WILLIAM DANIEL  GILLAM

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Office: 408 Mathematics Phone: (212)-854-5881 Fax: (212)-854-8962 Address: Department of Mathematics Columbia University 2990 Broadway, MC 4406 New York, NY 10027 Email: wgillam@math.columbia.edu

MATHEMATICAL ACTIVITY

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Education:
Mathematics B.A. Wesleyan University 2002
Mathematics M.A. Wesleyan University 2003 (Advisor: W. W. Comfort)
Mathematics M.A. Columbia University 2004
Columbia University Mathematics Ph.D. Program 2003-Present (Advisor: M. Thaddeus)

Research Interests:
Complex Algebraic Geometry
Knot Theory
Model Theory in Algebraic Geometry
Homological Algebra

Teaching:
Spring 2007 Calculus I Section 003 Instructor. Here is the course webpage and a printable syllabus.
Fall 2006 College Algebra Section 003 Instructor. Here are the syllabus and homework assignments.
Fall 2005 Modern Geometry I Teaching Assistant for John Morgan.  A copy of his final.
Fall 2005 Milbank Mathematics Helproom Employee (Wednesday 3-6pm 333 Milbank Hall)
Fall 2005 Calculus III Teaching Assistant for Dylan Thurston
Spring 2005 Algebraic Topology II Teaching Assistant for John Morgan
Fall 2004-Fall 2005 Graduate Student Seminar organizer with Boris Mezhericher
Fall 2004 Milbank Mathematics Helproom Employee
Fall 2004 Calculus I Section 006 Teaching Assistant for Julius Ross
Fall 2003-Spring 2004 Wesleyan Math Helproom Employee

Publications:

Cleanliness of geodesics in hyperbolic 3-manifolds.
(with C. Adams, A. Colestock, J. Fowler, and E. Katerman)
Pacific J. Math. 213 (2004), no. 2, 201-211.
[Download .PS] [Download .PDF]

Cusp size bounds from singular surfaces in hyperbolic 3-manifolds.
(with C. Adams, A. Colestock, J. Fowler, and E. Katerman)
Trans. Amer. Math. Soc. 358 (2006) 727-741.

The embeddability ordering of topological spaces.
Wesleyan University Master's Thesis. Advisor: W. W. Comfort

The embeddability ordering of topological spaces.
(with W. W. Comfort)
Top. App. 153 (2006) 2192-2198.
[Download .PS] [Download .PDF]

Embeddability properties of countable metric spaces.
Top. App. 148 (2005) 63-82.
[Download .PS] [Download .PDF]

Computability of a topological poset.
Top. App. 153 (2006) 1132-1140.
[Download .PS] [Download .PDF]
Some calculations for this paper were carried out by computer.
This C++ program should compile on most systems without difficulty.
[Download .CPP]


Unpublished Miscellanies:

A sheaf-theoretic description of Khovanov's knot homology.
[Download .PDF]

Knot homology of (3,m) torus knots.
[Download .PDF]

Computations of Heegaard Floer knot homology.
(with John A. Baldwin)
[Download .PDF]
Also see my related website where you can find a few computer programs.

The Crepant Resolution Conjecture for an involution of 3d flags.
Submitted to J. Alg. Geom.
[Download .PDF]

Hyperelliptic Hodge integrals following Cavalieri.
[Download .PDF]

The orbifold Gromov-Witten theory of a vector bundle involution.
(A very rough preliminary version.)
[Download .PDF]



Total Visits:

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W. D. Gillam