Research in Algebra

Including number theory, algebraic geometry, and combinatorics

We have large groups of researchers active in number theory and algebraic geometry, as well as many individuals who work in other areas of algebra: groups, noncommutative rings, Lie algebras and Lie super-algebras, representation theory, combinatorics, game theory, and coding. A number of members of the algebra group belong to the Research Training Group in Representation Theory, Geometry and Combinatorics, which runs activities and supports grad students and postdocs in its areas of interest.

Courses

Undergraduate upper division courses

Math 110 (and honors version, Math H110). Linear algebra.
Math 113 (and honors version, Math H113). Introduction to abstract algebra.
Math 114. Second course in abstract algebra. (Instructor's choice; usually Galois Theory)
Math 115. Introduction to number theory.
Math 116. Cryptography.
Math 143. Elementary algebraic geometry.
Math 172. Combinatorics.

The Mathematics Department also offers, at the undergraduate level, courses which may include algebraic topics along with others: Problem Solving (H90), Experimental Courses (191), a Special Topics course (195), and several courses of directed and independent individual and group work (196-199).

Graduate courses

Math 245A. General theory of algebraic structures.
Math 249. Algebraic combinatorics.
Math 250A. Groups, rings and fields.
Math 250B. Multilinear algebra and further topics.
Math 251. Ring theory.
Math 252. Representation theory.
Math 253. Homological algebra.
Math 254A-254B. Number theory.
Math 255. Algebraic curves.
Math 256A-256B. Algebraic geometry.
Math 257. Group theory.

Seminars

2008-2009

Math 290. Seminar - Commutative algebra and algebraic geometry, David Eisenbud
Math 290. Seminar - Number theory, Kenneth Ribet

Spring 2009

Math 274. Topics in Algebra - Tropical geometry, Bernd Sturmfels
Math 274. Topics in Algebra - Infinitesimal geometry, Mariusz Wodzicki

Fall 2008

Math 290. Seminar - Algebraic geometry, David Eisenbud and Daniel Erman
Math 290. Seminar - Discrete mathematics, Bernd Sturmfels
Math 290. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin
Math 290. Seminar - Student arithmetic geometry seminar, Martin Olsson
Student Seminar. Student algebraic and arithmetic geometry seminar, David Brown, Daniel Erman and Anthony Varilly

2007-2008

Math 270. Hot Topics - Derived algebraic geometry and topology, Peter Teichner
Math 290. Seminar - Commutative algebra and algebraic geometry, David Eisenbud
Math 290. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin

Spring 2008

Math 274. Topics in Algebra - Real p-adic analysis, Robert Coleman

Fall 2007

Math 274. Topics in Algebra - Locally finite lie algebras and their representations with a view toward open problems, Ivan Penkov
Math 290. Seminar - Student representation theory, geometry and combinatorics, Vera Serganova and Peter Tingley
Math 290. Seminar - Number theory, Kenneth Ribet
Math 290. Seminar - Perverse sheaves, Joel Kamnitzer and Xinwen Zhu

Earlier years, from 2006-2007

 

Senate Faculty

Name Title Research Interests
George M. Bergman Professor Emeritus, Professor of the Graduate School Associative rings, Universal algebra and category theory, Counterexamples
Richard E. Borcherds Professor Lie algebras, Vertex algebras, Automorphic forms
David Eisenbud Professor Algebraic geometry, Commutative algebra, Computation
Edward Frenkel Professor Representation theory, Integrable systems, Mathematical physics
Mark D. Haiman Professor Algebra, combinatorics, and algebraic geometry
Robin C. Hartshorne Professor Emeritus Algebraic geometry, History of geometry
Tsit-Yuen Lam (林節玄) Professor Emeritus, Professor of the Graduate School Algebra
Hendrik W. Lenstra, Jr. Professor Emeritus Algebraic number theory, Algorithms
David Nadler Professor Geometric representation theory, symplectic geometry
Andrew P. Ogg Professor Emeritus Number theory, Elliptic curves, Modular forms
Arthur E. Ogus Professor Algebraic geometry
Martin Olsson Professor Algebraic and arithmetic geometry
Nicolai Reshetikhin Professor Mathematical physics, Low-dimensional topology, Representation theory
John L. Rhodes Professor Emeritus Algebra, Semigroups, Automata
Kenneth A. Ribet Professor Algebraic number theory, Algebraic Geometry
Vera Serganova Professor Super-representation theory
Vivek Shende Assistant Professor Geometry
Sug Woo Shin Associate Professor Number theory, automorphic forms
Zvezdelina Stankova Teaching Professor & Director, Berkeley Math Circle Algebraic geometry, representation theory, combinatorics, Olympiad problem solving, Berkeley Math Circle
Bernd Sturmfels Professor Algebraic Geometry, Combinatorics, Optimization and Statistics
Constantin Teleman Professor Lie groups, Algebraic geometry, Topology, Quantum field theory
Paul A. Vojta Professor Diophantine approximation, Nevanlinna theory (especially as related to diophantine approximation), Arakelov theory
Lauren Williams Professor Combinatorics, and connections to representation theory, geometry, and statistical physics
Mariusz Wodzicki Professor Non-commutative and algebraic geometry, Analysis, K-theory
Xinyi Yuan Assistant Professor Number theory

Visiting Faculty

Name Title Research Interests
Hélène Barcelo Visiting Scholar Algebraic combinatorics, discrete homotopy and homology theory
Nic Ford Visiting Scholar Algebraic geometry, algebraic combinatorics, representation theory; syzygies of modules over polynomial rings
Emiliano Gómez Lecturer Number theory, Galois representation
Haseo Ki Visiting Scholar Number theory; Zeros of L-functions
Alexander Paulin Lecturer Number theory, p-adic automorphic forms
Earl Taft Visiting Scholar Hopf algebras, quantum groups
Kelli Talaska Lecturer Algebraic combinatorics

Postdocs

Name Title Research Interests
Kęstutis Česnavičius Miller Research Fellow Arithmetic geometry, the arithmetic of abelian varieties
David Dynerman Morrey Visiting Assistant Professor Applied algebra, cryo-electron microscopy, implementation of algorithms
Martin Helmer NSERC Postdoctoral Fellow Computational algebraic geometry; computational algebra
Michele Schiavina SNSF Postdoc Mathematical Physics, Field Theory, Quantum Information
Khrystyna Serhiyenko Postdoc Algebra, representation theory, cluster algebras
Andrey Smirnov Morrey Visiting Assistant Professor Representation theory, mathematical physics

Faculty with Related Research Interests

Name Title Research Interests
Denis Auroux Professor Symplectic topology and mirror symmetry
Elwyn R. Berlekamp Professor Emeritus Combinatorial game theory, Algebraic coding theory, Electrical engineering, Computer science
Olga Holtz Professor Numerical analysis, matrix theory, algebra and combinatorics, computational complexity
Ralph McKenzie Professor Emeritus General algebra, Logic
Calvin C. Moore Professor Emeritus Representations and actions of topological groups, Operator algebras
Lior Pachter Professor Mathematical and computational biology
Marc A. Rieffel Professor Non-commutative harmonic analysis, Operator algebras, Quantum geometry
Thomas Scanlon Professor Model theory and applications to number theory

Graduate Students

Name Dissertation Supervisor
Shishir Agrawal
Alexander Bertoloni Meli
Nicolas Brody
Anastasia Chavez Lauren Williams, Federico Ardila
Harrison Chen David Nadler
Justin Chen David Eisenbud
Yael Degany Katrin Wehrheim
Christopher Eur
Ravi Fernando Martin Olsson
Benjamin Gammage David Nadler
Anningzhe Gao
Bryan Gillespie Olga Holtz
Felix Gotti
Joe Kileel Bernd Sturmfels
Watson Ladd Ken Ribet
Luhang Lai
Bo Lin
Daniel Lowengrub
Shelly Manber Xinyi Yuan
Christopher R Miller
Kyle Miller
Ritvik Ramkumar
Melissa Sherman-Bennett
Minseon Shin
Tao Su Richard E.Borcherds, Vivek Shende
Emmanuel Tsukerman
Ben Wormleighton David Nadler
Dylan Yott
Mengyuan Zhang David Eisenbud
Qiao Zhou (Elaine) David Nadler

Recent Ph.D.s

Name Dissertation Title Dissertation Supervisor Year
Chang-Yeon Cho Topological types of Algebraic stacks 2016
Maria Monks Gillespie A combinatorial approach to the q,t-symmetry in Macdonald polynomials Mark Haiman 2016
Will Johnson Fun with Fields 2016
Olya Mandelshtam Combinatorics of the Asymmetric Simple Exclusion Process Lauren Williams 2016
Alexander Shapiro Grothendieck resolution, affine Grassmannian, and Yangian 2016
Piotr Achinger Arthur E. Ogus 2015
Natth Bejraburnin Lior Pachter 2015
Katrina Honigs Martin Olsson 2015
Adam Kalman Lauren Williams 2015
Eric C. Peterson Constantin Teleman 2015
Zvi Rosen 2015
Lasse Peter Mannisto Albanese and Picard 1-Motives in Positive Characteristic Martin Olsson 2014
Khoa Nguyen Arithmetic Dynamics of Diagonally Split Polynomial Maps Paul A. Vojta, Thomas Scanlon 2014
Andrew Niles Moduli of Elliptic Curves via Twisted Stable Maps Martin Olsson 2014
Qingchun Ren Computations and Moduli Spaces for Non-archimedean Varieties Bernd Sturmfels 2014
Pablo Solis Antimicrobial Applications of Ambient-Air Plasmas Constantin Teleman 2014
Thanh Quang Vu Combinatorial patterns in syzygies David Eisenbud 2014
Harold M. Williams Cluster Algebras and Integrable Systems Nicolai Reshetikhin 2014
Adam L. Boocher Superflatness David Eisenbud 2013
Andrew J. Critch Algebraic Geometry of Hidden Markov and Related Models Bernd Sturmfels 2013
Michael W. Daub Complex and p-adic Computations of Chow-Heegner Points Kenneth A. Ribet 2013
Daniel Halpern-Leistner Geometric Invariant Theory and Derived Categories of Coherent Sheaves Constantin Teleman 2013
Theodore Johnson-Freyd Perturbative Methods in Path Integration Nicolai Reshetikhin 2013
Lilit Martirosyan The Representation Theory of the Exceptional Lie Superalgebras F(4) and G(3) Vera Serganova 2013
Matthew Tucker-Simmons Marc A. Rieffel, Nicolai Reshetikhin 2013
Hwajong Yoo Modularity of residually reducible Galois representations and Eisenstein ideals Kenneth A. Ribet 2013
Morgan Brown Cox Rings and Partial Amplitude David Eisenbud 2012
Melody Chan Tropical curves and metric graphs Bernd Sturmfels 2012
Sarah Iveson Mark D. Haiman 2012
Chul Hee Lee Algebraic Structures in Modular q-hypergeometric Series Richard E. Borcherds 2012
Edgard Rincon Tropical Linear Spaces and Applications Olga Holtz, Bernd Sturmfels 2012
George Schaeffer 2012
George W. Melvin Constantin Teleman