Catherine Huafei Yan's Resume

[Research Interests] [Academic Positions] [Education] [Doctoral Disseration] [Experience] [Talks ] [Papers] [Awards] [Professional Affiliation] [Back Home]

Addresses

Work address:
Department of Mathematics, 102 Milner Hall, Texas A&M University, College Station, TX 77843, Tel: (979) 862-4476, E-mail: Catherine.Yan@math.tamu.edu
Home address:
1600 Southwest Parkway, Apartment 103, College Station, TX 77840, Tel: (979) 764-2919

Research Interests

Discrete Mathematics.
Algebraic Combinatorics.
Ordered Algebraic Structures.
Probabilistic Method.
I am also interested in Invariant Theory, Supersymmetric Algebra, Logic and Representation Theory.

Academic Positions

Academic Year 2000
Member at the Institute for Advanced Study
September, 1999 -- Present
Assistant Professor. Department of Mathematics, Texas A&M University
Summer, 1998, 1999
Consultant. AT&T Labs.
1997--1999.
Assistant Professor/Courant Instructor. Courant Institute of Mathematical Sciences, New York University.
1993--1997.
Graduate Teaching Assistant. Department of Mathematics, Massachusetts Institute of Technology.

Education

Doctor of Philosophy in Pure Mathematics.
Massachusetts Institute of Technology, MA, June 1997.
Bachelor of Science in Mathematics.
Peking University, China, July 1993.

Doctoral Dissertation

Title:
Theory of Commuting Boolean Algebras.
Advisor:
Gian-Carlo Rota, Professor of Mathematics, Massachusetts Institute of Technology.
Abstract:
In the thesis we give a definition of commutativity for Boolean subalgebras which generalizes the notion of commutativity for equivalence relations. We characterize the commutativity for complete Boolean subalgebras by a structure theorem.

We study lattices of commuting Boolean subalgebras of a complete Boolean algebra. We characterize this class of lattices, and more generally, a similar class of lattices in a complete Heyting algebra by developing a proof theory which extends Haiman's proof theory for lattices of commuting equivalence relations.

We study the representation theory of commuting Boolean subalgebras. To each complete subalgebra, we associate a normal, closed, completely additive operator. We prove that the commutativity of Boolean subalgebras is equivalent to the commutativity of the associated completely additive operators under composition. We then represent subalgebras of a Boolean algebra by partitions on the Boolean space, and obtain the following representation theorem: Two complete Boolean subalgebras commute if and only if they commute as partitions on the Boolean space.

As the conclusion of the thesis, we propose a notion of stochastic commutativity, which is a generalization of stochastic independence. We obtain a structure theorem for pairwise stochastically commuting $\sigma$-algebras and develop various applications in Probability and Universal Algebra.

Experience

AT&T Labs. Florham Park, NJ.
Summer 1998 and 1999. Consultant in Mathematics. Did research on recurrence relations of Turan numbers and the Apollonian packing.
Courant Institute of Mathematical Sciences, New York, NY.
Academic year 1997--1999. Courant Instructor. Taught differential equations, advanced calculus, and quatatitive reasoning.
Massachusetts Institute of Technology, Cambridge, MA.
Summer 1997. Mentor in the Summer Program of Undergraduate Research. Supervised students in doing mathematics research.
Massachusetts Institute of Technology, Cambridge, MA.
Academic year 1996--1997. Graduate Teaching Assistant. Department of Mathematics. Teaching and grading for multivariable calculus and algebra.
Massachusetts Institute of Technology, Cambridge, MA.
Summer 1996. Lecturer. Department of Mathematics. Taught and graded for differential equations.
Massachusetts Institute of Technology, Cambridge, MA
Academic year 1995--96. Graduate Teaching Assistant, Department of Mathematics. Taught calculus I, II and differential equations.
Research Science Institute, Cambridge, MA.
Summer 1995. Mentor. Led student discussion groups. Supervised students in doing research program.
Massachusetts Institute of Technology, Cambridge, MA.
Academic year 1993--95. Graduate Teaching Assistant, Department of Mathematics. Tutored and graded for complex analysis, differential equations, and linear algebra.
High School Olympiad in Mathematics, Beijing, China.
Summer 1991, 92, 93. Lecturer. Taught topics in discrete mathematics and led problem solving seminars.

Talks

Integral Apollonian Packings.
CombinaTexas Conference, March 2000.
On the enumeration of generalized parking functions.
31 Southeastern International Conference on Combinatorics, Graph Theory, & Computing, March 2000.
A ball-distrinution problem and the branching process.
Texas A&M University, Algebra and Combinatorics seminar, February, 2000.
Geometric identities in linear lattices.
Joint Mathematics Meetings, invited talk in AMS-MAA Special Session "In Memory of Gian-Carlo Rota", January, 2000.
Integral Apollonian packings.
Texas A&M University, Algebra and Combinatorics seminar, October, 1999.
A recurrence associated with extremal problems.
Vanderbilt University, colloqulum talk, January, 1999.
Theory of lattices of commuting Boolean algebras.
Texas A&M University, invited talk, December, 1998.
Theory of commuting Boolean algebras.
Dartmouth College, invited talk, February 1998.
Balancing game with a buffer.
University of Pennsylvania, Combinatorics seminar.
Theory of commuting Boolean algebras.
Denver University, Colloquium talk, February 1997.
k-Parking functions, tree inversions, and hyperplane arrangements.
Virginia Polytechnic Institute and State University, invited talk, January 1997.
k-Parking functions, tree inversions, and hyperplane arrangements.
Texas A&M University, invited talk, January 1997.
Generalized tree inversions and k-parking functions.
Massachusetts Institute of Technology, Combinatorics seminar, November 1996.

Papers

List of Publications

Funds and Awards

Challenge Fund Awards, New York University, June, 1999.
Morse Academic Plan Teaching Fund, New York University, September, 1998.
Jiu-Zhang mathematics Prize, highest honor in Department of Mathematics, Peking University, 1991.
Gold medal in the third Youth Science Awards of Beijing, China, 1991.
Freshman First Honor Prize, Peking University, 1990
Top award in the Science Prize Competition, Beijing, China, 1989.
Silver-Sail Prize for Science, Beijing, China, 1989.
Silver medal in International Olympiad Mathematics, Germany, 1989.

Professional Affiliation

American Mathematics Society (AMS).
Society for Industrial and Applied Mathematics (SIAM).
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