**Employment**- Department of Mathematics, University of Illinois, Urbana-Champaign, Associate Professor (2012-).

- Department of Mathematics, University of Illinois, Urbana-Champaign, Assistant Professor (2008-12).

- Department of Mathematics, University of Minnesota, Minneapolis, Dunham Jackson Assistant Professor (2005-2008).

- University of California, Berkeley, Visiting Assistant Professor (2003-2005).

**Education**- University of Michigan at Ann Arbor, Ph.D. in Mathematics (2003).

- University of Waterloo, Canada , M.Math. (1999) and B.Math. (1998).

**Research interests**: Combinatorics and relations to algebra, geometry and other areas of mathematics.**Homepage**at http://www.math.uiuc.edu/~ayong/ has links to downloadable papers (with brief abstracts), etc.**Honors:**- (2012-2013) Helen Corley Petit Scholar (College of Liberal Arts and Sciences, UIUC)
- (2011) G. de B. Robinson Award of the Canadian Math Society (with Hugh Thomas)
- (2011-2012) UIUC Center for Advanced Study/Beckman Fellow
- (2005-2006) National Science and Engineering Research Council of Canada (NSERC) Postdoctoral fellowship
- (1998) K.D. Fryer Gold Medal, University of Waterloo
**Grants/scholarships:**- (2012-2015) NSF standard grant DMS 1201595, PI
- (2014-2015) Campus reseach board UIUC, PI; funding for a Research Assistant
- (2012-2013) Campus research board UIUC, PI; funding for a Research Assistant
- (2011-2014) NSF Conference grant DMS 1146096
- (2010-2011) Campus Research Board UIUC, PI; funding for Research Assistant.
- (2009-2012) NSF standard grant DMS 0901331, PI
- (2006-2009) NSF standard grant DMS 0601010, Co-PI (PI: Victor Reiner)
- (2006-2007) U. Minnesota Digital Technology center grant (award amount total: $24,671); for research in applied algorithms, Co-PI with David Redish (Neuroscience), (PI Duane Nykamp)
- (2006) Fields Institute funding to organize "Workshop on Computational and Combinatorial commutative algebra" ($4000 Canadian), PI
- (2002) Rackham Dissertation Fellowship, U. Michigan
- (1998-1999) NSERC PGS A Scholarship for graduate studies
- (1994-1998) Descartes Mathematics Fellowship, University of Waterloo
- (1994-1998) Canada Fellowship, national 4 year award
**Teaching Experience** - (2008-Present) University of Illinois:

Courses: Fall 2009: Differential equations plus;

Spring 2009: Graduate course on symmetric functions and Young tableaux (List of teachers ranked excellent -- top 10%);

Fall 2010: Introduction to combinatorics;

Spring 2010: Introduction to combinatorics (List of teachers ranked excellent)

Spring 2011: Linear programming and combinatorial optimization (List of teachers ranked excellent); Graduate course on the Grassmannian

Fall 2011: Introduction to combinatorics (List of teachers ranked excellent); Introduction to Graduate combinatorics (List of teachers ranked excellent)

Fall 2012: Introduction to combinatorics; Polynomials - (2005-2008) University of
Minnesota.

Spring 2007: Graduate combinatorics;

Fall 2007: Linear algebra and differential equations (course coordinator), (undergraduate) enumerative combinatorics

- (2003-2005) Visiting Assistant Professor, University of
California, Berkeley.

Fall 2004: Abstract Algebra;

Spring 2004: Combinatorics, Complex Analysis;

Fall 2005: Combinatorics, Real Analysis. - (1999-2003) Instructor, University of Michigan. Courses:

Calculus II, Calculus I, Precalculus. - (1995-1999) Teaching Assistant, University of Waterloo. Courses:

Linear Algebra II, Linear Algebra I, Classical Algebra, Combinatorics for Engineers, Combinatorics I, History of Mathematics, Business Law.**Other Professional Activities:** - Mentoring: Li Li (postdoc, 2008-2010), Elizabeth Csima (postdoc, 2008-2011), Ben Wyser (postdoc, 2012-), Chayapa Darayon (graduate student, 2009-present), Dominic Searles (graduate student 2009-present), Oliver Pechenik (graduate student 2011-present), Immanuel McLaughlin (REGS Spring 2011), Alexandra Seceleanu (graduate student RA, Spring 2010), Colleen Ross (REU, Summer 2010)-present, Nicolas Tse (undergraduate research, Summer 2010), Bryan Poling (undergraduate research, Fall 2007; U. Minnesota)
- Referee (selected): Duke Math Journal, Math Annalen, Michigan Math J., Advances in math, Transactions of the AMS, Proc. LMS, Annales de l'Institut Fourier, Random Structures and Algorithms, Proceedings of the AMS, Journal of Algebraic combinatorics, Math Research Letters, Journal of Algebra, Journal of Combinatorial theory: series A, Annals of Combinatorics, Electronic Journal of Combinatorics, European Journal of Combinatorics, Pure and Applied Math Quarterly, Journal of pure and applied algebra, Experimental Math, Discrete Math, Journal of Commutative Algebra, Springer books.
- Upward Bound guest lecturer at UIUC
- Formal Power Series and Algebraic Combinatorics Conference 2014 Program committee
- Irving Reiner book award committee (UIUC Math grad student award in algebra). Spring 2011.
- Illinois High School Math finals oral presentation judge. April 2011 and 2014.
- Co-organizer of the January 2011 session on ``Combinatorial Algebraic geometry'' at the AMS joint annual meetings in New Orleans.
- Formal Power Series and Algebraic Combinatorics Conference 2010 Program committee
- U. Illinois Departmental service: Area chair (combinatorics) [2009-2010], Combinatorics comprehensive exam [2009-2010, 2011-2012], postdoc hiring committee [2008-2010], picnic committee [2010-2011], graduate admissions [2010-2011], executive committee [2012-2014]
- (January 2011) Co-organizer of Joint Math Meetings session on "Combinatorial algebraic geometry"
- (June 2010) Co-organizer of the June 2010 Canadian Math Society session on ``Algebraic combinatorics'' at U. New Brunswick.
- (November 2009, October 2010) Grant reviewer for Icelandic Research Fund.
- (September 2009) Local co-organizer of Illinois-Purdue algebra and combinatorics day
- (March 2009, 2010) Grant proposal reviewer: NSA.
- (April 2009) Co-organizer of the April 2008 AMS Special session on ``Algebra, geometry and combinatorics'' at UIUC.
- (August 2008-Present) Co-organizer of the UIUC Algebra, geometry and combinatorics seminar.
- (October 2007) Referee for proposed scientific program at the Banff International Research Station
- (December 2006, September 2008) Organizer/speaker at a panel on getting a postdoctoral math job, for graduate students at UMN, and at Illinois.
- (August 2006) Contributed article to the Fields Newsletter, a periodical documenting events at the Fields Institute.
- (July-August 2006) Co-organizer for Fields Institute workshop "Combinatorial and computational commutative algebra"
- (September 2005-Present) Co-organizer of the U. Minnesota Algebraic Geometry seminar.
- (September 2005-May 2007) Co-organizer of the U. Minnesota Combinatorics seminar.
- (August 2005) Contributed article to the Fields Newsletter, a periodical documenting events at the Fields Institute.
- (July 2006) Co-organizer for Fields Institute workshop "Schubert calculus"
- (May 2005-Present) Co-organizer of the San Francisco April 2006 Special session on ``Geometry of Grobner bases''
- (September 2004-April 2004) Co-organizer of the Santa Barbara AMS Special session on ``Algebraic geometry and combinatorics''.
- (June 2004-May 2005) Co-organizer of the UC Berkeley Combinatorics seminar.
- (May 2004-May 2005) Organizing committee for the Bay Area Discrete Math Day and local organizer for the Ninth Bay Area Discrete Math Day at UC Berkeley, in the Fall of 2004.
- (January-April 2003) Research assistant for A. Barvinok, studying ``Random weighting and asymptotic counting''
- (January-April 2002) Research assistant for A. Barvinok, proofreading a book on Convex Analysis.
- (2001-2003) Lectured for the King-Chavez-Parks mathematics program for disadvantaged youths.
- (October 2001) Lectured for the Undergraduate Math Club, University of Michigan.
- (2000-2001) Research assistant for P. Hanlon, studying ``optimization of cache misses in matrix multiplication''
- (Spring 1998) Organized the Student Mathematics Conference at the University of
Waterloo.
- Other formats for this CV (not necessarily up to date):
.ps
.pdf
**Recent/Selected Talks**

- (May 2015)
*Midwest combinatorics conference*, University of Minnesota

TBA

- (February 2, 2015)
*Combinatorics Seminar*, UC Berkeley

TBA

- (January 11, 2015)
*AMS Special Session*, San Antonio, Texas

TBA

- (June 2, 2014)
*Seminar*, Fields institute

TBA

- (March 19, 2014)
*MATRIX Undergraduate math club*, UIUC

Comparative linguistics and a combinatorial Fermi problem

- (January 15-18(?), 2014)
*AMS Special session on Geometric applications of algebraic combinatorics*, Baltimore Joint AMS Meeting

TBA

- (November 1, 2013)
*Colloquium*, DePaul U., Chicago

The Joseph Greenberg problem: combinatorics and comparative linguistics

- (October 18-20(?), 2013)
*AMS Special session on Topological combinatorics*, Washington U., St. Louis

Polynomials for GL_p x GL_q orbit closures in the flag variety

- (May 31, 2013)
*Seminar*, U. Quebec at Montreal

TBA

- (April 21, 2013)
*Discrete Math seminar*, U. British Columbia

TBA

- (April 20, 2013)
*Algebraic geometry seminar*, U. British Columbia

TBA

- (April 4, 2013)
*Colloquium*, U. New Brunswick

TBA

- (March 20, 2013)
*Seminar*, Loyola U.

TBA - (March 8, 2013)
*ICERM Workshop: Whittaker Functions, Schubert calculus and Crystals*, Brown U.

Equivariant jeu de taquin and eigenvalues of Hermitian matrices - (July 17-27?, 2012)
*International Schubert Calculus conference*, Osaka, Japan.

Schubert calculus via jeu de taquin and root datum

- (July 9-13?, 2012)
*SIAM conference*, Minneapolis, MN.

TBA

- (July 9-13?, 2012)
*SAGE days*, Minneapolis, MN.

Computational aspects of Schubert calculus

- (April 19, 2012)
*Colloquium*, Tulane U.

TBA - (April 6, 2012)
*Colloquium*, Virginia Tech.

TBA - (March 28-31, 2012)
*AMS Special session*, Lawrence, Kansas.

TBA - (Sept 24, 2011)
*AMS Special session*, Wake Forest U.

TBA - (April 21, 2011)
*Combinatorics Seminar*, Washington University at St. Louis

TBA - (March 17-20, 2011)
*AMS Special session on geometric commutative algebra and applications*, Iowa City.

Grobner bases and singularities of Schubert varieties - (March 18-20, 2011)
*AMS Special session on recent advances in Schubert calculus*, Iowa City.

Patch ideals and Peterson varieties - (March 4, 2011)
*Lie Groups/Quantum Math Seminar*, Rutgers U., NJ.

Patch ideals and Peterson varieties - (March 3, 2011)
*Philadephia Combinatorics and Algebraic Geometry seminar*, U. Penn, Philadephia.

Patch ideals and Peterson varieties - (October 22, 2010)
*Real algebraic systems workshop*, American Institute of Math, Palo Alto.

Drift configurations - (October 6, 2010)
*Combinatorics seminar*, U. Washington, Seattle.

Drift configurations - (September 29, 2010)
*Algebra-Geometry-Combinatorics seminar*, UIUC.

Drift configurations - (April, 2010)
*AMS Special Session on Combinatorial Representation Theory*, Macalester College, St. Paul, MN.

TBA

- (March, 2010)
*AMS Special Session on Algebraic and geometric combinatorics*, U. Kentucky, Lexington KT.

TBA - (March, 2010)
*Workshop on localization techniques in equivariant cohomology*, American Institute of Mathematics, Palo Alto CA.

Introduction to Schubert calculus - (March, 2010)
*Applied algebra seminar*, York. U., Toronto.

TBA - (December, 2009)
*Korean Math Society-AMS joint meeting*, Seoul Korea.

TBA - (December, 2009)
*KAIST*, Korea.

TBA - (November 12, 2009)
*Philadelphia Combinatorics and Algebraic Geometry seminar*, Philadelphia, PA.

TBA

- (October 21, 2009)
*MIT combinatorics seminar*, Cambridge MA.

TBA

- (June 16, 2009)
*VIGRE Workshop on Flag varieties:*, Iowa City, IA.

What's known in Schubert calculus.

- (Sometime May 26-29, 2009)
*Workshop on Representation Theory, Geometry and Combinatorics: Equivariant algebraic geometry and related topics*, UC Berkeley, Berkeley, CA.

Equivariant K-theory of Grassmannians

- (April 22, 2009)
*U. Illinois Algebra, Geometry and Combinatorics seminar*, Urbana, IL.

Equivariant K-theory of Grassmannians

- (April 4 or 5, 2009)
*AMS special session on Enumerative Geometry*, Raleigh, NC.

Equivariant K-theory jeu de taquin for Grassmannians

- (April 4 or 5, 2009)
*AMS special session on Applications of Algebraic and Geometric Combinatorics*, Raleigh, NC.

Longest strictly increasing subsequences and the Hecke insertion algorithm

- (March 13, 2009)
*U. Michigan Combinatorics seminar*, Ann Arbor, MI.

Equivariant K-theory of Grassmannians

- (March 4, 2009)
*Working Algebraic Geometry Seminar*, Purdue U., West Lafayette.

Equivariant K-theory of Grassmannians

- (November 24, 2008)
*U. Minnesota Combinatorics seminar*, Minneapolis, MN.

TBA

- (November 11, 2008)
*UIUC Combinatorics semianr*, Urbana, IL.

Algebraic combinatorics

- (February 12, 2008)
*Colloquium*University of Western Ontario, London ON

Schubert combinatorics and geometry

- (February 6, 2008)
*Colloquium*University of Alberta, Edmonton

Schubert combinatorics and geometry

- (February 4, 2008)
*Colloquium*Simon Fraser University, Burnaby BC

Schubert combinatorics and geometry

- (January 31, 2008)
*Colloquium*Texas A+M University, College Station

Schubert combinatorics and geometry

- (January 24, 2008)
*Colloquium*University of Oregon

Schubert combinatorics and geometry

- (January 18, 2008)
*Colloquium*University of Pittsburgh

Schubert combinatorics and geometry

- (January 10, 2008)
*Colloquium*Georgia Institute of Technology, Atlanta

Schubert combinatorics and geometry

- (December 7, 2007)
*Special Colloquium,*University of Illinois, Urbana-Champaign

Schubert combinatorics and geometry

- (November 1, 2007)
*Algebra seminar, U. Pittsburgh*

"Schubert combinatorics and geometry"

- (October 6 or 7, 2007)
*AMS Special session on Invariants of Lie Group Actions and Their Quotients, Rutgers University*

TBA

- (One of May 28-June 1, 2007 --upcoming)
*CRM workshop on algebraic geometry and algebaric combinatorics, CRM, Montreal*

Schubert combinatorics and geometry

- (May 9, 2007 --upcoming)
*IMA applications of algebraic geometry seminar, IMA, Minneapolis*

Schubert combinatorics and geometry

- (April 14 or 15, 2007)
*AMS Special session on Algebraic geometry and combinatorics, Hoboken, NJ*

"Cominuscule Schubert calculus and tableau combinatorics"

- (March 20, 2007)
*Banff workshop on Schubert calculus and varieties*

"Governing singularities of Schubert varieties"

- (March 9, 2007)
*Combinatorics Seminar, U. Michigan, Ann Arbor*

"Cominuscule Schubert calculus and tableau combinatorics"

- (January 20, 2007)
*CRM, Recent Advances in Combinatorics mini-workshop*

"Degeneration, an interface between AG, RT and CO"

- (December 2006)
*CMS Special Session on "Commutative algebra and algebraic geometry", Toronto*

"A combinatorial rule for (co)minuscule Schubert calculus"

- (November 10, 2006)
*Combinatorics seminar, U. Minnesota*

"A combinatorial rule for (co)minuscule Schubert calculus"

- (October 28 or 29, 2006)
*AMS Special Session on "Combinatorial methods in equivariant topology", U. Connecticut*

"A combinatorial rule for (co)minuscule Schubert calculus"

- (October 27, 2006)
*Combinatorics Seminar*, M.I.T., Cambridge.

"A combinatorial rule for (co)minuscule Schubert calculus"

- (October 11, 2006)
*Representation theory, geometry and combinatorics seminar*, UC Berkeley

TBA

- (June 1, 2006)
*Combinatorics Seminar*, Caltech, Pasedena.

"Combinatorial problems in Schubert calculus"

- (April 2006)
*AMS Special Session on "Homological and K-theory trends in Algebraic combinatorics", San Francisco*

"Stable Grothendieck polynomials and a K-theoretic tableau insertion algorithm"

- (April 4, 2006)
*Algebra seminar, U. Western Ontario, London*

Stable Grothendieck polynomials and a K-theoretic tableau insertion algorithm

- (February 24, 2006)
*Algebraic Combinatorics seminar, Fields Institute, Toronto*

"Having a ball with Young tableaux"

- (February 10, 2006)
*Combinatorics seminar, University of Minnesota, Minneapolis*

"Stable Grothendieck polynomials and a K-theoretic Edelman-Greene algorithm"

- (January 13, 14 or 15, 2006)
*Workshop on Combinatorial Inverse systems*, Fields Institute, Toronto.

"Computing singularities of Schubert varieties"

- (January 9, 2006)
*Symplectic geometry seminar,*University of Toronto

Tableau insertion algorithms in geometry and representation theory.

- (November 7, 2005)
*Algebraic geometry seminar*, University of Toronto, Toronto.

"Computing Singularities of Schubert varieties"

- (October 6, 2005 -- upcoming)
*Algebraic geometry Seminar*, University of Minnesota, Minneapolis.

"Computing Singularities of Schubert varieties" - (September 16, 2005 -- upcoming)
*Combinatorics Seminar*, University of Minnesota, Minneapolis.

"Tableau complexes" - (August 1-5?, 2005)
*Seattle Conference on Algebraic Geometry*, Seattle.

"On smoothness and Gorensteinness of Schubert varieties"

- (June 10, 2005)
*Fields Instiute Workshop on Schubert varieties and Schubert calculus*, Toronto.

"Degeneracy Loci"

- (June 8, 2005)
*Fields Instiute Workshop on Schubert varieties and Schubert calculus*, Toronto.

"Schubert calculus: algebraic geometry and combinatorics"

- (June 4/5 or 6, 2005)
*Combinatorics and Geometry special session of the CMS meeting,*Waterloo, Canada

"On smoothness and Gorensteinness of Schubert varieties"

- (May 10, 2005-- upcoming)
*Seminar*, Mittag-Leffler Institute, Sweden.

"A K-theoretic Robinson-Schensted algorithm, quiver degeneracy loci, and an expansion rule for Fomin and Kirillov's stable Grothendieck polynomials"

- (May 7, 2005-- upcoming)
*Seminar*, Mittag-Leffler Institute, Sweden.

"A ball of semistandard Young tableaux"

- (April 12, 2005)
*Algebraic geometry seminar*, University of Illinois, Urbana-Champaign.

"On smoothness and Gorensteinness of Schubert varieties"

- (April 6)
*Algebraic geometry seminar*, University of British Columbia, Vancouver.

"On smoothness and Gorensteinness of Schubert varieties"

- (March 28, 2004)
*Algebra Seminar*, York University, Toronto.

``Stable Grothendieck polynomials and a generalized Edelman-Greene correspondence''

- (March 11, 2005)
*Combinatorics seminar*, MIT, Cambridge

``On Smoothness and Gorensteinness of Schubert varieties''

- (March 4, 2005)
*Algebraic geometry seminar*, Texas A&M university, college station.

``On Smoothness and Gorensteinness of Schubert varieties''

- (March 2, 2005)
*Geometry and analysis seminar*, Rice university, Houston.

``On Smoothness and Gorensteinness of Schubert varieties''

- (February 18, 2005)
*Combinatorics seminar*, University of Michigan, Ann Arbor.

``A formula for K-theoretic truncation Schubert calculus''

- (February 16, 2005)
*Algebraic geometry seminar*, University of Michigan, Ann Arbor.

``On Smoothness and Gorensteinness of Schubert varieties''

- (January 25, 2005)
*Special Combinatorics seminar*, University of California, San Diego.

``When is a Schubert variety Gorenstein?''

- (January 17, 2005)
*Symplectic geometry seminar*, University of Toronto, Toronto.

``Enumerative formulas in Schubert calculus: problems, theorems and conjectures''

- (December 2004)
*Algebraic Geometry seminar*, Ohio State University, Columbus.

``Gorenstein Schubert varieties''

- (December 2004)
*Combinatorics seminar*, Ohio State University, Columbus.

``Gluing Young tableaux into a ball''

- (November 2004)
*Geometry, representation theory and combinatorics seminar*, University of California, Berkeley.

``When is a Schubert variety Gorenstein?''

- (October 2004)
*Special session on Modern Schubert Calculus*, AMS Eastern Section Meeting, Northwestern University, Evanston.

``Grobner geometry of Schubert and Grothendieck transition formulae''

- (July 2004)
*Park City Mathematics Institute Geometric Combinatorics Workshop*, Park City, Utah.

``Grobner geometry of geometric vertex decompositions''

- (May 2004)
*Bay Area Discrete Math Day Conference*, Stanford University, Stanford.

``Grobner degeneration, Schur polynomials and positivity''

- (April 2004)
*Commutative algebra/algebraic geometry Seminar*, University of California, Berkeley.

``Grobner degeneration, Schur polynomials and positivity''

- (January 2004)
*Pure Mathematics Colloquium*, University of Waterloo, Canada.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (December 2003)
*Combinatorics Seminar*, University of California, San Diego.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (November 2003)
*Combinatorics Seminar*, University of Washigton, Seattle.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (October 2003)
*Representation theory and geometry seminar*, University of North Carolina, Chapel Hill.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (October 2003)
*Algebraic Geometry Seminar*, Stanford University, Stanford.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (October 2003)
*Combinatorics Seminar*, University of California, Davis.

``Degeneracy Loci, Quiver coefficients and Schubert Calculus''

- (October 2003)
*Groups and Algebraic geometry seminar*, University of California, Berkeley.

``Cluster algebras''

- (August 2003)
*Combinatorial Commutative Algebra Workshop*, University of California, Berkeley.

``Quiver polynomials''

- (June 2003)
*Conference on Formal Power Series and Algebraic Combinatorics*, Linkoping University, Sweden.

``Schubert polynomials and quiver formulas''

- (April 2003)
*Valley Geometry Seminar*, University of Massachusetts, Amherst.

``Formulas for Schubert classes via Grobner bases and degeneracy loci''

- (December 2002)
*Combinatorics Seminar*, University of Pennsylvania, Philadelphia

``Schubert polynomials and quiver formulas''

- (November 2002)
*Combinatorics Seminar*, University of Minnesota, Minneapolis

``Schubert polynomials and quiver formulas''

- (November 2002)
*Combinatorics Seminar*, University of Michigan, Ann Arbor

``Schubert polynomials and quiver formulas''

- (October 2002)
*Special session on Modern Schubert Calculus*, AMS Eastern Section Meeting, Boston.

"Schubert class formulas"

- (October 2002)
*Combinatorics Seminar*, M.I.T.

"Schubert Polynomials and Quiver Formulas"

- (July 2002)
*Conference on Formal Power Series and Algebraic Combinatorics*, Melbourne.

"Degree bounds in quantum Schubert calculus"

- (April 2002)
*Combinatorics Seminar*, UC Berkeley

"Degree bounds in quantum Schubert calculus"

- (February 2002)
*Lie Theory Seminar*, University of Wisconsin, Madison

"Some combinatorics of quantum Schubert calculus"

- (January 2002)
*Moduli Spaces Seminar*, University of Michigan (two talks)

"Random trees and the asymptotics of Hurwitz numbers, I and II" - (December 2001)
*Canadian Math Society Winter Meeting,*Toronto.

"On the quantum cohomology of the Grassmannian" - (June 1999)
*Algebraic Combinatorics Seminar,*University of Waterloo.

"Hurwitz numbers and cycle factorizations" - (September 1998)
*Algebraic Combinatorics Seminar,*University of Waterloo.

"Multisets of hook numbers and a conjecture of Regev and Vershik" **Contacts**

*Address:*Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA.

*Email:*ayong@math.uiuc.edu

*Phone:*(217) 244-5120

*Fax:*(217) 333-9576

*Last modified: January 2013. *