Gordan Savin

Mathematics is Intelligent Design

Research:

Minimal Representations: These remarkable representations are the smallest faithful representations of Chevalley groups of adjoint type (A-D-E root sytems). Minimal representations are unramified, and correspond to the reflection representation of affine Hecke algebras. For more details on the definition and properties, see my paper published in Glasnik Mat. Vol. 31(51) (1996), 93-99. (The restrictive condition n_V=1 in Remark 1.2 has been since removed by Stephen DeBacker.) Minimal representations realize, in a most natural fashion, several instances of Langlands functoriality. Some other (mostly) recent e-prints:

Modular forms on non-linear double covers of algebraic groups - with H. Y. Loke, preprint (2008).
Functoriality and the inverse Galois problem II: groups of type G_2 and B_n - with C. Khare and M. Larsen, preprint (2008).
"Bernstein's center" for real groups - with G. Muic - Transactions of AMS 360 (2008) 3071-3092.
The smallest representation of non-linear covers of odd orthogonal groups - with H. Y. Loke - Amer. J. Math. 130 (2008) 763-798.
Uniqueness of the minimal representation - with H. Y. Loke - Math. Annalen 340 (2008) 195-208.
Functoriality and the inverse Galois problem - with C. Khare and M. Larsen - Compositio Math. 144 (2008) 541-564.
Lifting of generic depth zero supercusipdal representations - J. Algebra 319 (2008) 3244-3258.
Elliptic curve test for Fermat primes - with R. Denomme - J. Number Theory 128 (2008) 2398-2412.
Dual pair correspondences for non-linear covers of odd orthogonal groups - with H. Y. Loke - J. Funct. Anal. 255 (2008) 184-199.
On local lifts from G_2(R) to Sp_6(R) and F_4(R) - with H. Y. Loke - Israel J. of Math. 159 (2007), 349-372.
Structure of internal modules and a formula for the spherical vector of minimal representations - with M. Woodbury - J. Algebra 312 (2007) 755-772.

Figure:

upper.gif - this file contains the above picture of the fundamental domain for SL_2(Z) in the complex upper half plane.

2009 REU program:

NEW: syllabus .
Notes on Z-modules and SL(n,Z) .
Notes on quadratic fields .
Reduction of definite forms .
Reduction of indefinite forms .
Notes on Gauss Law and Bhargava's cube .

Math 5405:

Updated course syllabus .
Course notes .
First homework .
Second homework .
Third homework .
Fourth homework .
Fifth homework .
Lecture on fields of order p^2 .
Lecture on fields of order 2^n .
Third exam .

Mail address:

        Gordan Savin
        Department of Mathematics
        University of Utah
        Salt Lake City, UT 84112

Office phone: (801) 581-6175

Gordan Savin (savin@math.utah.edu)