People

Most of my research is motivated by the geometric Langlands conjecture. I believe that my results are valuable by themselves, but the Langlands philosophy provides a unifying point of view on my work. Currently, I am working on the following two projects. The first project concerns a new formulation of the categorical Langlands conjecture, which removes the contradictions that plague the ‘naive’ statement. The formulation requires new...

I am interested in how one uses computers to efficiently solve algebraic and number-theoretic problems (example: how does one tell if a 100-digit number is prime without examining all possible factors?). These problems have intrinsic mathematical interest, as well as applications to random number generation, codes for reliable and secure information transmission, computer algebra, and other areas. I am also interested in applying probability...

My research concerns pure and applied algebra. In pure algebra I work on finite and profinite group theory, algebraic number theory (especially Galois representations and pro-p extensions), computational algebra, and arithmetic geometry. In applied algebra I work on applications of algebra to electrical engineering and computer science, including classical ones such as coding theory, information theory, and cryptography and more novel ones...

My research interests include geometric group theory, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis.

My field is arithmetic algebraic geometry: my specific interests include rational points on varieties, enumeration of number fields and other arithmetic objects, incidence problems and algebraic methods in combinatorial geometry, Galois representations attached to varieties and their fundamental groups, representation stability and FI-modules, the geometry of large data sets, non-abelian Iwasawa theory, pro-p group theory, automorphic forms,...

I am interested in the study of syzygies and in the use of free complexes in algebraic geometry and commutative algebra. Recently, I have become particularly interested in the study of syzygies under various asymptotic constructions, and in the study of algebraic geometry over finite fields.

My research is concentrated around applications of group representations.

My research interests are in the areas of number theory and harmonic analysis. More specifically, I am interested in arithmetic manifolds, which are Riemannian manifolds with large amounts of symmetry that play a central role in number theory. I am primarily interested in the cohomology of these manifolds, and the asymptotic behaviour of their Laplace eigenfunctions. The questions I think about are connected to topics such as the quantum...

The main focus of my research is in number theory and algebraic geometry, but it also involves work in probability, additive combinatorics, and algebraic topology. My PhD work found new explicit descriptions of moduli spaces for algebras and modules for those algebras. In number theory, these descriptions are useful for parametrizing orders in number fields and ideal classes of those orders. In algebraic geometry, the work can be viewed as...

http://www.math.wisc.edu/~maxim/

Publications: http://www.math.wisc.edu/~maxim/preprints.html

My work is in the interface between commutative algebra, representation theory, and combinatorics. Recently, I have been interested in syzygies of algebraic varieties and asymptotic behavior of structure coefficients arising in combinatorial representation theory.

Publications:  http://www.math.wisc.edu/~svs/writings/

My main research interest is in number theory, in particular the interaction between arithmetic geometry, number theory, and representation theory on Shimura varieties.

My interests lie toward the algebraic side of things, with my current research being somewhere in the intersection of commutative algebra, algebraic geometry, and number theory. While my interestes are quite widespread three themes that run throughout most of my projects are: 1) describing algebraic phenomea asymtoptically, 2) working interdisipinarily, and 3) the use and substantial computation often in Macaulay2.

Both of these themes...

My interests lie mainly in representation stability and representation theory as well as their connection to combinatorics. Recently I have been particularly interested in bounded generation properties of secant ideals of various varieties. You can find a copy of my CV on my website listed above or by clicking here.

I study differential graded (dg) categories arising in algebraic geometry. Lately, I've been interested in computing invariants of such categories, such as algebraic/topological K-theory and cyclic homology.

Main topics: representation theory of categories, configuration space, homological algebra, computer algebra.

Website: https://sites.google.com/wisc.edu/jwg