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.


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.



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


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
Sylvie Corteel Professor Combinatorics
David Eisenbud Professor Algebraic geometry, Commutative algebra, Computation
Tony Feng Assistant Professor Number Theory, Arithmetic Geometry, Langlands Program, Algebraic Topology, Representation Theory
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
Hannah K. Larson Assistant Professor Algebraic geometry, intersection theory.
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 Emeritus Algebraic geometry
Martin Olsson Professor Algebraic and arithmetic geometry
Alexander Paulin Teaching Professor Number theory, p-adic automorphic forms
Nicolai Reshetikhin Professor Emeritus 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 Associate Professor Geometry
Sug Woo Shin 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 Emeritus Algebraic Geometry, Combinatorics, Optimization and Statistics
Yunqing Tang Assistant Professor Arithmetic geometry, number theory
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
Mariusz Wodzicki Professor Non-commutative and algebraic geometry, Analysis, K-theory

Visiting Faculty

Name Title Research Interests
Hélène Barcelo Research Associate Algebraic combinatorics, discrete homotopy and homology theory
Emiliano Gómez Academic Coordinator/Instructor Number theory, Galois representation
Arun Sharma Unit 18 Lecturer Combinatorics, Ramsey theory, error-correcting codes
Kelli Talaska Continuing Lecturer Algebraic combinatorics
Bernd Ulrich Chern Visiting Professor Commutative algebra and algebraic geometry, in particular, linkage and residual intersection, multiplicity theory, blowup algebras


Name Title Research Interests
Owen F. Barrett Morrey Visiting Assistant Professor Algebraic and arithmetic geometry, ℓ-adic cohomology, local acyclicity, singular support
Ivan Danilenko Morrey Visiting Assistant Professor Algebraic geometry, representation theory, mathematical physics.
Colleen Delaney Postdoctoral Scholar Mathematical physics, quantum topology, applied category theory, quantum computation
Nicolle Gonzalez Morrey Visiting Assistant Professor Diagrammatic categorification, representation theory, and algebraic combinatorics arising in connection to Macdonald polynomials, Demazure modules, and homological knot invariants
Peter Haine NSF Postdoctoral Scholar and UC President's Postdoctoral Fellow Homotopy theory, (derived) algebraic geometry, and related subjects
Sergei Korotkikh Morrey Visiting Assistant Professor Algebraic combinatorics, integrable probability, representation theory, vertex models
Borislav Mladenov Morrey Visiting Assistant Professor Algebraic geometry, mathematical physics
Kendric Schefers Morrey Visiting Assistant Professor Microlocal geometry, derived algebraic geometry, and related subjects
Alexandra Utiralova Morrey Visiting Assistant Professor Algebra, representation theory, tensor categories
Andrés R. Vindas Meléndez NSF Postdoctoral Scholar Algebraic and geometric combinatorics
Yegor Zenkevich Postdoctoral Fellow Mathematical physics, representation theory

Faculty with Related Research Interests

Name Title Research Interests
Vadim Gorin Associate Professor Integrable probability, random matrices, asymptotic representation theory
Olga Holtz Professor Numerical analysis, matrix theory, algebra and combinatorics, computational complexity
Ralph McKenzie Professor Emeritus General algebra, Logic
Marc A. Rieffel Professor Non-commutative harmonic analysis, Operator algebras, Quantum geometry
Thomas Scanlon Professor Model theory and applications to number theory
Ruixiang Zhang Assistant Professor Harmonic analysis, analytic number theory, additive combinatorics

Recent Ph.D.s

Name Dissertation Title Dissertation Supervisor Year
Daniel Chupin Comonadicity for Localizations   David Nadler 2023
Ravi Fernando Saturated de Rham-Witt complexes with unit-root coefficients Martin Olsson 2023
Nicolas Brody Groups Acting on Products of Trees   Ian Agol 2022
Christopher Kuo Symplectic geometric methods in microlocal sheaf theory   Vivek Shende 2022
Kyle Miller Singularity Theory for Extended Cobordism Categories and an Application to Graph Theory   Ian Agol 2022
Ritvik Ramkumar The Geometry of Hilbert Schemes on Projective Space David Eisenbud 2022
Weitong Wang Distribution of Class Groups Melanie Wood 2022
Michael Christianson Combinatorial Invariants on Smooth Projective Spherical Varieties   Martin Olsson 2021
Anningzhe Gao Some results on arithmetic aspects of K3 surfaces and abelian varieties   Martin Olsson 2021
Ian Gleason Specialization maps for Scholze’s category of diamonds   Sug Woo Shin 2021
Calvin McPhail-Snyder SL_2(C)-holonomy invariants of links   Nicolai Reshetikhin 2021
Isabelle Shankar Sums of Squares and Symmetric Polynomials Serkan Hosten, Jon Wilkening 2021
Melissa Sherman-Bennett On the combinatorics of cluster structures on positroid varieties   Lauren Williams, Sylvie Corteel 2021
German Stefanich Higher Quasicoherent Sheaves   David Nadler 2021
Alexander Bertoloni Meli The Local Langlands Correspondence, Rapoport-Zink Spaces, and Shimura Varieties 2020
Madeline Brandt Tropical Geometry of Curves Bernd Sturmfels 2020
Christopher Eur The Geometry of Divisors on Matroids David Eisenbud 2020
Alexander Sherman Spherical and Symmetric Supervarieties 2020
Ben Wormleighton Numerics and stability for orbifolds with applications to symplectic embeddings David Eisenbud 2020
Mengyuan Zhang Liaison of curves and bundles David Eisenbud 2020
Alexander Carney The arithmetic Hodge-index theorem and rigidity of algebraic dynamical systems over function fields Xinyi Yuan 2019
Benjamin Gammage Microlocal sheaves and mirror symmetry David Nadler 2019
Felix Gotti Matroids and convex geometry in combinatorics and algebra Lauren Williams 2019
Christopher R Miller On the k-Schur Positivity of k-Bandwidth LLT Polynomials 2019
Minseon Shin Computations of the cohomological Brauer group of some algebraic stacks Martin Olsson 2019
Dylan Yott Special Cycles on GSpin Shimura Varieties Xinyi Yuan 2019
Shishir Agrawal Deformations of overconvergent isocrystals on the projective line   David Nadler 2018
Harrison Chen A Localization Theorem for Derived Loop Spaces and Periodic Cyclic Homology   David Nadler 2018
Justin Chen On Betti Tables, Monomial Ideals, and Unit Groups   David Eisenbud 2018
Bryan Gillespie The Generalized External Order, and Applications to Zonotopal Algebra   Olga Holtz 2018
Watson Ladd Algebraic Modular Forms on SO5(Q) and the Computation of Paramodular Forms   Ken Ribet 2018
Daniel Lowengrub Applications of the Intersection Theory of Singular Varieties   Vivek Shende 2018
Shelly Manber Asymptotics of the Tate-Shafarevich Group   Xinyi Yuan 2018
Tao Su A Hodge-theoretic study of augmentation varieties associated to Legendrian knots/tangles   Vivek Shende, Richard E.Borcherds 2018
Brandon Williams Computing modular forms for the Weil representation   Richard Borcherds 2018