Dima Arinkin Professor Research Interests: Geometric Langlands Program, Derived Categories of Sheaves, and Moduli of Vector Bundles http://www.math.wisc.edu/~arinkin/ 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... 
Eric Bach Professor Research Interests: Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, sixstring automata http://pages.cs.wisc.edu/~bach/ I am interested in how one uses computers to efficiently solve algebraic and numbertheoretic problems (example: how does one tell if a 100digit 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... 
Nigel Boston Professor Research Interests: Algebraic Number Theory, Computational Algebra, Arithmetic Geometry, Applied Algebra http://www.math.wisc.edu/~boston/ 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 prop 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... 
Andrei Caldararu Professor Research Interests: Algebraic geometry, homological algebra, string theory http://www.math.wisc.edu/~andreic/ 
Tullia Dymarz Assistant Professor Research Interests: Geometric group theory, Quasiconformal analysis Working with: Abbott http://www.math.wisc.edu/~dymarz/ My research interests include geometric group theory, quasiisometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis.

Jordan Ellenberg Professor Research Interests: Arithmetic Algebraic Geometry http://www.math.wisc.edu/~ellenber/ 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 FImodules, the geometry of large data sets, nonabelian Iwasawa theory, prop group theory, automorphic forms,... 
Daniel Erman Assistant Professor Research Interests: Commutative Algebra, Applications of syzygies to Algebraic Geometry http://www.math.wisc.edu/~derman/ 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.

Shamgar Gurevich Associate Professor Research Interests: Representation Theory http://www.math.wisc.edu/~shamgar My research is concentrated around applications of group representations. 
Simon Marshall Assistant Professor Research Interests: Discontinuous Groups and Automorphic Forms, Spectral Theory and Eigenvalue Problems for PDOs http://www.math.wisc.edu/~marshall/ 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... 
Melanie Matchett Wood Assistant Professor Research Interests: Number Theory and Algebraic Geometry http://www.math.wisc.edu/~mmwood/ 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... 
Laurentiu Maxim Professor Research Interests: Singularity Theory: hypersurface singularities, intersection homology, perverse sheaves and applications, characteristic classes of singular varieties. http://www.math.wisc.edu/~maxim/ Publications: http://www.math.wisc.edu/~maxim/preprints.html

Steven Sam Assistant Professor Research Interests: Commutative Algebra, Combinatorics Working with: Laudone http://math.wisc.edu/~svs/ 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/ 
Tonghai Yang Professor https://www.math.wisc.edu/~thyang/ My main research interest is in number theory, in particular the interaction between arithmetic geometry, number theory, and representation theory on Shimura varieties. 