Faculty Research Interests
Click on the topics below to see a list of our senior faculty with research interests in that area. Scroll down to see webpages maintained by our research groups.
 Actuarial Science

Mark Matthew Maxwell
Clinical Professor, Paul V. Montgomery Fellow, Actuarial Studies Program Director
PhD, Oregon State University, 1994
RLM 11.168, ASA, 2003, (512) 4717169
maxwell@math.utexas.edu

Mark Matthew Maxwell
 Algebra

Daniel Allcock
My current interests focus on discrete groups and their role in algebraic geometry and other fields. Especially interesting are Coxeter groups and their related braid groups. Although group theory is officially "algebra", the part of it that I like is more a branch of geometry.

Raymond Heitmann
I work in commutative algebra, principally dealing with questions concerning the homological properties of local rings. My specialty is rings of mixed characteristic  the ring itself has characteristic zero but its residue field has characteristic p.

Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry

Daniel Allcock
 Algebraic Geometry

Daniel Allcock
My current interests focus on discrete groups and their role in algebraic geometry and other fields. Especially interesting are Coxeter groups and their related braid groups. Although group theory is officially "algebra", the part of it that I like is more a branch of geometry.

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

Daniel Allcock
 Algebraic Ktheory

Andrew Blumberg
Associate Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 4713147
blumberg@math.utexas.eduI work in stable homotopy theory, focusing primarily on research problems arising from constructions made possible by the modern theory of structured ring spectra (and the homotopy theory of module categories over such "geometric" rings).

Andrew Blumberg
 Algebraic Topology

Andrew Blumberg
Associate Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 4713147
blumberg@math.utexas.eduI work in stable homotopy theory, focusing primarily on research problems arising from constructions made possible by the modern theory of structured ring spectra (and the homotopy theory of module categories over such "geometric" rings).

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Andrew Blumberg
 Analysis

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 4713160, 4758635
caffarel@math.utexas.edu 
Thomas Chen
Associate Professor, Department Chair
PhD ETH Zurich, 2001
RLM 12.138, RLM 8.152,
tc@math.utexas.eduSpectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.

Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Dan Knopf
Professor
Ph.D., University of WisconsinMilwaukee, 1999
RLM 9.152, 5124718131
danknopf@math.utexas.eduI work on problems in geometric analysis. The broad motivations for my research program are to find and classify optimal geometries by using evolution equations like Ricci flow, mean curvature flow, and cross curvature flow. I use techniques from analysis to understand the behavior, singularity formation, and stability of solutions to the nonlinear partial differential equations governing these flows. These equations have applications to the geometry and topology of manifolds, as well as to problems originating in materials science and physics.

Hans Koch
renormalization in dynamical systems, computerassisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.

Natasa Pavlovic
Professor
Ph. D. University of Illinois at Chicago, 2002
RLM 12.162, (512) 4711187
natasa@math.utexas.eduMy research interests are focused on PDEs that arise in fluid dynamics and on nonlinear dispersive equations. More precisely, I have been investigating problems related to wellposedness and regularity of fluid equations and nonlinear dispersive equations. Also, recently I extended research interests in a new direction, to include topics on derivation of the nonlinear dispersive equations as the mean field limits of interacting Boson gases.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Alexis Vasseur
Professor, Associate Chairman
John T. Stuart III Centennial Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 4712363
vasseur@math.utexas.eduI am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.

William Beckner
 Applied Mathematics

Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 4710166, 4758628
arbogast@math.utexas.eduTodd Arbogast's areas of expertise include the development and analysis of numerical algorithms for the approximation of partial differential systems, high performance and parallel scientific computation, and mathematical modeling. He specializes in applications to fluid flow and transport in porous media, such as the Earth's subsurface. His research accomplishments include the development of: EulerianLagrangian schemes for advective flow; cellcentered finite difference, mixed finite element, and mortar techniques for geometrically irregular problems; homogenization, modeling, and simulation of flow through multiscale fractured and vuggy geologic media; and variational multiscale methods for heterogeneous media and nonlinear problems.

Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 4713160, 4758635
caffarel@math.utexas.edu 
Thomas Chen
Associate Professor, Department Chair
PhD ETH Zurich, 2001
RLM 12.138, RLM 8.152,
tc@math.utexas.eduSpectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.

Bjorn Engquist
Professor, CAM Chair (No. 1)
Ph.D, Uppsala University, 1969
RLM 11.148, ACES 3.324, (512) 4717163, 4712160
engquist@math.utexas.edu 
Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Oscar Gonzalez
My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focused on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Kui Ren
My research focuses on 1) mathematical and numerical analysis of inverse problems of partial differential equations, with applications in imaging sciences, and 2) numerical simulation of the propagation of waves and particles in random media.

YenHsi Richard Tsai

Alexis Vasseur
Professor, Associate Chairman
John T. Stuart III Centennial Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 4712363
vasseur@math.utexas.eduI am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.

Rachel Ward
Associate Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 4710144
rachel@math.utexas.edu

Todd Arbogast
 Arithmetic Geometry

Mirela Ciperiani
Associate Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 4714188
mirela@math.utexas.eduMy research at this point is focused on analyzing local and global points of elliptic curves as the field of definition changes. One of the tools that I use is Iwasawa Theory.

Mirela Ciperiani
 Calculus of Variations

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

William Beckner
 Category Theory

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

David BenZvi
 Combinatorics

Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

Sean Keel
 Computational Science

Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 4710166, 4758628
arbogast@math.utexas.eduTodd Arbogast's areas of expertise include the development and analysis of numerical algorithms for the approximation of partial differential systems, high performance and parallel scientific computation, and mathematical modeling. He specializes in applications to fluid flow and transport in porous media, such as the Earth's subsurface. His research accomplishments include the development of: EulerianLagrangian schemes for advective flow; cellcentered finite difference, mixed finite element, and mortar techniques for geometrically irregular problems; homogenization, modeling, and simulation of flow through multiscale fractured and vuggy geologic media; and variational multiscale methods for heterogeneous media and nonlinear problems.

Bjorn Engquist
Professor, CAM Chair (No. 1)
Ph.D, Uppsala University, 1969
RLM 11.148, ACES 3.324, (512) 4717163, 4712160
engquist@math.utexas.edu 
Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Oscar Gonzalez
My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focused on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.

YenHsi Richard Tsai

Rachel Ward
Associate Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 4710144
rachel@math.utexas.edu

Todd Arbogast
 Differential Equations, Ordinary and Partial

Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 4710166, 4758628
arbogast@math.utexas.eduTodd Arbogast's areas of expertise include the development and analysis of numerical algorithms for the approximation of partial differential systems, high performance and parallel scientific computation, and mathematical modeling. He specializes in applications to fluid flow and transport in porous media, such as the Earth's subsurface. His research accomplishments include the development of: EulerianLagrangian schemes for advective flow; cellcentered finite difference, mixed finite element, and mortar techniques for geometrically irregular problems; homogenization, modeling, and simulation of flow through multiscale fractured and vuggy geologic media; and variational multiscale methods for heterogeneous media and nonlinear problems.

Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 4713160, 4758635
caffarel@math.utexas.edu 
Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Oscar Gonzalez
My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focused on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.

Dan Knopf
Professor
Ph.D., University of WisconsinMilwaukee, 1999
RLM 9.152, 5124718131
danknopf@math.utexas.eduI work on problems in geometric analysis. The broad motivations for my research program are to find and classify optimal geometries by using evolution equations like Ricci flow, mean curvature flow, and cross curvature flow. I use techniques from analysis to understand the behavior, singularity formation, and stability of solutions to the nonlinear partial differential equations governing these flows. These equations have applications to the geometry and topology of manifolds, as well as to problems originating in materials science and physics.

Alexis Vasseur
Professor, Associate Chairman
John T. Stuart III Centennial Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 4712363
vasseur@math.utexas.eduI am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.

Todd Arbogast
 Dynamical Systems and Ergodic Theory

Hans Koch
renormalization in dynamical systems, computerassisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 4717121, 4758141
sadun@math.utexas.eduI study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multidimensional generalizations of symbolic dynamics, with geometry playing a substantial role. I am also interested in the interplay of differential geometry, statistical mechanics, and quantum mechanics.

Hans Koch
 Education Policy

Philip Uri Treisman
Professor, Director, Charles A. Dana Center for Mathematics and Science Education
Ph.D., University of California (Berkeley), 1985
RLM 10.162, UTA 3.206, (512) 2322271, 4716190
uri@math.utexas.eduI work on the design, implementation, and analysis of largescale improvement initiatives in mathematics and science education both in higher education and in urban school districts. I am actively involved in the formulation and analysis of public policies that affect educationespecially efforts to address systemic inequality in access to highquality education. programming.

Philip Uri Treisman
 Financial Mathematics

Mihai Sirbu
Associate Professor
Ph.D Carnegie Mellon University, 2004
RLM 11.140, (512) 4715161
sirbu@math.utexas.eduMy research area is Mathematical Finance and Stochastic Control. I am mainly interested in pricing/hedging and optimal investment in incomplete markets and markets with frictions and the stochastic control methods associated to these models.

Thaleia Zariphopoulou
Professor (Mathematics and IROM), Chair in Mathematics, V.F.Neuhaus Centennial Professor of Finance
Ph.D., Brown University, 1989.
RLM 11.170, CBA 6.316, (512) 4717170, 4719432
zariphop@math.utexas.edu 
Gordan Zitkovic
Associate Professor
Ph. D. Columbia University, 2003
RLM 11.132, (512) 4711159
gordanz@math.utexas.eduStochastic analysis and optimal stochastic control with applications to mathematical finance.

Mihai Sirbu
 Functional Analysis

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

William Beckner
 Geometric Representation Theory

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

David BenZvi
 Geometric Topology

Jeff Danciger

Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 4718182
gompf@math.utexas.eduTopology of 4manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.

Cameron Gordon
Professor, Sid W. Richardson Foundation Regents Chair (No. 2)
Ph.D, Cambridge (England), 1971
RLM 12.112, (512) 4711173
gordon@math.utexas.edu 
John Luecke
Professor
Ph.D., University of Texas (Austin), 1985
RLM 12.122, (512) 4714176
luecke@math.utexas.edu

Jeff Danciger
 Geometry

Daniel Allcock
My current interests focus on discrete groups and their role in algebraic geometry and other fields. Especially interesting are Coxeter groups and their related braid groups. Although group theory is officially "algebra", the part of it that I like is more a branch of geometry.

Jeff Danciger

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 4718182
gompf@math.utexas.eduTopology of 4manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.

Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry

Dan Knopf
Professor
Ph.D., University of WisconsinMilwaukee, 1999
RLM 9.152, 5124718131
danknopf@math.utexas.eduI work on problems in geometric analysis. The broad motivations for my research program are to find and classify optimal geometries by using evolution equations like Ricci flow, mean curvature flow, and cross curvature flow. I use techniques from analysis to understand the behavior, singularity formation, and stability of solutions to the nonlinear partial differential equations governing these flows. These equations have applications to the geometry and topology of manifolds, as well as to problems originating in materials science and physics.

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

Timothy Perutz
Associate Professor
Ph. D. University of London, 2005
RLM 10.136, (512) 4716142
perutz@math.utexas.eduMy interests are in symplectic topology, lowdimensional topology (with an emphasis on 4manifolds) and interactions between these areas. My preferred techniques are those of pseudoholomorphic curves, gauge theory and Floer cohomology theories.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 4717121, 4758141
sadun@math.utexas.eduI study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multidimensional generalizations of symbolic dynamics, with geometry playing a substantial role. I am also interested in the interplay of differential geometry, statistical mechanics, and quantum mechanics.

Daniel Allcock
 Homotopy Theory

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

Andrew Blumberg
Associate Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 4713147
blumberg@math.utexas.eduI work in stable homotopy theory, focusing primarily on research problems arising from constructions made possible by the modern theory of structured ring spectra (and the homotopy theory of module categories over such "geometric" rings).

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 4718182
gompf@math.utexas.eduTopology of 4manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.

David BenZvi
 Math Education

Michael Starbird
Professor, Distinguished Teaching Professor
Ph.D., Wisconsin, 1974
RLM 11.122, (512) 4715156
starbird@mail.utexas.edu

Michael Starbird
 Mathematical Biology

Oscar Gonzalez
My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focused on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.

John Luecke
Professor
Ph.D., University of Texas (Austin), 1985
RLM 12.122, (512) 4714176
luecke@math.utexas.edu

Oscar Gonzalez
 Mathematical Modeling

Philip Uri Treisman
Professor, Director, Charles A. Dana Center for Mathematics and Science Education
Ph.D., University of California (Berkeley), 1985
RLM 10.162, UTA 3.206, (512) 2322271, 4716190
uri@math.utexas.eduI work on the design, implementation, and analysis of largescale improvement initiatives in mathematics and science education both in higher education and in urban school districts. I am actively involved in the formulation and analysis of public policies that affect educationespecially efforts to address systemic inequality in access to highquality education. programming.

Philip Uri Treisman
 Mathematical Physics

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

Thomas Chen
Associate Professor, Department Chair
PhD ETH Zurich, 2001
RLM 12.138, RLM 8.152,
tc@math.utexas.eduSpectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Hans Koch
renormalization in dynamical systems, computerassisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 4717121, 4758141
sadun@math.utexas.eduI study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multidimensional generalizations of symbolic dynamics, with geometry playing a substantial role. I am also interested in the interplay of differential geometry, statistical mechanics, and quantum mechanics.

Alexis Vasseur
Professor, Associate Chairman
John T. Stuart III Centennial Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 4712363
vasseur@math.utexas.eduI am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.

William Beckner
 Mathematical String Theory

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

David BenZvi
 Mathematics Education

Philip Uri Treisman
Professor, Director, Charles A. Dana Center for Mathematics and Science Education
Ph.D., University of California (Berkeley), 1985
RLM 10.162, UTA 3.206, (512) 2322271, 4716190
uri@math.utexas.eduI work on the design, implementation, and analysis of largescale improvement initiatives in mathematics and science education both in higher education and in urban school districts. I am actively involved in the formulation and analysis of public policies that affect educationespecially efforts to address systemic inequality in access to highquality education. programming.

Philip Uri Treisman
 Number Theory

Mirela Ciperiani
Associate Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 4714188
mirela@math.utexas.eduMy research at this point is focused on analyzing local and global points of elliptic curves as the field of definition changes. One of the tools that I use is Iwasawa Theory.

Mirela Ciperiani
 Numerical Analysis

Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 4710166, 4758628
arbogast@math.utexas.eduTodd Arbogast's areas of expertise include the development and analysis of numerical algorithms for the approximation of partial differential systems, high performance and parallel scientific computation, and mathematical modeling. He specializes in applications to fluid flow and transport in porous media, such as the Earth's subsurface. His research accomplishments include the development of: EulerianLagrangian schemes for advective flow; cellcentered finite difference, mixed finite element, and mortar techniques for geometrically irregular problems; homogenization, modeling, and simulation of flow through multiscale fractured and vuggy geologic media; and variational multiscale methods for heterogeneous media and nonlinear problems.

Bjorn Engquist
Professor, CAM Chair (No. 1)
Ph.D, Uppsala University, 1969
RLM 11.148, ACES 3.324, (512) 4717163, 4712160
engquist@math.utexas.edu 
Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Oscar Gonzalez
My general interests are in computational and applied mathematics with an emphasis on classical continuum mechanics. My current efforts are focused on modeling the mechanical properties of DNA at various length scales. Keywords: modeling, numerical analysis, differential equations, integral equations, geometry of curves and surfaces.

Kui Ren
My research focuses on 1) mathematical and numerical analysis of inverse problems of partial differential equations, with applications in imaging sciences, and 2) numerical simulation of the propagation of waves and particles in random media.

YenHsi Richard Tsai

Rachel Ward
Associate Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 4710144
rachel@math.utexas.edu

Todd Arbogast
 Partial differential equations

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 4713160, 4758635
caffarel@math.utexas.edu 
Irene Gamba
Professor, W.A. Tex Moncreif, Jr. Chair in Computational Engineering and Sciences III
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 4717150, 4717422
gamba@math.utexas.eduApplied and Computational Analysis, Mathematical and Statistical Physics, nonlinear Kinetic and Partial Differential Equations.

Dan Knopf
Professor
Ph.D., University of WisconsinMilwaukee, 1999
RLM 9.152, 5124718131
danknopf@math.utexas.eduI work on problems in geometric analysis. The broad motivations for my research program are to find and classify optimal geometries by using evolution equations like Ricci flow, mean curvature flow, and cross curvature flow. I use techniques from analysis to understand the behavior, singularity formation, and stability of solutions to the nonlinear partial differential equations governing these flows. These equations have applications to the geometry and topology of manifolds, as well as to problems originating in materials science and physics.

Natasa Pavlovic
Professor
Ph. D. University of Illinois at Chicago, 2002
RLM 12.162, (512) 4711187
natasa@math.utexas.eduMy research interests are focused on PDEs that arise in fluid dynamics and on nonlinear dispersive equations. More precisely, I have been investigating problems related to wellposedness and regularity of fluid equations and nonlinear dispersive equations. Also, recently I extended research interests in a new direction, to include topics on derivation of the nonlinear dispersive equations as the mean field limits of interacting Boson gases.

Alexis Vasseur
Professor, Associate Chairman
John T. Stuart III Centennial Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 4712363
vasseur@math.utexas.eduI am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.

William Beckner
 Probability

William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 4717711
beckner@math.utexas.eduFourier Analysis  Sharp Inequalities and Geometric Manifolds Geometric inequalities provide insight into the structure of manifolds. The principal objective of my research is to develop a deeper understanding of the way that sharp constants for functionspace inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize largescale structure. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and reflect the dilation character of the manifold. Sharp estimates constitute a critical tool to determine existence and regularity for solutions to pde's, to demonstrate that operators and functionals are welldefined, to explain the fundamental structure of spaces and their varied geometric realizations and to suggest new directions for the development of analysis on a geometric manifold. Model problems and exact calculations in differential geometry and mathematical physics are a source of insight and stimulus, particularly conformal deformation, fluid dynamics, quantum physics, statistical mechanics, stellar dynamics, string theory and turbulence.

Charles Radin
I use geometric features of dense packings, of spheres and other bodies, in the modeling of equilibrium and nonequilibrium materials. Probability and ergodic theory often play a role.

Mihai Sirbu
Associate Professor
Ph.D Carnegie Mellon University, 2004
RLM 11.140, (512) 4715161
sirbu@math.utexas.eduMy research area is Mathematical Finance and Stochastic Control. I am mainly interested in pricing/hedging and optimal investment in incomplete markets and markets with frictions and the stochastic control methods associated to these models.

Thaleia Zariphopoulou
Professor (Mathematics and IROM), Chair in Mathematics, V.F.Neuhaus Centennial Professor of Finance
Ph.D., Brown University, 1989.
RLM 11.170, CBA 6.316, (512) 4717170, 4719432
zariphop@math.utexas.edu 
Gordan Zitkovic
Associate Professor
Ph. D. Columbia University, 2003
RLM 11.132, (512) 4711159
gordanz@math.utexas.eduStochastic analysis and optimal stochastic control with applications to mathematical finance.

William Beckner
 Representation Theory

David BenZvi
Joe B. and Louise Cook Professor of Mathematics
Ph.D., Harvard University, 1999
RLM 10.168, (512) 4718151
benzvi@math.utexas.eduI study interactions between algebraic geometry, representation theory and mathematical physics. In particular I'm interested in applications of techniques from homotopy theory and topological quantum field theory to geometric representation theory and the geometric Langlands program.

Mirela Ciperiani
Associate Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 4714188
mirela@math.utexas.eduMy research at this point is focused on analyzing local and global points of elliptic curves as the field of definition changes. One of the tools that I use is Iwasawa Theory.

Ronny Hadani

Andrew Neitzke
Associate Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 4711132
neitzke@math.utexas.eduI work on geometric problems which are influenced by high energy physics, more specifically supersymmetric field theory and string theory. For the last several years my main focus has been on using N=2 supersymmetry to understand hyperkahler geometry. This has led to surprising connections between wallcrossing phenomena for DonaldsonThomas invariants (and their generalizations) and new constructions of hyperkahler metrics.

David BenZvi
 Statistics
 Topology

Daniel Allcock
My current interests focus on discrete groups and their role in algebraic geometry and other fields. Especially interesting are Coxeter groups and their related braid groups. Although group theory is officially "algebra", the part of it that I like is more a branch of geometry.

Jeff Danciger

Dan Freed
Professor, Mildred Caldwell and Baine Perkins Kerr Centennial Professor of Mathematics
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 4717136
dafr@math.utexas.eduI work on problems in geometry and topology, often with an eye towards quantum field theory and string theory. My collaboration with Michael Hopkins and Constantin Teleman began with the discovery that the Verlinde ring in conformal field theory may be expressed in terms of twisted Ktheory. We are now investigating various extensions of these ideas and also aspects of topological quantum field theory. I am also currently collaborating with Jacques Distler and Gregory Moore on problems arising more directly from physics.

Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 4718182
gompf@math.utexas.eduTopology of 4manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.

Timothy Perutz
Associate Professor
Ph. D. University of London, 2005
RLM 10.136, (512) 4716142
perutz@math.utexas.eduMy interests are in symplectic topology, lowdimensional topology (with an emphasis on 4manifolds) and interactions between these areas. My preferred techniques are those of pseudoholomorphic curves, gauge theory and Floer cohomology theories.

Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 4717121, 4758141
sadun@math.utexas.eduI study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multidimensional generalizations of symbolic dynamics, with geometry playing a substantial role. I am also interested in the interplay of differential geometry, statistical mechanics, and quantum mechanics.

Daniel Allcock