopy theory and
motivic integration. Part of his thesis is published in
Adv. Math. 354 (2019), 106744.
He is now at the Max Planck Institute, on leave from USC.
Glen Wilson is working with the motivic Adams Spectral sequences
to determine the motivic homotopy groups of spheres.
He is now at the University of Trømso, Norway.
Jaret Flores is working on the homological properties of commutative
monoids and monoid schemes, including extensions and divisor class groups.
He is now working for GIS Workshop.
Knight Fu is working with Motives in algebraic geometry.
His thesis studied the restriction of the slice filtration to
the category of homotopy invariant sheaves with transfers (HI)
and the Rost-Déglise category of homotopy modules.
He is now working for MediaMath.
Carlo Mazza is working in Motivic Cohomology.
His thesis introduced and studied the notion of a "Schur-finite" motive.
In 2005, we finished writing up the
Lectures in Motivic Cohomology,
based upon a course taught by Voeovdsky in 1999-2000.
He is now in the Mathematics Department of the
Università di Milano.
Jason Jones defined the quantum coordinate algebra of any semisimple algebraic
group G. If G is a classical group (SL, SO, Sp) his construction agrees
with the pre-existing definition. The idea is to study those quantum
representations of the associated Lie algebra whose weights lie in a certain
lattice, and to use Tannaka-Krein reconstruction.
He is now working for S&P Global Ratings.
Jean Rynes classified nonsingular affine surfaces on which the group
k* acts algebraically, using a graph which is an equivariant invariant.
The thesis is published in
Trans. AMS 332 (1992), 889-921.
The main families are obtained from a line bundle over a smooth curve (where
k* acts on the fibers) by a sequence of operations, encoded by the graph.
Each such operation amounts to adding a fixed point at infinity,
blowing it up, and removing a line.
She has been on the faculty of Delaware Valley College in Doylestown PA.
Charles Weibel/
weibel @
math.rutgers.edu