Algebraic Geometry

Sándor Kovács (PhD Utah, 1995)
Max Lieblich (PhD MIT, 2004)
S. Paul Smith (PhD Leeds, 1981)
Bianca Viray (PhD UC Berkeley, 2010)
 Algebra Seminar
arXiv.org ePrint archive (recent postings in Algebraic Geometry)
Algebraic Geometry (from Eric Weisstein's World of Mathematics)
Algebraic Topology

Ethan Devinatz (PhD MIT, 1985)
Stephen Mitchell (PhD University of Washington, 1981)
John Palmieri (PhD MIT, 1991)
 Topology Seminar
Hopf Archive
arXiv.org ePrint archive (recent postings in Algebraic Topology)
Algebraic Topology (from Eric Weisstein's World of Mathematics)
Combinatorics and Discrete Geometry

Sara Billey (PhD UC San Diego, 1994)
Ioana Dumitriu (PhD MIT, 2003)
Christopher Hoffman (PhD Stanford, 1996)
James Morrow (PhD Stanford, 1967)
Hariharan Narayanan (PhD University of Chicago, 2009)
Isabella Novik (PhD Hebrew University, 1999)
David Wilson (Affiliate) (PhD MIT, 1996)
 Combinatorics Seminar
arXiv.org ePrint archive (recent postings in Combinatorics)
Math Archives (University of Tennessee, Knoxville) [Combinatorics]
Combinatorics (from Eric Weisstein's World of Mathematics)
Complex Analysis

John Garnett (Affiliate) (PhD University of Washington, 1966)
Donald Marshall (PhD UCLA, 1976)
Steffen Rohde (PhD Technische Universität Berlin, 1989)
 Complex Analysis Seminar
Math Archives (University of Tennessee, Knoxville) [Complex Analysis]
Complex Analysis (from Eric Weisstein's World of Mathematics)
Differential Geometry

Judith M. Arms (PhD Berkeley, 1977)
Thomas Duchamp (PhD Illinois, 1976)
John M. Lee (PhD MIT, 1982)
Daniel Pollack (PhD Stanford, 1991)
C. Robin Graham (PhD Princeton, 1981)
Yu Yuan (PhD Minnesota, 1998)
 Differential Geometry/PDE Seminar
The Pacific Northwest Geometry Seminar
arXiv.org ePrint archive (recent postings in Differential Geometry)
Math Archives (University of Tennessee, Knoxville) [Differential Geometry]
Differential Geometry (from Eric Weisstein's World of Mathematics)
Ergodic Theory and Symbolic Dynamics

Jayadev S. Athreya (PhD University of Chicago, 2006)
Christopher Hoffman (PhD Stanford, 1996)
Boris Solomyak (Affiliate) (PhD Leningrad, 1986)
Selim Tuncel (PhD Warwick, 1982)

Ergodic Theory (from Eric Weisstein's World of Mathematics)
NonSmooth Analysis

Jayadev S. Athreya (PhD University of Chicago, 2006)
Don Marshall (Complex Analysis), (PhD UCLA, 1976)
Steffen Rohde (Complex Analysis & Probability), (PhD Technische Universität Berlin, 1989)
Boris Solomyak (Affiliate) (Fractal Geometry & Ergodic Theory), (PhD Leningrad, 1986)
Tatiana Toro (Geometric Measure Theory), (PhD Stanford, 1992)
 Measure Theory (from Eric Weisstein's World of Mathematics)
Rainwater Seminar
Inverse Problems
The classical theory of differential equations is concerned with "forward problems": given a differential equation, find a solution. But in many realworld situations, one has to go in the reverse direction: given some information about the solutions to a differential equation, find the unknown coefficients in the governing equation. The Mathematics Department has a strong group working on various aspects of inverse problems. Professors Gunther Uhlmann and John Sylvester study various kinds of tomography, which is a powerful method for probing the world around us by directing energy in the form of waves or electric currents at an object and observing the energy after it has interacted with the object. Professor Ken Bube works on inverse problems related to seismic exploration of the earth. Professor Jim Morrow studies how to determine the structure of an electrical network from measurements of voltage and currents at its boundary terminals.
For more information, see the home page of the Inverse Problems Group.

Kenneth P. Bube (PhD Stanford, 1978)
James Morrow (PhD Stanford, 1967)
John Sylvester (PhD Courant, 1980)
Gunther Uhlmann (PhD MIT, 1976)
 Inverse Problems Seminar
Inverse Problems (from Eric Weisstein's World of Mathematics)
Mathematical Physics

Ioana Dumitriu (PhD MIT, 2003)
Garth Warner (PhD Michigan, 1966)
 arXiv.org ePrint archive (recent postings in Mathematical Physics)
Noncommutative Algebra

Ken Goodearl (Affiliate) (PhD University of Washington, 1971)
Ronald Irving (PhD MIT, 1977)
Julia Pevtsova (PhD Northwestern, 2002)
S. Paul Smith (PhD Leeds, 1981)
James Zhang (PhD MIT, 1991)
 Algebra Seminar
Algebra (from Eric Weisstein's World of Mathematics)
Number Theory

Ralph Greenberg (PhD Princeton, 1971)
Neal I. Koblitz (PhD Princeton, 1974)
William Stein (PhD UC Berkeley, 2000)
Bianca Viray (PhD UC Berkeley, 2010)
 arXiv.org ePrint archive (recent postings in Number Theory)
Math Archives (University of Tennessee, Knoxville) [Number Theory]
Number Theory (from Eric Weisstein's World of Mathematics)
Numerical Analysis

Kenneth P. Bube (PhD Stanford, 1978)
Ioana Dumitriu (PhD MIT, 2003)
Anne Greenbaum (Adjunct) (PhD Berkeley, 1981)
Randall LeVeque (Adjunct) (PhD Stanford, 1982)
 arXiv.org ePrint archive (recent postings in Numerical Analysis)
Math Archives (University of Tennessee, Knoxville) [Numerical Analysis]
Optimization and Variational Analysis
Applications of optimization, including stochastic optimization, are emphasized in projects which combine theory and computation in cooperation with nearby industries such as Boeing.
At the UW we have an interdisciplinary program in theoretical, numerical, and applied optimization. Current research activities of this group include collaborative activities in the Departments of Statistics (numerical methods for robust statistics), Bioengineering (population analysis and biomedical imaging), Computer Science and Engineering (Markovian decision processes), Finance (portfolio optimization), and the School of Fisheries (hydropower optimization). Most of these projects have graduate student involvement.
 James Burke (PhD Illinois/Urbana, 1983)
Dmitriy Drusvyatskiy (PhD Cornell, 2013)
Hariharan Narayanan (PhD University of Chicago , 2009)
Thomas Rothvoß (PhD École polytechnique fédérale de Lausanne, 2009)
Rekha Thomas (PhD Cornell, 1994)
 Optimization Seminar
arXiv.org ePrint archive (recent postings in Optimization and Control)
Optimization Theory (from Eric Weisstein's World of Mathematics)
Partial Differential Equations

C. Robin Graham (PhD Princeton, 1981)
John M. Lee (PhD MIT, 1982)
Daniel Pollack (PhD Stanford, 1991)
Hart Smith (PhD Princeton, 1989)
John Sylvester (PhD Courant, 1980)
Tatiana Toro (PhD Stanford, 1992)
Gunther Uhlmann (PhD MIT, 1976)
Yu Yuan (PhD Minnesota, 1998)
 Differential Geometry/PDE Seminar
Math Archives (University of Tennessee, Knoxville) [Partial Differential Equations]
Partial Differential Equations (from Eric Weisstein's World of Mathematics)
Probability

Krzysztof Burdzy (PhD Berkeley, 1984)
ZhenQing Chen (PhD Washington University, 1992)
Ioana Dumitriu (PhD MIT, 2003)
Christopher Hoffman (PhD Stanford, 1996)
Alexander Holroyd (Affiliate) (PhD University of Cambridge, 2000)
Eyal Lubetzky (Affiliate) (PhD TelAviv University, 2007)
Hariharan Narayanan (PhD University of Chicago , 2009)
Soumik Pal (PhD Columbia, 2006)
David Wilson (Affiliate) (PhD MIT, 1996)
 Probability Seminar
arXiv.org ePrint archive (recent postings in Probability Theory)
Math Archives (University of Tennessee, Knoxville) [Probability]
Probability (from Eric Weisstein's World of Mathematics)
The Probability Web
Representation Theory of Lie Groups and Lie Algebras

Sara Billey (PhD UC San Diego, 1994)
David Collingwood (PhD Utah, 1983)
Ronald Irving (PhD MIT, 1977)
Arnold Kas (Affiliate) (PhD Stanford, 1966)
William McGovern (PhD MIT, 1987)
Julia Pevtsova (PhD Northwestern, 2002)
S. Paul Smith (PhD Leeds, 1981)
 arXiv.org ePrint archive (recent postings in Representation Theory)
Semisimple Lie Group (from Eric Weisstein's World of Mathematics)
