Eliana M. Zoque
Visiting Assistant Professor, UC Riverside.
Contact Information
/ · Departmental address: Department of Mathematics, UC Riverside, 900. University Ave., Riverside, CA 92521, USA· Office phone: 951-827-3118
Education
/ · PhD in MathematicsThe University of Chicago, Chicago, IL
GPA: N/A
· PhD studies in Mathematics
University of Michigan, Ann Arbor, MI
GPA: 8.8/9.0
· M.Sc. in Mathematics
Universidad de los Andes, Bogota, Colombia
GPA: 4.85/5.00 in an absolute scale (no curve)
· B.S. in Mathematics
Universidad de los Andes, Bogota, Colombia
Graduated with honors.
Minor: Computer Engineering.
GPA: 4.61/5.00 in an absolute scale (no curve) / 2004-2009
2003-2004
2000-2002
1996-2000
Skills and Tools
/ · Fluent in Mathematica, Matlab and C, basic knowledge of C++.· Took undergraduate classes in data structures, logical and functional programming, algorithm development, probability, real analysis and numerical analysis. Took graduate classes in real and complex analysis.
Professional Experience
/ · Visiting Assistant Professor, University of California Riverside.· Lecturer, The University of Chicago.
· College Fellow, The University of Chicago.
· Coordination Director, XX Iberoamerican Mathematical Olympiad, Cartagena de Indias, Colombia. Directed the grading team
· International Advisor, VI Centroamerican Mathematical Olympiad, Managua, Nicaragua. Member of the Advisory Committee to prepare the test.
· Graduate Student Instructor, The University of Michigan.
· Lecturer, Universidad de los Andes.
· Research Assistant, Universidad de los Andes
Model Theory and Algebraic geometry.
· Graduate teaching assistant, Universidad de los Andes
· Apprentice Teacher, Universidad de los Andes / 2009-2001
2005-2009
2004-2005
2005
2004
2003
2003-2004
2002
2000-2003
1999-2000
Honors and Awards
/ · B.S. with Honors, Universidad de los Andes, Bogota, Colombia· Fellowship: Beca Cuarenta años, Universidad de los Andes
· Fellowship: Beca de Excelencia, Universidad de los Andes
· Gold Medal: II Iberoamerican Mathematical Olympiad for University Students
· Silver Medal: I Iberoamerican Mathematical Olympiad for University Students
· Silver Medal: XXXVII International Mathematical Olympiad, Mumbai, India
· Bronze Medal: XXXVI International Mathematical Olympiad, Toronto, Canada
· Bronze Medal: XXXV International Mathematical Olympiad, Hong Kong
· Gold Medal: XI Iberoamerican Mathematical Olympiad, San Jose, Costa Rica
· Bronze Medal: VIII Iberoamerican Mathematical Olympiad, Mexico City, Mexico / 2000
1996-2000
1998-1999
1999
1998
1996
1995
1994
1996
1993
Research Interests and Projects
/ · I am interested in Algebra, including Combinatorics, Representation Theory and Algebraic Geometry.· While I got my minor in Computer Engineering, I learned data structures in C and also logical and functional programming. The largest project I worked on was a simulation of a train system using data structures.
· In my undergraduate thesis I found a basis for the top homology of the non-crossing partition lattice. Though it is not a geometric lattice, I was able to adapt techniques used on geometric lattices to find a basis with elements that are in bijection with binary trees. Then I analyze the action of the dihedral group on this basis.
· During my first quarter at the University of Chicago I was working on the Abelian sand pile model. I used the software Matlab to design and implement an algorithm to find the equilibrium state on a graph with four vertices, one of them being a sink. The idea of the algorithm is to apply successive combinations of avalanches considering them one single operation. Our algorithm was computationally efficient.
· In my PhD thesis I studied the algebraic variety of n by n matrices with commutator of rank at most one. I describe its irreducible components; two of them correspond to the pairs of commuting matrices, and n-2 components of smaller dimension corresponding to the pairs of rank one commutator. Even though these matrices don’t commute as endomorphisms of the n-dimensional vector space, they act as commutative operators on a smaller space. By considering this action we define a map to the zero fiber of the Hilbert scheme of points and study the image and the fibers. We used the software Mathematica to produce explicit examples of conjugation classes for matrices of various sizes and for these examples we were able to define the maps that we generalized and used in the proofs. The numerical evidence allowed us to conjecture which maps have homogeneous fibers, and we proved the conjectures algebraically later. We also used Mathematica to disprove the irreducibility of a class of principal nilpotent pairs of nilpotent commuting matrices.
· As a postdoc at UC Riverside I have been studying a family of partitions defined recursively, and was able to find a non-recursive description with inequalities. Mathematica was used to create the family and check the new description
Talks
/ · Kostka polynomials in Lie Theory. Lie theory seminar. University of California Riverside. November 9, 2010.· Pares de matrices nilpotentes que casi conmutan. Seminario de posgrado. Universidad de los Andes, Bogotá, Colombia. August 14, 2010.
· On the variety of almost commuting nilpotent matrices. Lie theory seminar. University of California Riverside. October 13 and 15, 2009.
· A Counterexample to the Existence of a Poisson Structure on a Twisted Group Algebra. Representation Theory and related topics Seminar. Northeastern University. October 17, 2008.
· Almost commuting nilpotent matrices and Hilbert schemes. Geometry-Algebra-Singularities-Combinatorics Seminar. Northeastern University. October 15, 2008.
· Some results on pairs of commuting and almost commuting matrices. Ginzburg student seminar. University of Chicago. October 6, 2008
· Un contraejemplo para la existencia de una estructura de Poisson en un algebra de grupo torcida. XVII Coloquio Latinoamericano de Algebra. Medellin, Colombia. July 23, 2007.
Publications and preprints
/ · Partitions, Kostka polynomials and pairs of trees. (Submitted)· T-orbits of principal nilpotent pairs. Appendix to Some combinatorial identities related to commuting varieties and Hilbert schemes by Gwyn Bellamy and Victor Ginzburg. arXiv:1011.5957v1.
· Partitions, pairs of trees and Catalan numbers. arXiv:1006.5706v1.
· On the variety of almost commuting nilpotent matrices. Transformation Groups, Volume 15, Number 2 (2010).
· A counterexample to the existence of a Poisson structure on a twisted group algebra. São Paulo J. Math. Sci. 3 (2009), no. 1, 109--113.
· A basis for the non-crossing partition lattice top homology. J. Algebraic Combin. 23 (2006), no. 3, 231-242.
Teaching Experience
/ Visiting Assistant Professor, UC Riverside· Winter Quarter 2011: Calculus: Several Variables-2, First Year Calculus-2.
· Fall Quarter 2010: First Year Calculus-2, First Year Calculus-3.
· Spring Quarter 2010: Calculus: Several Variables-1, Calculus for Business.
· Winter Quarter 2010: First Year Calculus-1, Calculus for Business.
· Fall quarter 2009: First Year Calculus-2, Introduction to College math for Sciences.
Lecturer, The University of Chicago
· Summer Quarter 2010: Calculus-1
· Spring Quarter, 2009: Mathematical Methods for the Social Sciences-1.
· Winter Quarter, 2009: Calculus-3.
· Autumn Quarter, 2008: Calculus-2.
· Spring Quarter, 2008: Calculus-1.
· Winter Quarter, 2008: Calculus-2.
· Autumn Quarter, 2007: Calculus-3.
· Spring Quarter, 2007: Mathematical Methods for the Social Sciences-2.
· Winter Quarter, 2007: Mathematical Methods for the Social Sciences-1.
· Autumn Quarter, 2006: Calculus-3.
· Spring Quarter, 2006: Elementary functions and Calculus-1.
· Winter Quarter, 2005: Elementary functions and Calculus-2.
· Autumn Quarter, 2005: Elementary functions and Calculus-3. / 2009-2011
2005-2009
Teaching Experience
/ College Fellow, The University of Chicago· Spring Quarter, 2005: Basic Complex Variables.
· Winter Quarter, 2005: Honors Calculus 2.
· Autumn Quarter, 2004: Logic.
Graded the homework and held office hours and problem sessions.
Graduate Student Instructor, The University of Michigan
· Winter Term, 2004: Calculus 1.
· Fall Term, 2003: Data, Functions and Graphs.
Taught the course and graded exams and homework.
Lecturer, Universidad de los Andes
· First Semester 2003: Numerical Analysis.
Taught the course and graded exams and homework.
Graduate Teaching assistant, Universidad de los Andes
· Second Semester, 2002: Linear Algebra.
· First Semester, 2002: Integral Calculus.
· First Semester, 2002: Numerical Analysis.
· Second Semester, 2001: Numerical Analysis.
· First Semester, 2001: Linear Algebra.
· First Semester, 2001: Numerical Analysis.
· Second Semester, 2000: Linear Algebra.
· Second Semester, 2000: Numerical Analysis.
Taught the course and wrote and graded the exams.
Apprentice Teacher, Universidad de los Andes
· First Semester, 2000: Differential Calculus.
· Second Semester, 1999: Linear Algebra.
Taught the course, wrote and graded the exams under the supervision of a coordinator. / 2004-2005
2003-2004
2003
2000-2003
1999-2000