Fu Liu 刘拂

Ostensible contact info:
3220 Mathematical Science Building
(530) 754-9381
Actual contact info:
 Mailing address:
Department of Mathematics
University of California, Davis
One Shields Avenue
Davis, CA 95616 USA
Research interests: Enumerative and algebraic combinatorics.


Vital biographical info: I am currently an Assistant Professor in the math department at the University of California, Davis. I received my PhD in June 2006 from MIT under the guidance of Richard Stanley. Before joining Davis, I spent the Fall of 2006 at MSRI as a postdoc fellow.

Here is my curriculum vitae (or PDF).

Teaching info: In Spring 2008, I am teaching MAT16B and also offering a reading course on posets.


Papers and preprints

Mochizuki's indigenous bundles and Ehrhart polynomials, with Brian Osserman (or PDF) Spring 2004
A short paper applying certain finite-flatness results of Mochizuki to obtain identities for numbers of lattice points in different polytopes, and conversely applying the theory of Ehrhart polynomials to show that Mochizuki's indigenous bundles are counted by polynomials in the characteristic of the base field.
Journal of Algebraic Combinatorics 23 (2006), no. 2, 125-136.

Ehrhart polynomials of cyclic polytopes (arXiv) Fall 2004
A paper proving the conjecture made in math.CO/0402148 about the coefficients of the Ehrhart polynomials of cyclic polytopes.
Journal of Combinatorial Theory Ser. A 111 (2005), no. 1, 111-127.

(k,m)-Catalan numbers and Hook length polynomials for plane trees, with Rosena Du (arXiv) Winter 2005
A short paper defining the hook length polynomials for m-ary trees and plane forests, and introducing a new generalization of Catalan numbers, by using which we prove our hook length polynomials have a simple binomial expression.
European Journal of Combinatorics 28 (2007), no. 4, 1312-1321.

Hook length polynomials for plane forests of a certain type (arXiv) Summer 2005
A short note defining the hook length polynomials for plane forests of a given degree sequence type. Some other enumerative results on trees are also given.
To appear in Annals of Combinatorics.

Ehrhart polynomials of lattice-face polytopes (arXiv) Fall 2005
A paper defining a new family of polytopes, lattice-face polytopes, which is a generalization of cyclic polytopes. We show that the Ehrhart polynomial of a lattice-polytope has the same simple form as cyclic polytopes.
Transactions of the AMS 360 (2008), no. 6, 3041-3069.

The irreducibility of certain pure-cycle Hurwitz spaces, with Brian Osserman (arXiv) Fall 2006
We use a combination of geometric and group-theoretic techniques to prove that Hurwitz spaces of genus-0 covers of the projective line having a single ramified point over each branch point are irreducible.
To appear in the American Journal of Mathematics.

Formulas for the volumes of the polytope of doubly-stochastic matrices and its faces, with Jesus A. De Loera and Ruriko Yoshida (arXiv) Fall 2006 - Winter 2007
We provide an explicit combinatorial formula for the volume of the polytope of n by n doubly-stochastic matrices, also known as the Birkhoff polytope. We do this through finding the multivariate generating function for the lattice points of the polytope.
Submitted for publication.