People

Academic Staff

Steve Goldstein
Research Facilitator



Faculty

Dima Arinkin 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 Eric Bach
Professor
Research Interests: Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata

http://pages.cs.wisc.edu/~bach/

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...

Nigel Boston 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 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...

Andrei Caldararu 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, quasi-isometric rigidity, large scale geometry of finitely generated groups, solvable groups and quasiconformal analysis.

 

Jordan Ellenberg 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 FI-modules, the geometry of large data sets, non-abelian Iwasawa theory, pro-p group theory, automorphic forms,...

Daniel Erman 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 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 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 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 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 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/

Rebecca Willett
Associate Professor
Research Interests: signal processing, machine learning, large-scale data science


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.

Graduate

Carolyn Abbott
Graduate Fellow

Working with:
Dymarz

www.math.wisc.edu/~abbott
Brandon Alberts
Graduate Fellow

Working with:
Boston

www.math.wisc.edu/~blalberts
Juliette Bruce
Graduate Fellow
Research Interests: Algebraic Geometry, Commutative Algebra, Number Theory
Working with:
Erman

https://juliettebruce.github.io

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...

Zachary Charles
Graduate Fellow

Working with:
Boston


Nathan Clement
Graduate Fellow

Working with:
Arinkin


Edward Dewey
Graduate Fellow

Working with:
Arinkin


Eva Elduque
Graduate Fellow

Working with:
Maxim


Christian Geske
Graduate Fellow
Research Interests: Topology of Singular Spaces
Working with:
Maxim


 

Daniel Hast
Graduate Fellow

Working with:
Ellenberg


 

 

Ryan Julian
Graduate Fellow



Robert Laudone
Graduate Fellow
Research Interests: Representation stability, representation theory, algebraic combinatorics
Working with:
Sam

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

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.

Julia Lindberg
Graduate Fellow

Working with:
Boston


Megan Maguire
Graduate Fellow

Working with:
Matchett Wood

http://mmaguire.weebly.com/
Vlad Matei
Graduate Fellow

Working with:
Hast


Solly Parenti
Graduate Fellow



Jeff Poskin
Graduate Fellow

Working with:
Del Pia


Eric Ramos
Graduate Fellow

Working with:
Ellenberg


Jason Steinberg
Graduate Fellow

Working with:
Yang


Micky Steinberg
Graduate Fellow

Working with:
Dymarz


Yun Su
Graduate Fellow

Working with:
Maxim


Kai-ho Wong
Graduate Fellow

Working with:
Maxim


Jay Yang
Graduate Fellow

Working with:
Erman


Postdoctoral, Graduate

Joseph Gunther
Postdoctoral Fellow, Graduate Fellow

Working with:
Matchett Wood


Joseph Gunther
Postdoctoral Fellow, Graduate Fellow

Working with:
Matchett Wood


Postdoctoral

Michael Brown
Postdoctoral Fellow
Research Interests: K-theory, algebraic geometry, commutative algebra
Working with:
Caldararu

http://www.math.wisc.edu/~mkbrown5/

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.

John Wiltshire-Gordon John Wiltshire-Gordon
Postdoctoral Fellow
Research Interests: Representation theory, algebraic topology, combinatorics
Working with:
Ellenberg


 

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

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

Undergraduate

James Boudouris
Undergraduate Student



Bernard Daley
Undergraduate Student



Samuel Ilic
Undergraduate Student



Sho Kawakami
Undergraduate Student



Jacob Kettinger
Undergraduate Student