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
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Mark M. Maxwell
Clinical Professor, Paul V. Montgomery Fellow, Actuarial Studies Program Director
PhD, Oregon State University, 1994
RLM 11.168, ASA, 2003, (512) 471-7169
maxwell@math.utexas.edu
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Mark M. Maxwell
- Algebra
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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.
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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.
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Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry
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Daniel Allcock
- Algebraic Geometry
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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 Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas invariants (and their generalizations) and new constructions of hyperkahler metrics.
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Daniel Allcock
- Algebraic K-theory
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Andrew Blumberg
Assistant Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 471-3147
blumberg@math.utexas.edu
I 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).
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Andrew Blumberg
- Algebraic Topology
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Andrew Blumberg
Assistant Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 471-3147
blumberg@math.utexas.edu
I 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).
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Dan Freed
Professor
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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.
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Andrew Blumberg
- Analysis
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William Beckner
Professor, Paul V. Montgomery Centennial Memorial Professor in Mathematics
Ph.D., Princeton University, 1975
RLM 10.140, (512) 471-7711
beckner@math.utexas.edu
Fourier 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 function-space inequalities over a manifold encode information about the geometric structure of the manifold. Asymptotic arguments identify geometric invariants that characterize large-scale 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 well-defined, 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.
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Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 471-3160, 475-8635
caffarel@math.utexas.edu
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Thomas Chen
Assistant Professor
Ph.D., ETH Zurich (Switzerland), 2001
RLM 12.138, (512) 471-7180
tc@math.utexas.edu
Spectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.
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Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear Kinetic and Partial Differential Equations.
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Dan Knopf
Associate Professor, Graduate Adviser
Ph.D., University of Wisconsin-Milwaukee, 1999
RLM 9.152, 8.146, (512) 471-8131, 475-8141
danknopf@math.utexas.edu
I 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, computer-assisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.
-
Edward Odell
Professor, Associate Chair, Undergraduate Studies
John T. Stuart III Centennial Professor of Mathematics
Ph.D., Massachusetts Institute of Technology, 1975
RLM 11.124, (512) 471-4157
odell@math.utexas.edu
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Natasa Pavlovic
Associate Professor
Ph. D. University of Illinois at Chicago, 2002
RLM 12.162, (512) 471-1187
natasa@math.utexas.edu
My 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 well-posedness 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.
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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.
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Alexis Vasseur
Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 471-2363
vasseur@math.utexas.edu
I am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.
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William Beckner
- Applied Mathematics
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Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 471-0166, 475-8628
arbogast@math.utexas.edu
Todd 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: Eulerian-Lagrangian schemes for advective flow; cell-centered 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.
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Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 471-3160, 475-8635
caffarel@math.utexas.edu
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Thomas Chen
Assistant Professor
Ph.D., ETH Zurich (Switzerland), 2001
RLM 12.138, (512) 471-7180
tc@math.utexas.edu
Spectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.
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Bjorn Engquist
Professor, CAM Chair (No. 1)
Ph.D, Uppsala University, 1969
RLM 11.148, ACES 3.324, (512) 471-7163, 471-2160
engquist@math.utexas.edu
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Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear Kinetic and Partial Differential Equations.
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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.
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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.
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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.
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Yen-Hsi Richard Tsai
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Alexis Vasseur
Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 471-2363
vasseur@math.utexas.edu
I am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.
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Rachel Ward
Assistant Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 471-0144
rachel@math.utexas.edu
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Lexing Ying
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Todd Arbogast
- Arithmetic Geometry
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Mirela Ciperiani
Assistant Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 471-4188
mirela@math.utexas.edu
My 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.
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Mirela Ciperiani
- Calculus of Variations
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Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Alessio Figalli
- Category Theory
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David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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.
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David Ben-Zvi
- Coding Theory
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Jose Felipe Voloch
Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.
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Jose Felipe Voloch
- Combinatorics
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Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry
-
Andrew Neitzke
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas invariants (and their generalizations) and new constructions of hyperkahler metrics.
-
Sean Keel
- Computational Science
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Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 471-0166, 475-8628
arbogast@math.utexas.edu
Todd 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: Eulerian-Lagrangian schemes for advective flow; cell-centered 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) 471-7163, 471-2160
engquist@math.utexas.edu
-
Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear 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.
-
Yen-Hsi Richard Tsai
-
Rachel Ward
Assistant Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 471-0144
rachel@math.utexas.edu
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Lexing Ying
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Todd Arbogast
- Cryptography
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Jose Felipe Voloch
Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.
-
Jose Felipe Voloch
- Differential Equations, Ordinary and Partial
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Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 471-0166, 475-8628
arbogast@math.utexas.edu
Todd 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: Eulerian-Lagrangian schemes for advective flow; cell-centered 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) 471-3160, 475-8635
caffarel@math.utexas.edu
-
Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear 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
Associate Professor, Graduate Adviser
Ph.D., University of Wisconsin-Milwaukee, 1999
RLM 9.152, 8.146, (512) 471-8131, 475-8141
danknopf@math.utexas.edu
I 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.
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Karen Uhlenbeck
Professor, Sid W. Richardson Foundation Regents Chair (No. 3)
Ph.D., Brandeis University, 1968
RLM 9.160, 512-560-0557, 512-471-7711
uhlen@math.utexas.edu
I am interested in the partial differential equations which arise in mathematical physics. The most famous of these are Einstein equations of relativity and Maxwell's equation for electrodynamics. My best known work has been on the Yang-Mills equations. However, there are other integrable systems which are connected to quantum topology, as well as newer version of gauge theoretic equations. My most recent students have worked in analytical aspects of these gauge theoretic equations.
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Alexis Vasseur
Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 471-2363
vasseur@math.utexas.edu
I am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.
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Todd Arbogast
- Dynamical Systems and Ergodic Theory
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Rafael de la Llave
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Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Hans Koch
renormalization in dynamical systems, computer-assisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.
-
Amir Mohammadi
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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) 471-7121, 475-8141
sadun@math.utexas.edu
I study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multi-dimensional 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.
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Rafael de la Llave
- Financial Mathematics
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Mihai Sirbu
Associate Professor
Ph.D Carnegie Mellon University, 2004
RLM 11.140, (512) 471-5161
sirbu@math.utexas.edu
My 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.
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Thaleia Zariphopoulou
Professor (on leave), MSIS: V.F.Neuhaus Centennial Professor in Finance
Ph.D., Brown University, 1989.
RLM 11.170, CBA 6.316, (512) 471-7170, 471-9432
zariphop@math.utexas.edu
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Gordan Zitkovic
Associate Professor
Ph. D. Columbia University, 2003
RLM 11.132, (512) 471-1159
gordanz@math.utexas.edu
My interests include probability theory and stochastic analysis and their applications in mathematical finance.
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Mihai Sirbu
- Functional Analysis
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Edward Odell
Professor, Associate Chair, Undergraduate Studies
John T. Stuart III Centennial Professor of Mathematics
Ph.D., Massachusetts Institute of Technology, 1975
RLM 11.124, (512) 471-4157
odell@math.utexas.edu
-
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.
-
Edward Odell
- Geometric Measure Theory
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Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Alessio Figalli
- Geometric Representation Theory
-
David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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 Ben-Zvi
- Geometric Topology
-
Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 471-8182
gompf@math.utexas.edu
Topology of 4-manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.
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Cameron Gordon
Professor, Sid W. Richardson Foundation Regents Chair (No. 2)
Ph.D, Cambridge (England), 1971
RLM 12.112, (512) 471-1173
gordon@math.utexas.edu
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John Luecke
Professor
Ph.D., University of Texas (Austin), 1985
RLM 12.122, (512) 471-4176
luecke@math.utexas.edu -
Hossein Namazi
Assistant Professor
Ph. D. Stony Brook University, 2005
RLM 12.156, (512) 471-1184
hossein@math.utexas.edu
A major focus in my research is a study of hyperbolic 3-manifolds and Kleinian groups and attempting to understand their geometries. I am also interested in various related areas in the study of topology of 3-manifolds and geometry of surfaces and Teichmuller theory.
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Alan Reid
Professor, Department Chair
Pennzoil Company Regents Professor
Ph.D., University of Aberdeen (U.K.), 1988
RLM 10.172, RLM 8.152, (512) 471-3153, 471-0117
areid@math.utexas.edu
My interests are in hyperbolic manifolds, discrete groups and low-dimensional topology with a particular interest in connections with number theory.
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Robert Gompf
- Geometry
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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.
-
Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
-
Dan Freed
Professor
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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) 471-8182
gompf@math.utexas.edu
Topology of 4-manifolds, 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
Associate Professor, Graduate Adviser
Ph.D., University of Wisconsin-Milwaukee, 1999
RLM 9.152, 8.146, (512) 471-8131, 475-8141
danknopf@math.utexas.edu
I 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
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas invariants (and their generalizations) and new constructions of hyperkahler metrics.
-
Timothy Perutz
Assistant Professor
Ph. D. University of London, 2005
RLM 10.136, (512) 471-6142
perutz@math.utexas.edu
My interests are in symplectic topology, low-dimensional topology (with an emphasis on 4-manifolds) and interactions between these areas. My preferred techniques are those of pseudo-holomorphic 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.
-
Alan Reid
Professor, Department Chair
Pennzoil Company Regents Professor
Ph.D., University of Aberdeen (U.K.), 1988
RLM 10.172, RLM 8.152, (512) 471-3153, 471-0117
areid@math.utexas.edu
My interests are in hyperbolic manifolds, discrete groups and low-dimensional topology with a particular interest in connections with number theory.
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Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 471-7121, 475-8141
sadun@math.utexas.edu
I study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multi-dimensional 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.
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Karen Uhlenbeck
Professor, Sid W. Richardson Foundation Regents Chair (No. 3)
Ph.D., Brandeis University, 1968
RLM 9.160, 512-560-0557, 512-471-7711
uhlen@math.utexas.edu
I am interested in the partial differential equations which arise in mathematical physics. The most famous of these are Einstein equations of relativity and Maxwell's equation for electrodynamics. My best known work has been on the Yang-Mills equations. However, there are other integrable systems which are connected to quantum topology, as well as newer version of gauge theoretic equations. My most recent students have worked in analytical aspects of these gauge theoretic equations.
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Daniel Allcock
- Homotopy Theory
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David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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.
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Andrew Blumberg
Assistant Professor
Ph. D. University of Chicago, 2005
RLM 10.160, (512) 471-3147
blumberg@math.utexas.edu
I 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).
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Dan Freed
Professor
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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.
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Robert Gompf
Professor, Jane and Roland Blumberg Centennial Professor
Ph.D., University of California (Berkeley), 1984
RLM 12.150, (512) 471-8182
gompf@math.utexas.edu
Topology of 4-manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.
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David Ben-Zvi
- Math Education
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Efraim Armendariz
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Michael Starbird
Professor, Distinguished Teaching Professor
Ph.D., Wisconsin, 1974
RLM 11.122, (512) 471-5156
starbird@mail.utexas.edu
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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) 232-2271, 471-6190
uri@math.utexas.edu
I work on the design, implementation, and analysis of large-scale 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 education--especially efforts to address systemic inequality in access to high-quality education. programming.
-
Efraim Armendariz
- Mathematical Biology
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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.
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John Luecke
Professor
Ph.D., University of Texas (Austin), 1985
RLM 12.122, (512) 471-4176
luecke@math.utexas.edu
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Oscar Gonzalez
- Mathematical Physics
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David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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.
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Thomas Chen
Assistant Professor
Ph.D., ETH Zurich (Switzerland), 2001
RLM 12.138, (512) 471-7180
tc@math.utexas.edu
Spectral and dynamical problems in quantum field theory, random Schrodinger equations, renormalization group methods, mean field and macroscopic scaling limits of quantum dynamics, Hamiltonian dynamics.
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John Dollard
Currently doing administration full time.
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Dan Freed
Professor
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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.
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Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear Kinetic and Partial Differential Equations.
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Hans Koch
renormalization in dynamical systems, computer-assisted proofs in dynamical systems and PDEs, phase transitions in statistical mechanics.
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Andrew Neitzke
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas 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) 471-7121, 475-8141
sadun@math.utexas.edu
I study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multi-dimensional 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.
-
Karen Uhlenbeck
Professor, Sid W. Richardson Foundation Regents Chair (No. 3)
Ph.D., Brandeis University, 1968
RLM 9.160, 512-560-0557, 512-471-7711
uhlen@math.utexas.edu
I am interested in the partial differential equations which arise in mathematical physics. The most famous of these are Einstein equations of relativity and Maxwell's equation for electrodynamics. My best known work has been on the Yang-Mills equations. However, there are other integrable systems which are connected to quantum topology, as well as newer version of gauge theoretic equations. My most recent students have worked in analytical aspects of these gauge theoretic equations.
-
Alexis Vasseur
Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 471-2363
vasseur@math.utexas.edu
I am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.
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David Ben-Zvi
- Mathematical String Theory
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David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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.
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Sean Keel
I am an algebraic geometer with particular interests in moduli spaces and birational geometry
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Andrew Neitzke
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas invariants (and their generalizations) and new constructions of hyperkahler metrics.
-
Karen Uhlenbeck
Professor, Sid W. Richardson Foundation Regents Chair (No. 3)
Ph.D., Brandeis University, 1968
RLM 9.160, 512-560-0557, 512-471-7711
uhlen@math.utexas.edu
I am interested in the partial differential equations which arise in mathematical physics. The most famous of these are Einstein equations of relativity and Maxwell's equation for electrodynamics. My best known work has been on the Yang-Mills equations. However, there are other integrable systems which are connected to quantum topology, as well as newer version of gauge theoretic equations. My most recent students have worked in analytical aspects of these gauge theoretic equations.
-
David Ben-Zvi
- Number Theory
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Mirela Ciperiani
Assistant Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 471-4188
mirela@math.utexas.edu
My 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.
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David Helm
Assistant Professor
Ph. D. University of California, Berkeley 2003
RLM 9.118, (512) 471-5179
dhelm@math.utexas.edu
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Amir Mohammadi
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Alan Reid
Professor, Department Chair
Pennzoil Company Regents Professor
Ph.D., University of Aberdeen (U.K.), 1988
RLM 10.172, RLM 8.152, (512) 471-3153, 471-0117
areid@math.utexas.edu
My interests are in hyperbolic manifolds, discrete groups and low-dimensional topology with a particular interest in connections with number theory.
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Fernando Rodriguez-Villegas
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Jeffrey Vaaler
Professor, Associate Chair
Ph.D., University of Illinois (Urbana-Champaign), 1974
RLM 9.126, (512) 471-7125
vaaler@math.utexas.edu
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Jose Felipe Voloch
Arithmetic of function fields. Diophantine geometry over function fields. Geometry of algebraic curves. Algebraic varieties over finite fields. Modular forms, elliptic curves and abelian varieties. Finite fields and applications to coding theory and cryptography.
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Mirela Ciperiani
- Numerical Analysis
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Todd Arbogast
Professor
Ph.D., University of Chicago, 1987
RLM 11.162, ACE 5.334, (512) 471-0166, 475-8628
arbogast@math.utexas.edu
Todd 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: Eulerian-Lagrangian schemes for advective flow; cell-centered 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.
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Bjorn Engquist
Professor, CAM Chair (No. 1)
Ph.D, Uppsala University, 1969
RLM 11.148, ACES 3.324, (512) 471-7163, 471-2160
engquist@math.utexas.edu
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Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear 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.
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Yen-Hsi Richard Tsai
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Rachel Ward
Assistant Professor
Ph.D, Princeton University, 2009
RLM 10.144, (512) 471-0144
rachel@math.utexas.edu
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Lexing Ying
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Todd Arbogast
- Partial differential equations
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Luis Caffarelli
Professor, Sid W. Richardson Foundation Regents Chair (No. 1)
Ph.D., University of Buenos Aires, 1972.
10.150A, ACE 3.328, (512) 471-3160, 475-8635
caffarel@math.utexas.edu
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Alessio Figalli
Professor
Ph.D., SNS Pisa (Italy) and ENS Lyon (France), 2007
RLM 10.148, (512) 475-8145
figalli@math.utexas.edu
My research focuses on different areas, related to both analysis and geometry. One of my main field of research is optimal transport: given a mass distribution, find the most effective way of moving this mass from one place to another, minimizing the transportation cost. This problem has found in recent years important applications to many other different areas, such as Monge-Ampère type equations, evolution partial differential equations, isoperimetric and functional inequalities, Riemannian geometry. I have been working in all of these areas. I also work in variational problems in the calculus of variations, as for instance studying geometric and regularity properties of minimizers of functionals modeling liquid drops and crystals. More recently, I also started to work on regularity theory for elliptic partial differential equations (both of local and non-local type) and free boundary problems.
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Irene Gamba
Professor
Ph.D., University of Chicago, 1989
RLM 10.166, ACES 3.340, (512) 471-7150, 471-7422
gamba@math.utexas.edu
Applied and Computational Analysis, Mathematical and Statistical Physics, non-linear Kinetic and Partial Differential Equations.
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Dan Knopf
Associate Professor, Graduate Adviser
Ph.D., University of Wisconsin-Milwaukee, 1999
RLM 9.152, 8.146, (512) 471-8131, 475-8141
danknopf@math.utexas.edu
I 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.
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Natasa Pavlovic
Associate Professor
Ph. D. University of Illinois at Chicago, 2002
RLM 12.162, (512) 471-1187
natasa@math.utexas.edu
My 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 well-posedness 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.
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Karen Uhlenbeck
Professor, Sid W. Richardson Foundation Regents Chair (No. 3)
Ph.D., Brandeis University, 1968
RLM 9.160, 512-560-0557, 512-471-7711
uhlen@math.utexas.edu
I am interested in the partial differential equations which arise in mathematical physics. The most famous of these are Einstein equations of relativity and Maxwell's equation for electrodynamics. My best known work has been on the Yang-Mills equations. However, there are other integrable systems which are connected to quantum topology, as well as newer version of gauge theoretic equations. My most recent students have worked in analytical aspects of these gauge theoretic equations.
-
Alexis Vasseur
Professor
Ph.D., Ecole Normale Superieure / Paris VI, 1999
RLM 11.172, (512) 471-2363
vasseur@math.utexas.edu
I am working on Partial Differential equations. I am particularly interested in the PDE's used in Fluid mechanics.
-
Luis Caffarelli
- Probability
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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) 471-5161
sirbu@math.utexas.edu
My 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.
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Thaleia Zariphopoulou
Professor (on leave), MSIS: V.F.Neuhaus Centennial Professor in Finance
Ph.D., Brown University, 1989.
RLM 11.170, CBA 6.316, (512) 471-7170, 471-9432
zariphop@math.utexas.edu
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Gordan Zitkovic
Associate Professor
Ph. D. Columbia University, 2003
RLM 11.132, (512) 471-1159
gordanz@math.utexas.edu
My interests include probability theory and stochastic analysis and their applications in mathematical finance.
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Charles Radin
- Public Policy
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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) 232-2271, 471-6190
uri@math.utexas.edu
I work on the design, implementation, and analysis of large-scale 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 education--especially efforts to address systemic inequality in access to high-quality education. programming.
-
Philip Uri Treisman
- Representation Theory
-
David Ben-Zvi
Associate Professor
Ph.D., Harvard University, 1999
RLM 10.168, (512) 471-8151
benzvi@math.utexas.edu
I 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
Assistant Professor
Ph. D. Princeton University, 2006
RLM 12.164, (512) 471-4188
mirela@math.utexas.edu
My 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
Assistant Professor (on leave fall 2012)
Ph. D. Tel-Aviv University
RLM 12.118, (512) 471-0175
hadani@math.utexas.edu
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Andrew Neitzke
Assistant Professor
Ph.D., Harvard University, 2005
RLM 9.134, (512) 471-1132
neitzke@math.utexas.edu
I 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 wall-crossing phenomena for Donaldson-Thomas invariants (and their generalizations) and new constructions of hyperkahler metrics.
-
David Ben-Zvi
- Statistics
- Topology
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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.
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Dan Freed
Professor
Ph.D., University of California (Berkeley), 1985
RLM 9.162, (512) 471-7136
dafr@math.utexas.edu
I 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 K-theory. 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) 471-8182
gompf@math.utexas.edu
Topology of 4-manifolds, symplectic and contact topology (especially in dimensions 4 and 3), topological construction of Stein surfaces and domains of holomorphy.
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Hossein Namazi
Assistant Professor
Ph. D. Stony Brook University, 2005
RLM 12.156, (512) 471-1184
hossein@math.utexas.edu
A major focus in my research is a study of hyperbolic 3-manifolds and Kleinian groups and attempting to understand their geometries. I am also interested in various related areas in the study of topology of 3-manifolds and geometry of surfaces and Teichmuller theory.
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Timothy Perutz
Assistant Professor
Ph. D. University of London, 2005
RLM 10.136, (512) 471-6142
perutz@math.utexas.edu
My interests are in symplectic topology, low-dimensional topology (with an emphasis on 4-manifolds) and interactions between these areas. My preferred techniques are those of pseudo-holomorphic curves, gauge theory and Floer cohomology theories.
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Alan Reid
Professor, Department Chair
Pennzoil Company Regents Professor
Ph.D., University of Aberdeen (U.K.), 1988
RLM 10.172, RLM 8.152, (512) 471-3153, 471-0117
areid@math.utexas.edu
My interests are in hyperbolic manifolds, discrete groups and low-dimensional topology with a particular interest in connections with number theory.
-
Lorenzo Sadun
Professor
Ph.D., University of California (Berkeley), 1987
RLM 9.114, (512) 471-7121, 475-8141
sadun@math.utexas.edu
I study the topology and dynamics of tiling spaces, mostly (but not exclusively) tilings of Euclidean space. These are multi-dimensional 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