Previous Positions
- Consultant, Viz and Scientific Computation Group, Sandia National
Laboratories, April '09, Dec. '08
- Consultant, Combustion Research Facility, Sandia National Laboratories,
Aug. & Dec. '07
- Workshop Organizer and Visiting Member,
Institute for Mathematics and its Applications,
Minneapolis, MN, Apr.-May '07
- JAMI Visiting Professor,
Johns Hopkins University, Baltimore, MD, Mar. '07
- Consultant,
Computational Biology Group, CCIM Center, Sandia National Laboratories
Oct.-Nov. '05
- Associate Professor (tenured), Department of Mathematics, Texas A&M
University, Sep. 2004 - Aug. 2007
- JAMI Visiting Member, Mathematical Sciences Research Institute, Apr. '04
- Visiting Professor, Johns Hopkins University, Mar. '04
- New Directions Cellular Physiology Course Participant, Institute
for Mathematics and its Applications, Jun. '03
- Assistant Professor, Tenure Track, Department of Mathematics, Texas A&M
University, Jan. '01 - Aug. '04
- National Science Foundation Postsdoctoral Fellow and Applied Mathematics
Instructor, MIT, Fall '96 - Fall '97 and Fall '95 (mentor: Alan Edelman)
- National Science Foundation Postdoctoral Fellow,
MSRI (Berkeley), Spring 1996
- Visiting Professor Appointments:
City University of Hong Kong (Jan. '98 - Jan. '01, May '96) and
Universitat Pompeu Fabra (Barcelona, Spain, Fall '94)
-
Summer Research Mathematician:
MIT Lincoln Laboratories (Lexington, Mass.) in '97;
AT&T Bell Laboratories (Murray Hill, NJ in '95 and Naperville, IL in '93);
NAWCAD (Office of Naval Research, Warminster, Pennsylvania) in
'96 and '95; IBM T. J. Watson Research Center (Yorktown Heights, NY) in '94;
Center for Communications Research (Princeton, NJ) in '92
- Chateaubriand Fellow (mentor: Marie-Francoise Roy), IRMAR,
Universite de Rennes I, France, Spring '95
Grants and Awards (Rojas is the principal investigator unless otherwise
noted)
``ASCR: Topology for Statistical Modeling of Petascale Data,'' (TAMU
amount $214,795, co-PI: Rojas, PI: P. Pebay of Sandia National Laboratories,
and other co-PIs from University of Utah), Advanced Scientific Computing
Research (Mathematics for Analysis of Petascale Data), Department of Energy,
DE-SC0002505, 9/1/2009-8/31/2012.
``MCS: Randomization in Algorithmic Fewnomial Theory Over
Complete Fields,'' ($400,001, PI: Rojas, co-PIs: Martin Avendano, Scott
Zrebiec) Mathematics/Computer Science Interface Program, NSF,
DMS-0915245, 9/1/2009-8/31/2012.
Wenner-Gren Foundation Visiting Researcher Grant (75000 Swedish
Kroner), to visit and work with Mikael Passare and Boris Shapiro at
Stockholm University, Sweden (awarded 12/2008, visit will be during
Mar.-Jun. 2009)
``TAGS (Texas Algebraic Geometry Seminar) 2009,'' ($8690, PI: Rojas,
co-PIs: J. M. Landsberg, Paulo Lima-Filho, Laura Matusevich, Frank Sottile),
conference proposal, NSF, DMS-0915235, 4/1/2009-3/31/2010
Editor, Houston Journal of Mathematics (Jan. 2008 - Present)
Outstanding Teaching Award, Department of Mathematics, Texas A&M
University (awarded December 2007).
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-0850470), $314600, 2009-2012.
Senior Personnel on NSF REU grant (DMS-0552610), $398400, 2006-2009.
Consultant on Texas MTC Grant: Curriculum Alignment, $10000, 2006-2007.
National Science Foundation grants before 2007:
DMS-0211458 (individual), supplement to DMS-0211458, CARGO
grant (DMS-0138446, co-PI with John Keyser), CBMS Conference
grant (co-PI with Paulo Lima-Filho and Hal Schenck)
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.
Students Advised
Rusek, Korben (Ph.D., Mathematics), Fall 2007 - Present
Ibrahim, Ashraf (Ph.D., Mathematics),
Spring 2006 - December 2009
Sethuraman, Swami (Ph.D., Mathematics),
Spring 2003 - May 2009
Kyriopolos, Theodoros (Ph.D., Mathematics),
Spring 2004 - December 2007
Advised in 2006 or earlier: Michael Muzheve (M.S. Mathematics, Dec. 2005);
Casey Stella (M.S. Mathematics, May 2005);
Jennifer Dieringer (Mathematics, B.S.);
Brian Worthen (Mathematics, B.S.);
Robert Bliss (Biochemistry, B.S., co-advised with Dr. Jerry Tsai);
Brad Holmes (Biochemistry, B.S., co-advised with Dr. Jerry Tsai)
Selected Talks
Some Invited Seminar Talks (complete list on full CV)
``Number Theory, Randomization, and Real Topology Computation,''
Colloquium, Mathematics Department, Technical University of
Lisboa, Portugal, May 20, 2009
``Number Theory and the Hardness of Complex Geometry,'' Several Complex
Variables Seminar, Stockholm University, April 28, 2009
``Real Topology Computation via Amoebae I,'' Several Complex
Variables Seminar, Stockholm University, April 14, 2009
``Statistical Modelling and Real Solving,'' Sandia National Laboratories,
Livermore, California, April 1, 2009
``ABCs of Real Solving,'' San Francisco State University, March 4, 2009
``Hilbert's 10th Problem in Low Dimensions,''
University of Utah, Salt Lake City, Nov. 21, 2008
``ABCs of Real Algebraic Geometry,'' colloquium, University of Utah,
Salt Lake City, Nov. 20, 2008
``ABCs of Real Algorithmic Geometry,'' colloquium, Center for
Communications Research, Institute for Defense Analyses, Princeton, NJ,
Oct. 24, 2008
``Unifying Algorithms for Real and p-adic Geometry,'' special
seminar, University of Illinois, Urbana-Champaign, Aug. 15, 2008
1 Week Invited Undergraduate Course on Algorithic Fewnomial Theory,
July 7-11, 2008, Institute for Advanced Study - Park City Mathematics
Institute, Park City, Utah
``A Number-Theoretic Approach to the P vs. NP Problem II:
Short Interval Estimates and Complex Roots,''
Number Theory Seminar, Texas A&M University, Jan. 30, 2008.
``A Number-Theoretic Approach to the P vs. NP Problem I,''
Number Theory Seminar, Texas A&M University, Jan. 23, 2008.
``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.
Talks during 2006 and earlier delivered at institutions including the
following:
Colorado State University (August 22, 2006);
NEC Research Laboratories, Princeton (May 18, 2006);
Sandia National Laboratories (Nov. 15, 2005);
Los Alamos National Laboratories (Nov. 13, 2005);
Princeton University (Feb. 4, 2003).
Some Research Conference Talks
``Chamber Cones and Faster Real Solution Counting,''
Southwest AMS meeting, special session on applicable
algebraic geometry, Waco, Texas, October 18, 2009
``Optimizing Certain Fewnomials Faster,''
Symbolic and Numeric Computation, Kyoto, Japan,
August 3, 2009
``Faster Real Feasibility and Discriminant Complexity,''
International Symposium on Symbolic and Algebraic Computation,
Seoul, Korea, July 31, 2009
``Refined Asymptotics for Sparse Sums of Squares,''
MEGA 2009 (Effective Methods in Algebraic Geometry),
Barcelona, Spain, June 5, 2009 [Cancelled due to scheduling conflict
with summer REU class Rojas was teaching.]
``Randomization and Real Solving,''
NSF Workshop on the Future of Symbolic Computation, Rhode
Island University, April 30, 2009
``Statistical Modelling and Real Solving,''
Texas A&M University Computational Biology Meeting, College Station,
Texas, March 7, 2009
``Randomization and Discriminant Chambers,''
joint AMS/SMB meeting, Rio de Janeiro, June 4-8, 2008
``Sharper, High Probability Bounds for Real Fewnomial Zero Sets,''
Enumeration and bounds in real algebraic geometry, April 21--26, 2008
``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.
``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.
Some Conference Talks before 2007
Talks during 2006 and earlier delivered at conferences
including the following:
invited plenary lectures at Midatlantic Algebra Conference, James Madison
University, Virginia (April 29-30, 2006); Workshop on Random Analytic
Functions and Surfaces, American Institute of Mathematics (January 16, 2006);
Quantum Computing Conference (Texas A&M University, Nov. 11, 2005);
MEGA (Effective Methods in Algebraic Geometry, 2005, Sardinia,
Italy, May 27, 2005);
Workshop on Resolution of Singularities, Factorization of Birational
Mappings, and Toroidal Geometry (Banff International
Research Station, Dec. 12, 2004);
Workshop on Algorithmic, Combinatorial, and Applicable
Real Algebraic Geometry (Mathematical Sciences Research
Institute, April 12, 2004);
SIAM Conference on Geometric Design and Computing (Seattle, Washington,
Nov. 10-13, 2003)
Outreach Talks
``Secret Codes, Rotating, and Adding,'' enrichment talk for
middle school students, College Station, Texas, July 1, 2009
``When Pretty Pictures Fail,'' enrichment talk for high school students,
Texas A&M University, June 17, 2009
``Polynomial System Solving: Introduction and Applications,''
UBM undergraduate seminar, Nov. 10, 2008
``From Linear Algebra to Real Algebraic Geometry,'' summer bridge
program talk, July 23, 2008
``Most Hard Equations are Easy,'' Aggieland Saturday (presentation
to prospective undergraduate students and their parents), Feb. 16, 2008
``Most Hard Equations are Easy,'' Graduate Student Seminar talk,
Feb. 14, 2008
``Codes and Numbers,'' mathematics enrichment demonstration, 1st -
4th grade classes, Aggieland Country School, College Station,
October 25, 2007.
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 2009, 2008, 2007, 2006, 2005, 2004
Reviewer for AMS MathSciNet, Sept. 2005 - Present
Panelist for the NSF: 2008, 2002-2006
Reviewer for NSF/FONDECYT Program: 2008
Reviewer for NSF/CONICYT Program: 2006
Reviewer for NSF Proposals: 2004-Present
Reviewer for NSA Proposal: 2009
Reviewer for DOE Proposal: 2005
Referee for various journals and international
conferences, including Algebra and Number Theory, Advances in
Applied Mathematics, Computational
Complexity, Discrete and Computational Geometry,
Duke Mathematical Journal, Foundations of Computational
Mathematics, Journal of the AMS, Journal of Symbolic Computation,
ISSAC 2008, MEGA 2009, MEGA 2007, MEGA 2005, CSR 2007,
and FoCM 2005.
This C.V. was last updated on Feb. 1, 2010.