Short C.V. for J. Maurice Rojas (Last Updated February 4, 2008)

Biographical Information

Address

TAMU 3368 Department of Mathematics
Texas A&M University
College Station, Texas 77843-3368.
Tel: (979) 845-2083
FAX: (979) 845-6028
e-mail: rojas@math.tamu.edu

Education

• Ph.D., Applied Mathematics, University of California, Berkeley, 1995; Steve Smale, advisor.
• C. Phil., Applied Mathematics, University of California, Berkeley, 1993.
• M.S., Computer Science, University of California, Berkeley, 1991; John Canny, advisor.
• M.A., Mathematics, University of California, Berkeley, 1991.
• B.S., Mathematics/Applied Science, University of California, Los Angeles, 1988.

Research Interests:

Algorithmic Algebraic Geometry, Algorithmic Number Theory, Polyhedral Combinatorics, Complexity Theory, Scientific Computation, Cryptology, Bioinformatics

Current Position

Professor, Department of Mathematics, Texas A&M University, September 2007 - Present

Previous Positions

• Consultant, Combustion Research Facility, Sandia National Laboratories, Aug. & Dec. '07
• Workshop Organizer and Visiting Member, Institute for Mathematics and its Applications, Minneapolis, MN, April-May '07
• JAMI Visiting Professor, Johns Hopkins University, Baltimore, MD, March '07
• Consultant, Computational Biology Group, CCIM Center, Sandia National Laboratories Oct.-Nov. 2005
• Assistant Professor, Tenure Track, Department of Mathematics, Texas A&M University, January 2001 - August 2004
• JAMI Visiting Member, Mathematical Sciences Research Institute, April 2004
• Visiting Professor, Johns Hopkins University, March 2004
• New Directions Cellular Physiology Course Participant, Institute for Mathematics and its Applications, June 2003
• Research Assistant Professor, City University of Hong Kong (January 1998 - January 2001)
• National Science Foundation Postsdoctoral Fellow and Applied Mathematics Instructor, MIT, Fall 1996 - Fall 1997
• Summer Staff Member, MIT Lincoln Laboratories, Lexington, Massachusetts, Summer '97
• Research Mathematician, NAWCAD (Office of Naval Research), Warminster, Pennsylvania, Summer '96
• Visiting Professor, City University of Hong Kong, May 1996
• National Science Foundation Postdoctoral Fellow, MSRI (Berkeley), Spring 1996
• National Science Foundation Postdoctoral Fellow (mentor: Alan Edelman), Massachusetts Institute of Technology, Fall 1995
• Research Mathematician, AT&T Bell Laboratories, Murray Hill, NJ, August '95
• Research Mathematician, NAWCAD (Office of Naval Research), Warminster, Pennsylvania, July '95
• Chateaubriand Fellow (mentor: Marie-Francoise Roy), IRMAR, Universite de Rennes I, France, Spring '95
• Visiting Professor, Universitat Pompeu Fabra, Barcelona, Fall '94
• Research Mathematician, IBM T. J. Watson Research Center, Yorktown Heights, NY, Summer '94
• Research Mathematician, AT&T Bell Laboratories, Naperville, IL, Summer '93
• Research Mathematician, Center for Communications Research, Princeton, NJ, Summer '92

Grants and Awards (Rojas is the principal investigator unless otherwise noted)

NSF CAREER Award DMS-0349309: ``Complexity, Reality, and Rationality in Large Nonlinear Equations Solving'', $400000, 2004-2009. (One of 11 awarded in mathematics in 2004).

Senior Personnel on NSF REU grant (DMS-0552610), $45000, 2005-2008.

Consultant on Texas MTC Grant: Curriculum Alignment, $10000, 2006-2007.

National Science Foundation: ``Real Solving and Protein Structures: Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences (supplement to DMS-0211458, jointly funded by the Directorate for Biological Sciences and the Division of Mathematical Sciences), $99760, 2003-2005.

National Science Foundation: ``Robust Output Sensitive Algorithms for Subanalytic Geometry'', DMS-0211458 (jointly funded by the Computational Mathematics and Algebra/Number Theory/Combinatorics programs), $98800, 2002-2005.

National Science Foundation and Defense Advanced Research Projects Agency: ``Degeneracy Detection for Curved Solids'' (co-PI with John Keyser), DMS-0138446, Incubation grant from the NSF/DARPA CARGO (Computational and Algorithmic Representation of Geomtric Objects) program, $103636, 2002-2003.

National Science Foundation: ``NSF/CBMS Regional Conference in the Mathematical Sciences: Solving Systems of Polynomial Equations'', DMS-0122220, (co-PI with Paulo Lima-Filho and Hal Schenck), $35000, May 2002.

Texas A&M College of Science: Start-Up Funds, January 2001 to January 2003.

Journal of Complexity 2000 Best Paper Award, (for "Some Speed-Ups and Speed Limits in Real Algebraic Geometry"), awarded at FoCM 2002 (University of Minnesota), Aug. 6, 2002.

Please click HERE for my Publications List

Students Advised

Rusek, Korben (Ph.D., Mathematics), Fall 2007 - Present

Ibrahim, Ashraf (Ph.D., Mathematics), Spring 2006 - Present

Sethuraman, Swami (Ph.D., Mathematics), Spring 2003 - Present

Kyriopolos, Theodoros (Ph.D., Mathematics), Spring 2004 - Present

Muzheve, Michael (M.S. Mathematics, Dec. 2005), Spring 2003 - Fall 2005

Stella, Casey (M.S. Mathematics, May 2005) Sept. 2003 - Spring 2005

Dieringer, Jennifer (Mathematics, B.S.), June 2004 - Spring 2005

Worthen, Brian (Mathematics, B.S.) June 2004 - Fall 2005

Bliss, Robert (Biochemistry, B.S., co-advised with Dr. Jerry Tsai), Oct. 2003 - Spring 2005

Holmes, Brad (Biochemistry, B.S., co-advised with Dr. Jerry Tsai), Oct. 2003 - Spring 2005

Selected Talks

Invited Seminar Talks

``Most Hard Equations are Easy,'' invited mathematics colloquium, University of Houston, November 28, 2007.

``Torsion Points and Algorithmic Fewnomial Theory,'' Number Theory Seminar, Univeristy of Texas at Austin, September 27, 2007.

``Efficient Polynomial System Solving: An Introduction,'' invited series of 10 talks, Sandia National Laboratories, Combustion Research Facility, Livermore, California, August 8-12, 2007.

``Random Polynomial Systems and Balanced Metrics on Toric Varieties,'' algebraic geometry seminar, Institute for Mathematics and its Applications, July 27, 2007.

``The Complete Fewnomial Conjecture,'' algebraic geometry seminar, University of Chicago, May 9, 2007.

``Feasibility of Complex Equations and Primes in Arithmetic Progressions,'' computer science seminar, University of Wisconsin, May 7, 2007.

``Large Chambers, Discriminants, and Fewnomials,'' invited series of 3 talks, Johns Hopkins University, March 21, 22, 27.

``The Complete Fewnomial Conjecture,'' geometry seminar, Courant Institute of Mathematical Sciences, New York University, March 20, 2007.

``On the Effectiveness of Number Theory in Algorithmic Geometry,'' promotion talk, Texas A&M University, September 13, 2006.

``On the Effectiveness of Number Theory in Algorithmic Geometry,'' Algebra Seminar, Colorado State University, Ft. Collins, Colorado, August 24, 2006.

Extremal Real Algebraic Geometry, Applied Mathematics Seminar, Colorado State University, Ft. Collins, Colorado, August 22, 2006.

Interpolating Between Quantum and Classical Complexity, NEC Research Laboratories, Princeton, New Jersey, May 18, 2006.

Algebraic Geometry Tools for Inverse QSAR, Sandia National Laboratories, Nov. 15, 2005.

A $p$-adic Quantum Complexity Threshold, Los Alamos National Laboratories, Nov. 13, 2005.

Mixed Subdivisions and Resultants, University of New Mexico, Albuquerque, New Mexico, Nov. 8, 2005.

Polytopes, Polynomials, and Volume, University of New Mexico, Albuquerque, New Mexico, Nov. 2, 2005.

An Introduction to Arithmetic Fewnomial Theory, University of New Mexico, Albuquerque, New Mexico, Oct. 26, 2005.

Why Polyhedra Matter in Nonlinear Equation Solving, Sandia National Laboratories, Oct. 24, 2005.

Algorithms for Real and $p$-Adic Geometry, UT San Antonio, Oct. 14, 2005.

Arithmetic and Algorithmic Aspects of Fewnomial Theory, Algebra Seminar, University of Texas, Austin, March 29, 2005.

An Introduction to p-adic Fewnomial Theory, Algebraic Geometry Seminar, Princeton University, February 4, 2003.

Research Conference Talks

``Discriminant Chambers and Smale's 17th Problem,'' [cancelled due to family emergency]

NSF CDI Workshop, NSF, Arlington, Virginia, October 30-31, 2007

``Most Hard Equations are Easy,''

Introductory Talk, Modern Mathematics Workshop, Kansas City, Missouri, October 11, 2007.

``P=NP, Optimization, and Algebraic Geometry,''

IMA summer school in algebraic geometry, Texas A&M University, July 27, 2007.

``Complex Feasibility and Primes in Arithmetic Progression,'' [cancelled due to conflict with 2007 REU at Texas A&M]

Number Theory and Computability, ICMS (International Centre for Mathematical Sciences), Edinburgh, June 25-29, 2007.

``New Complexity Bounds for Certain Real Fewnomial Zero Sets,'' [lectured delivered by co-author, due to conflict with 2007 REU at Texas A&M]

MEGA (Effective Methods in Algebraic Geometry) 2007, Johann Radon Institute for Computational and Applied Mathematics, June 25-29, 2007.

``Discriminants and New Real Topological Complexity Bounds,''

poster session on Non-linear Computational Geometry , Institute for Mathematics and its Applications, Minnesotta, May 29, 2007.

``A Critical Radius for Low Complexity,''

Workshop on Complexity, Coding, and Communication , Institute for Mathematics and its Applications, Minnesotta, April 20, 2007.

``Toward Descartes' Rule for Complete Fields and Arbitrary Codimension,''

post session on Complexity, Coding, and Communication , Institute for Mathematics and its Applications, Minnesotta, April 16, 2007.

On the Effectiveness of Number Theory in Algebraic Geometry, Algorithms in Algebraic Geometry Workshop, Institute for Mathematics and its Applications, Minnesotta, September 20, 2006.

Convexity and a Phase Transitions for Detecting Real Roots, MAA MathFest 2006, Invited Paper Session on Computational Convexity and its Applications, Knoxville, Tennessee, August 10, 2006.

Understanding Polynomial Equations: Complexity and Reality, two invited plenary lectures, Midatlantic Algebra Conference, James Madison University, Virginia, April 29--30, 2006.

Basic Tropicalia (or, How to Use Polyhedra to Understand Polynomials), Workshop on Random Analytic Functions and Surfaces, American Institute of Mathematics, January 16, 2006.

From Quantum to Classical Complexity via Sparse Polynomials, Quantum Computing Conference, Texas A&M University, College Station, Texas, Nov. 11, 2005.

Extremal and Algorithmic Algebraic Geometry, Midwest Algebra, Geometry, and their Interactions Conference; Notre Dame, October 9, 2005.

Parallels Between Real and $p$-Adic Complexity, Foundations of Computational Mathematics Meeting, Real Number Complexity Workshop, University of Cantabria, Santander, Spain, July 8, 2005.

A Subexponential Algorithm for Containment and Intersection Between Translated Subtori and Algebraic Sets, MEGA (Effective Methods in Algebraic Geometry) 2005, Sardinia, Italy, May 27, 2005.

Some Speed-Ups and Speed Limits for Real Fewnomials, Joint Mathematics Meeting, Atlanta, Georgia, Special Session on Algorithmic Algebraic and Analytic Geometry, January 8, 2005.

Torsion Points on Algebraic Sets and A-Discriminants, Workshop on Resolution of Singularities, Factorization of Birational Mappings, and Toroidal Geometry; Banff International Research Station (Banff, Alberta, Canada), Dec. 12, 2004.

Some Algorithmc Aspects of Fewnomials, Workshop on Algorithmic, Combinatorial, and Applicable Real Algebraic Geometry, Mathematical Sciences Research Institute, April 12, 2004.

Some Recent Advances in Real Solving, SIAM Conference on Geometric Design and Computing (Seattle, Washington), Nov. 10-13, 2003.

Outreach Talks

``Codes and Numbers,'' mathematics enrichment demonstration, 1st - 4th grade classes, Aggieland Country School, College Station, October 25, 2007.

``Lines and Space,'' mathematics enrichment demonstration, 1st - 4th grade classes, Aggieland Country School, College Station, Texas, Dec. 10, 2006.

``Robots and Polynomials,'' invited talk, Texas A&M Mathematics Contest, October 28, 2006.

``Optimization and High School Geometry,'' invited talk, State of Texas MTC curriculum planning meeting, Sep. 30, 2006

``From Pick's Theorem to Euler Characteristic,'' 3 hour interactive course for SEEMATH middle-school students (co-taught with Prof. Paulo Lima-Filho), Texas A&M University, June 22-23, 2006.

``Distances and Angles,'' mathematics enrichment demonstration, 1st - 4th grade classes, Aggieland Country School, College Station, Texas, May 15, 2006.

``Believe it or Prove it,'' expository talk, delivered to 8 pre-calculus classes at Bryan High School, Bryan, Texas, May 5, 2006.

Software

• HKPLOT: Visualizing A-Discriminants for generic (n+3)-sets in Z^n.
• AMOEBA: Visualizing the zero sets of bivariate polynomials over non-Archimedean complete fields (co-authored with Zhigang Zhang).

Activities

Summer REU Instructor 2007, 2006, 2005, 2004

Reviewer for AMS MathSciNet, Sept. 2005 - Present

Panelist for the NSF: 2006, 2005, 2004, 2003, 2002

Reviewer for NSF/CONICYT (joint US/Chile) Bicentennial Program in Science and Technology, 2006

Reviewer for NSF Proposals: 2004-Present

Reviewer for DOE Proposal: 2005

Referee for various journals and international conferences, including Computational Complexity, Discrete and Computational Geometry, Duke Mathematical Journal, Foundations of Computational Mathematics, Journal of the AMS, Journal of Symbolic Computation, MEGA 2005, MEGA 2007, CSR 2007, and FoCM 2005.

This C.V. was last updated on April 3, 2008.