Andrei Gabrielov

Departments of Mathematics
and Earth and Atmospheric Sciences
Purdue University
West Lafayette, IN 47907, USA

OFFICE: Mathematics 648
PHONE: (765) 494-7911
FAX: (765) 494-0548
E-MAIL: agabriel@math.purdue.edu

Home Vita Publications Preprints Teaching Research

Research interests

In mathematics:

Real algebraic and analytic geometry.

Tame geometry and o-minimal structures

Spectral problems for the Schrodinger operator with polynomial potential.

In geophysics:

Earthquake prediction.

Modeling of seismicity and other extreme events.

Sponsored Research

Co-Principal Investigator, Geometric Methods in the Analytic Theory of Differential Equations, National Science Foundation , 2017-2020. PI - A. Eremenko, Purdue

Principal Investigator, Perspectives of modern complex analysis
National Science Foundation , 2014.

Principal Investigator, Semi-monotone sets and triangulation of definable families
National Science Foundation , 2012-2017.

Co-Principal Investigator Meromorphic functions and their applications
National Science Foundation , 2011-2014. PI - A. Eremenko, Purdue

Principal Investigator, Homotopy, Complexity and O-Minimality
National Science Foundation , 2008-2012.

Principal Investigator, Topological Complexity and Quantitative O-Minimality
National Science Foundation , 2003-2006.

Principal Investigator, CMG Collaborative Research: Cellular Automata, Directed Graphs, and the Modeling of Earthquakes and Landforms
National Science Foundation , 2003-2006.

Principal Investigator, Effective non-oscillation of solutions of Fuchsian systems of differential equations and Abelian integrals
National Science Foundation , 2002-2005.

Purdue Research Foundation, International travel grant, 2001.

Co-Principal Investigator, Understanding and prediction of critical transitions in complex systems
James S. McDonnell Foundation, The 21st Century Collaborative Activity Award for Studying Complex Systems , 2001-2003. PI - V. Keilis-Borok, UCLA.

Principal Investigator, Complexity of operations with Pfaffian and Noetherian functions and effective o-minimality
National Science Foundation , 2000-2003.

Principal Investigator, "Modeling of the impact of migrating fluids on dynamics of blocks-and-faults system with special attention to instability and critical phenomena"
Civilian Research and Development Foundation , 2000-2002.

Co-Principal Investigator, Application of Dynamical Systems to Earthquake Prediction
National Science Foundation , 1995-1998, 1999-2001. PI - D.L. Turcotte, Cornell.

Principal Investigator, Subanalytic Sets, Pfaffian Functions, and Complexity of Quantifier Simplification
National Science Foundation , 1997-2000.

Principal Investigator, "Program for Nonlinear Dynamics of Geologic Catastrophes"
Purdue Research Foundation, President Beering's seed grant, 1997-1998.

Purdue Research Foundation, International travel grant, 1997.

Seminars and Presentations (1995-present):

Lipschitz geometry of real surface singularities. International Conference on Lipschitz Geometry of Singularities, Bedlewo, Poland, August6-12, 2017.

Bi-Lipschitz classification of surface singularities. Workshop on O-Minimality and its Applications to Number Theory and Analysis, Oberwolfach, Germany, April 30 - May 6, 2017.

Circular quadrilaterals and non-algebraic dessins d'enfants. Workshop on Deterministic and Random Aspects of the Topology of Real Algebraic Varieties, Vanderbilt University, Nashville, TN, March 11, 2017.

Classification of spherical and circular quadrilaterals. Differential Algebra and Related Topics (DART VII), CUNY, New York, NY, Sept 30 - Oct 4, 2016.

Spherical quadrilaterals and non-algebraic dessins d'enfants. Workshop on Model Theory: From Fields to Hardy Fields, The Fields Institute, Toronto, Canada, August 3, 2016.

Classification of spherical quadrilaterals. Mathematical Institute of UNAM, Cuernavaca, Mexico, June 20, 2016.

Classification of spherical quadrilaterals. Department of Mathematics, Strassbourg University, France, June 5, 2015.

Classification of spherical quadrilaterals. Workshop on Real Analytic Geometry and Trajectories of Vector Fields, CIRM, Luminy, France, June 8-12, 2015.

Classification of spherical quadrilaterals. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel, December 23, 2014.

Lipschitz contact equivalence of functions in two variables. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel, December 18, 2014.

Classification of spherical quadrilaterals. Colloquium, Department of Mathematics, Ben Gurion University, Beer Sheva, Israel, December 16, 2014.

Classification of spherical quadrilaterals. Colloquium, Department of Mathematics, Tel Aviv University, Tel Aviv, Israel, December 15, 2014.

Monotone maps and triangulation of monotone families. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel, December 9, 2014.

Classification of spherical quadrilaterals. Conference on The Legacy of Vladimir Arnold, The Fields Institute, Toronto, Canada, November 24-28, 2014.

Multiplicity of a Noetherian intersection. Department of Mathematics, Stony Brook University, November 21, 2014.

Classification of spherical quadrilaterals. Department of Mathematics, Stony Brook University, November 19, 2014.

Classification of spherical quadrilaterals. Colloquium IMPAN, Warsaw, Poland, July 31, 2014.

Co-convener, International Conference "Perspectives of modern complex analysis." The Banach Center, Bedlewo, Poland, July 21-25, 2014.

Co-convener, Special session "Qualitative and Analytic Theory of ODE's." Second Joint International Meeting of the Israeli Mathematical Union and the American Mathematical Society, Tel-Aviv, Israel, June 16-19, 2014.

Keilis-Borok's vision of predictive understanding of extreme events. 30th IUGG Conference on Mathematical Geophysics, Merida, Mexico, June 2, 2014.

Multiplicities of Noetherian intersections. CIMAT, Guanajuato, Mexico, May 30, 2014.

Irreducibility of some spectral determinants. Colloquium, Department of Applied Mathematics, UNAM, Mexico City, Mexico, May 28, 2014.

Classification of spherical quadrilaterals. Department of Applied Mathematics, UNAM, Mexico City, Mexico, May 26, 2014.

Co-convener, Conference "Celebration of the life of Vladimir Keilis-Borok." Department of Earth and Planetary Sciences, UCLA, March 17, 2014.

Classification of spherical quadrilaterals. Workshop on Optimization, Moment Problems and Geometry, Inverse moment problems, IMS NUS, Singapore, December 2013.

Irreducibility of some spectral determinants. Workshop on Optimization, Moment Problems and Geometry, Inverse moment problems, IMS NUS, Singapore, December 2013.

Lipschitz contact equivalence of functions in two variables. Workshop on Optimization, Moment Problems and Geometry, Inverse moment problems, IMS NUS, Singapore, December 2013.

Semi-Monotone Sets, Monotone Maps, and Triangulation of Monotone Families. Joint Mathematics Meetings, San Diego, January 11, 2013.

On Predictive Understanding of Extreme Events: Pattern Recognition Approach; Prediction Algorithms; Applications to Disaster Preparedness. AGU Union Session "Predicting Extreme Events in Natural and Socioeconomic Systems: State-of-the-Art and Emerging Possibilities," San Francisco, December 6, 2011.

Tame geometry: from subanalytic sets to o-minimal theory. Resolution of Singularities and Related Topics. In honor of the 80th birthday of H. Hironaka, Tordesillas, Spain, September 18-23, 2011.

Eigenfunctions of the quartic oscillator and identities between elementary integrals. Department of Mathematics Colloquium, IUPUI, Indianapolis, September 9, 2011.

Semi-monotone sets and triangulation of tame monotone families. O-minimal structures and real analytic geometry retrospective workshop. Fields Institute, Toronto, Canada, August 8-12, 2011.

Semi-monotone sets and triangulation of tame monotone families. Real algebraic geometry conference, Rennes, France, June 20-24, 2011.

Singular Perturbation of Polynomial Potentials and Real Spectral Loci. Weizmann Inst. of Science, Rehovot, Israel, January 4, 2011.

Semi-monotone sets and triangulation of monotone families. Weizmann Inst. Of Science, Rehovot, Israel, December 28, 2010.

Semi-monotone sets and triangulation of tame monotone families. Real structures on complex manifolds : achievements and perspectives, Luminy-Marseille, France, June 14-18, 2010.

Semi-monotone sets. Seminaire de Geometrie Algebrique Reelle, Universite de Rennes I, France, June 2, 2010.

Triangulation of monotone families. Seminaire de Geometrie Algebrique Reelle, Universite de Rennes I, France, May 27, 2010.

Dessins d'Enfants for the Eigenfunctions of the Schrodinger equation. Geometry Seminar, University of Rennes I, France, May 26, 2010.

Singular Perturbation of Polynomial Potentials and Real Spectral Loci. Analytic and Algebraic Methods in Physics IV, Prague, May 9-11, 2010.

Dessins d'Enfants for the Eigenfunctions of Anharmonic Oscillator. Ssession on Real and Complex Singularities, Canadian Mathematical Society Winter Meeting, Windsor, December 5-7, 2009.

Irreducibility of some spectral determinants. Spectral Theory and Geometric Analysis, Northeastern University, Boston July 29 - August 2, 2009.

Triangulation of monotone o-minimal families. Workshop on Finiteness Problems in Dynamical Systems, Fields Institute, Toronto, June 22-26, 2009.

Multiplicity of a Noetherian intersection and degree of nonholonomy. Mini-workshop on Decidability and Effective Results in O-minimality, Fields Institute, Toronto, June 5-6, 2009.

Phase transitions in cluster dynamics. AGU Joint Assembly, Toronto, May 24-27, 2009.

Predictive understanding of disasters: universality of precursory phenomena. AGU Joint Assembly, Toronto, May 24-27, 2009.

Extreme events and their predictability in a branching diffusion model. AGU Joint Assembly, Toronto, May 24-27, 2009.

Dessins d'enfants for the eigenfunctions of the Schrodinger operator.
"Around Hilbert's 16th Problem" Conference in honor of Jean Jacques Risler, IMPA, Rio de Janeiro, August 4-8, 2008.

Approximation by monotone families of compact sets and topological complexity of the sets definable in o-minimal structures.
Geometry seminar, Math. Dept., Univ. Savoy, Chambery, France, May 30, 2008

Dessins d'enfants for the eigenfunctions of the quartic oscillator.
Workshop on "Effective real analytic geometry", ICMS, Edinburgh, UK, May 5-9, 2008

Approximation by monotone families of compact sets and topological complexity of the sets definable in o-minimal structures.
Workshop on "Enumeration and bounds in real algebraic geometry", Bernoulli Centre, EPFL, Lausanne, Switzerland, April 21-25, 2008

Clustering analysis of seismicity and aftershock identification.
Session IS67, European Geosciences Union General Assembly, Vienna, Austria, April 15-20, 2008

Graphs, braids, and eigenfunctions of the Schrodinger operator.
Bernoulli Centre, EPFL, Lausanne, Switzerland, March 25, 2008

Dessins d'enfants for the eigenfinctions of the quartic oscillator.
Math. Dept. Colloquium, Tel Aviv University, Tel Aviv, Israel, January 31, 2008

Dessins d'enfants for the eigenfinctions of the quartic oscillator.
Math. Dept. Colloquium, Technion, Haifa, Israel, January 28, 2008

Topological complexity of semi- and sub-algebraic sets.
The Weizmann Inst. of Science, Rehovot, Israel, January 15 and 22, 2008

Predictability of extreme events in spatially distributed driven hierarchical systems.
AGU Fall Meeting, San Francisco, December 10-14, 2007

Aftershock identification problem via the nearest-neighbor analysis for marked point processes.
AGU Fall Meeting, San Francisco, December 10-14, 2007

Multiplicity of a Noetherian intersection and degree of nonholonomy.
Kyoto University, Kyoto, Japan, June 5, 2007

Topological complexity of semi- and sub-algebraic sets.
Kyoto University, Kyoto, Japan, May 30, 2007

Wronski map, Schubert calculus, and pole placement.
Hokkaido University, Sapporo, Japan, May 22, 2007

Mystery of point charges.
Hokkaido University, Sapporo, Japan, May 21, 2007

Multiplicity of a Noetherian intersection and degree of nonholonomy.
Nihon University, Tokyo, Japan, May 16, 2007

Some mathematical problems related to modeling of seismicity.
Kinki University, Osaka, Japan, May 12, 2007

Earthquakes: an introduction.
Kinki University, Osaka, Japan, May 12, 2007

Non-algebraic dessins d'enfants and eigenfunctions of anharmonic oscillators.
Workshop on Real Algebraic Geometry, Oberwolfach, Germany, March 11-17, 2007.

Mystery of point charges.
Annual meeting of the AMS, New Orleans, January 5-8, 2007

Universal Pre-Disaster Transformation of Frequency-Magnitude Relation.
AGU Fall Meeting, San Francisco, December 11-15, 2006

Deviations from Scale-Invariance in Extreme Event Phenomena: A Theoretical Analysis
AGU Fall Meeting, San Francisco, December 11-15, 2006

Invariants of maximally inflected real rational quintics. Workshop on Singularities, Mathematische Forschungsinstitut Oberwolfach, Germany, September 10-16, 2006.

Reverse Tracing of Precursors: Ongoing Experiment in the Months-in-Advance Earthquake Prediction
AGU Fall Meeting, San Francisco, December 5-9, 2005

Rational functions with real critical points, the Catalan numbers, and real Schubert calculus
Mathematics Department Colloquium, IUPUI, November 18, 2005

Real Schubert calculus and the B. and M. Shapiro conjecture
Institute Henri Poincare, Paris, France, October 27-28, 2005

Topological complexity of definable sets
Logic Seminar, Universite Paris VII, France, October 24, 2005

Pfaffian functions and Sparsity
Institute Henri Poincare, Paris, France, October 20-21, 2005

Lower bounds in some problems of real Schubert calculus
Workshop on Computational Algebraic Geometry, Santander, Spain, June 30 - July 2, 2005

Rational functions and real Schubert calculus,
The Isaac Newton Institute, Cambridge, UK, May 26, 2005

The mystery of point charges,
The Isaac Newton Institute, Cambridge, UK, May 25, 2005

Degrees of the real Wronski maps,
Department of Mathematics, Durham University, UK, May 16, 2005

The mystery of point charges,
Department of Computer Sciences, University of Bath, UK, May 11, 2005

Betti numbers of sets defined by formulas with quantifiers,
The Isaac Newton Institute, Cambridge, UK, May 4, 2005

Betti numbers of sets defined by quantifier-free formulas,
The Isaac Newton Institute, Cambridge, UK, May 3, 2005

The mystery of point charges,
Department of Mathematics, Tel Aviv University, Israel, December 29, 2004

Degree of the real Wronski map and the pole placement problem in control theory,
Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel, December 21, 2004.

Hierarchical Description of Evolution of an Inverse Cascade in Percolation Model,
AGU Fall Meeting, December 13-16, 2004.

Short-Term Earthquake Prediction Based on the Reverse Tracing of Lithosphere Dynamics,
AGU Fall Meeting, December 13-16 2004.

Lower bounds in some problems of real Schubert calculus,
AMS Fall Central Section Meeting, Northwestern University, October 23-24, 2004.

Betti numbers of semi- and subalgebraic sets,
Mathematical Sciences Research Institute, Berkeley, April 14, 2004.

Betti numbers of semialgebraic and sub-Pfaffian sets,
Singularity Theory - in honor of S. Lojasiewicz, Jagiellonian University, Cracow, Poland, March 21-27, 2004

Rational functions with real critical points,
Mathematics Department Colloquium, Georgia Tech, March 18, 2004.

Betti numbers of semialgebraic sets,
Mathematics Department, Georgia Tech, March 17, 2004.

Geometry of faults and earthquake prediction,
Science of Earthquake Prediction, SCEC/USGS/CGS Workshop, USC, February 20, 2004.

Short-term premonitory rise of the earthquake correlation range,
American Geophysical Union Fall Meeting, San Francisco, December 8-12, 2003.

Betti numbers of sub-algebraic and sub-Pfaffian sets,
Workshop on Singularities, Mathematische Forschungsinstitut Oberwolfach, Germany, September 25-27, 2003.

Rational functions with real critical points,
Mathematics Department Colloquium, University of North Carolina at Chapel Hill, August 21, 2003.

Betti numbers of definable sets,
Joint meeting AMS and RSME, Seville, Spain, June 18-21, 2003.

Multiplicity of a Noetherian intersection,
Department of Mathematics, Univ. Autonoma de Madrid, Spain, June 16, 2003.

Betti numbers of definable sets,
Logic and Mathematics, University of Illinois at Urbana-Champaign, May 21-25, 2003.

Degree of the real Wronski map,
MIT Combinatorics Seminar, May 7, 2003.

Betti numbers of definable sets,
Centro de Giorgi, Pisa, Italy, March 20, 2003.

Cascade of clusters - from metaphor to algorithm?,
American Geophysical Union Fall Meeting, San Francisco, December 6-10, 2002.

On the short-term earthquake prediction: renormalization algorithm and observational evidence in S. California, E. Mediterranean, and Japan,
American Geophysical Union Fall Meeting, San Francisco, December 6-10, 2002.

Multiscale trend analysis: a new approach to studying complex time series,
American Geophysical Union Fall Meeting, San Francisco, December 6-10, 2002.

Counterexamples to pole placement by real static output feedback.
Fifteenth International Symposium on Mathematical Theory of Networks and Systems, University of Notre Dame, August 12-16, 2002.

Betti numbers of semialgebraic and sub-Pfaffian sets (Semi-plenary lecture).
Computational Algebraic Geometry, Foundations of Computational Mathematics, Institute for Mathematics and its Applications, Minneapolis, August 8-10, 2002.

Complexity of computations with Pfaffian and Noetherian functions (4 lectures).
Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Seminaire de Mathematiques Superieures, Seminaire Scientifique OTAN, Universite de Montreal, Canada, July 8-19, 2002.

Understanding and prediction of critical transitions in complex systems.
The James S. McDonnell Foundation 21st Century Science Initiative Annual Meeting, Tarrytown, NY, June 17-20, 2002.

Betti numbers of sub-Pfaffian sets.
Reelle Algebraische und Analytische Geometrie, Oberwolfach, Germany, March 17-23, 2002.

Colliding Cascades and Boolean Delay Equations.
American Geophysical Union Fall Meeting, San Francisco, December 10-14, 2001.

Ensemble of premonitory seismicity patterns.
American Geophysical Union Fall Meeting, San Francisco, December 10-14, 2001.

Degree of the real Wronski map.
Mathematics Department, University of Michigan, Ann Arbor, November 2, 2001.

Modeling of seismicity: a mathematician's perspective.
Complexity in Geophysical Systems, Institute for Mathematics and its Applications, University of Minnesota, October 8-12, 2001.

Conference Convener, "Vladimir Keilis-Borok's 80th Birthday Festschrift."
Institute for Mathematics and its Applications, University of Minnesota, October 5-6, 2001.

An Exactly Soluble Hierarchical Clustering Model: Inverse Cascades, Self-Similarity, and Scaling.
Institute for Mathematics and its Applications, University of Minnesota, October 1, 2001.

Workshop Convener, "Spatio-temporal Patterns in the Geosciences."
Institute for Mathematics and its Applications, University of Minnesota, September 25-29, 2001.

Combinatorics of the real Wronski map.
Mathematics Department, University of Minnesota, September 19, 2001.

Degree of the real Grassmann variety.
Mathematics Department, University of Minnesota, September 17, 2001.

Degrees of real Grassmann varieties.
Geometrie Moderee et Integrales Abeliennes, CIRM, Luminy-Marseille, France, June 25-29, 2001.

Degrees of real Grassmann varieties.
International Conference on Geometrie Moderee et Integrales Abeliennes, CIRM, Luminy-Marseille, France, June 25-29, 2001.

Computations with Pfaffian and Noetherian functions.
International Conference on Real Algebraic and Analytic Geometry, University of Rennes I, France, June 11-15, 2001.

Pfaffian complexity.
DIMACS Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science. DIMACS Center, Rutgers University, March 12-16, 2001.

Scaling in a hierarchical model of clustering.
American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2000.

Premonitory change of scaling in seismicity.
American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2000.

Selforganization of critical transitions in the colliding cascades with applications to earthquake prediction.
American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2000.

Premonitory redistribution of seismicity over the fault network in southern California.
American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2000.

Migration of fluids and dynamics of blocks-and-faults system.
American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2000.

Rational functions with real critical points, the Catalan numbers, and the Schubert calculus.
Mathematics Department Colloquium, Notre Dame University, December 4, 2000.

Multiplicity of a Noetherian intersection and resolution of Noetherian singularities.
AMS Meeting, San Francisco, CA, October 21-22, 2000.

Rational functions with real critical points, the Catalan numbers, and the Schubert calculus.
Mathematics Department Colloquium, Ohio State University, October 10, 2000.

Scaling in a hierarchical model of clustering.
The Earth: Earthquakes and Seismic Waves, Leon Knopoff Anniversary Symposium, UCLA, September 14, 2000.

Geodynamic background of earthquake prediction.
Keynote lecture, Special Symposium B-9 - New Perspective in Earthquake Prediction, International Geological Congress, Rio de Janeiro, August 2000.

Complexity of cylindrical decomposition for restricted sub-Pfaffian sets.
International Meeting "Effective Methods in Algebraic Geometry" (MEGA) Bath, UK, June 20-24, 2000.

Rational functions with real critical points and real enumerative geometry.
Mathematics Department Colloquium, Purdue University, February 29, 2000.

Rational functions with real critical points, real Schubert calculus, and a conjecture of Shapiro and Shapiro.
Workshop on Computational Algebraic Analysis, MSRI, Berkeley, CA, January 5-7, 2000.

Earthquake prediction: recent results and what comes next.
International Union of Geodesy and Geophysics, General Assembly, Birmingham, UK, July 18-30, 1999

Connection between structure, dynamics and instability of the Lithosphere.
International Union of Geodesy and Geophysics, General Assembly, Birmingham, UK, July 18-30, 1999

Precursory seismicity patterns: recent results and emerging possibilities
European Geophysical Society, General Assembly, Hague, Netherlands, April 19-23, 1999

Complexity of the Complement of a Sub-Pfaffian Set.
Joint Mathematics Meeting, San Antonio, TX, January 13-16, 1999.

Complexity of the complement of a subpfaffian set.
Working Group in Real Algebraic Geometry and Algorithms, MSRI, Berkeley, CA, September 24, 1998.

Multiplicity of a solution of a system of Noetherian equations.
Intnl. Conference on Solving Systems of Equations, MSRI, Berkeley, CA, September 14-18, 1998.

Multiplicity of a solution of a system of Noetherian equations.
Intnl. Conference on Solving Systems of Equations, MSRI, Berkeley, CA, September 14-18, 1998.

The multiplicity of a polynomial on the solution of a differential equation.
Seminar on Commutative Algebra, Algebraic Geometry, and Combinatorics, UC Berkeley, CA, September 8, 1998.

Complexity of computations with Pfaffian and Noetherian functions.
Workshop on Model Theory, Algebra and Arithmetic, MSRI, Berkeley, CA, June 1-6, 1998.

Multiplicity of a Noetherian Intersection.
Meeting of the American Mathematical Society, Montreal, Canada, September 26-28, 1997.

Geometric Incompatibility of a Fault System. Lattice Models of Failure: From Earthquakes to Groebner Bases.
Fourth Workshop on Non-Linear Dynamics and Earthquake Prediction, International Center for Theoretical Physics, Trieste, Italy, October 6-24, 1997.

The multiplicity of a Noetherian intersection.
International Workshop on Geometry and Complexity, Toronto, May 5-10, 1997.

Multiplicity of a zero of an analytic function on a trajectory of a vector field.
Meeting of the American Mathematical Society, College Park, MD, April 12-13, 1997.

Finiteness properties for Pfaffian function and complexity of quantifier simplification.
International Workshop on Model Theory of Analytic Functions, Toronto, March 17-21, 1997.

Geometric Incompatibility of Tectonic Faults and Dynamics of Seismicity.
International Conference on Mathematical Geophysics, Santa Fe, NM, June 16-21, 1996.

Complexity of Frontier and Closure of Semi-Pfaffian Sets and Quantifier Simplification for Semi-Pfaffian Expressions.
Meeting of the American Mathematical Society, Baton-Rouge, Louisiana, April 19-21, 1996

Complexity of Frontier and Closure of Semi-Pfaffian Sets and Quantifier Simplification for Semi-Pfaffian Expressions.
Meeting of the American Mathematical Society, Baton-Rouge, Louisiana, April 19-21, 1996

Finiteness Properties for Functions Defined by polynomial Pfaffian Equations.
AMS-SIAM Summer Seminar in Applied Mathematics Park City, Utah, July 17 - August 11, 1995.

Geometric Incompatibility in a Fault System.
IUGG XXI General Assembly, Boulder, Colorado, July 2-14, 1995.



Last update: June 7, 2017
URL: http://www.math.purdue.edu/~agabriel/research.html