Part B. Project summary

proposal title goes here

Summary of proposal goes here. The summary is required to address both merit review criteria separately. The numbering (“lettering”) of the Parts of the proposal are as in the Grant Proposal Guide (GPG). Intellectual merit. This is the first merit review criterion. Broader impact. This is the second merit review criterion.

Part C. Table of Contents (this is just for the PI’s convenience)

B Project summary 1 C Table of Contents (this is just for the PI’s convenience) ii D Project description 1

1 Results from prior NSF support 1 2 Research projects 1 2.1 Title of Section 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Title of Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.3 Title of Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.4 Title of Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.5 Title of Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.6 Title of Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Broader impact 1

E References cited 1 F Biographical sketch 1

4.1 Professional preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4.2 Appointments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4.3 Publications most closely related to project . . . . . . . . . . . . . . . . . . . . . 1 4.4 Other significant publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4.5 Synergistic activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4.6 Recent collaborators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4.7 Advisees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4.8 Graduate advisor: Bernd Sturmfels, UC Berkeley . . . . . . . . . . . . . . . . . 2 4.9 Postdoctoral advisor: Richard Stanley, MIT . . . . . . . . . . . . . . . . . . . . 2

G Budget 1 J Special information & supplementary documentation 1 K List of suggested reviewers 1 L Appendices 1

Part D. Project description My proposal title

Project description for Ezra Miller, Duke University

Project description goes here.

1. Results from prior NSF support

2. Research projects 2.1. Project section 1 2.2. Project section 2 2.3. Project section 3 2.4. Project section 4 2.5. Project section 5 2.6. Project section 6

3. Broader impact

1 Results from prior NSF support

NSF award number: DMS-xxxxxxx Award amount: $... Award period: ... Title: ...

And now, an up-to-five page report on NSF supported work you’ve done in the past five years.

2 Research projects

2.1 Title of Section 1

Definition 2.1. A definition looks like this.

2.2 Title of Section 2

Theorem 2.2. A theorem looks like this.

Conjecture 2.3. A conjecture looks like this.

2.3 Title of Section 3

Some references [1] to the PI’s publications [2].

2.4 Title of Section 4

In contrast, some references to publications by others [ABC09, Oop88], as opposed to more [3, 4] by the PI.

2.5 Title of Section 5 2.6 Title of Section 6

3 Broader impact

Broader impact statement goes here.

Part E. References cited

Publications by PI accepted during prior NSF support

[1] (with Coauthor 1 and Coauthor 2) Some paper I wrote with two others, preliminary acceptance subject to revision at Some Journal, 33 pages. arXiv:math.??/xxxx.xxxx

Submitted preprints

[2] Some paper I wrote myself, Journal of Solo Writing 3 (2006), 66–99. arXiv:math.??/xxxx.xxxx Papers in progress

[3] (with Coauthor) Some paper I wrote with someone, Journal of Duo Writing 3 (2006), 66–99. arXiv:math.??/xxxx.xxxx

Other papers by the PI

[4] (with Collaborator) Something else to fill the space, Journal of Space-filling Papers, 1 (2001), 100–1000. arXiv:math.??/xxxx.xxxx

Papers by other authors

[ABC09] Adam Alpha, Betty Beta, and Charlie Coauthor, On the mathematics of writing coauthored papers without the PI, Journal of Important Reviews 100 (2009), no. 1, 1–10.

[Oop88] Whoops Oops, I made a mistake all by myself, Incorrectness, 1988.

Part F. Biographical sketch

Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320 ezra@math.duke.edu http://math.duke.edu/˜ ezra/ phone: (919) 660–2846

4.1 Professional preparation

Brown University, Providence, RI  Mathematics Sc.B. (with Honors) 1995
Brown University, Providence, RI  Music  A.B. 1995
University of California, Berkeley  Mathematics  Ph.D. 2000
Massachusetts Institute of Technology (NSF Postdoc) Combinatorics  2000–2002
Mathematical Sciences Research Institute, Berkeley Commutative algebra  2002–2003

4.2 Appointments

Duke University  Professor  2009–
University of Minnesota  Associate Professor  2006–2008
University of Michigan  Visiting Faculty  2006–2007
University of Minnesota  Assistant Professor  2002–2006

4.3 Publications most closely related to project

• (with I. Pak) Metric combinatorics of convex polyhedra: cut loci and nonoverlapping unfoldings, Discrete and Comput. Geometry 39 (2008), no. 1–3, 339–388. DOI: 10.1007/s00454-006-1249-0, pages OF1–OF50. arXiv:math.MG/0312253

• (with A. Dickenstein and L. Matusevich) Combinatorics of binomial primary decomposition, Mathematische Zeitschrift, 19 pages. DOI: 10.1007/s00209-009-0487-x

• (with A. Guo) Lattice point methods for combinatorial games, submitted to Advances in Applied Mathematics, 18 pages. arXiv:math.CO/0908.3473

• (with D. Anderson and S. Griffeth) Positivity and Kleiman transversality in equivariant Ktheory of homogeneous spaces, submitted to JEMS, 23 pages. arXiv:math.AG/0808.2785

• (book with B. Sturmfels) Combinatorial Commutative Algebra, Graduate Texts in Mathematics, vol. 227, Springer–Verlag, New York, 2004. (xiv+417 pages)

4.4 Other significant publications

• (with A. Knutson and M. Shimozono) Four positive formulae for type A quiver polynomials, Inventiones Mathematicae 166 (2006), no. 2, 229–325. arXiv:math.AG/0308142

• (with A. Knutson) Gröbner geometry of Schubert polynomials, Annals of Mathematics 161 (2005), 1245–1318. arXiv:math.AG/0110058

• (with L. Matusevich and U. Walther) Homological methods for hypergeometric families, JAMS 18 (2005), no. 4, 919–941. arXiv:math.AG/0406383

• (with A. Knutson) Subword complexes in Coxeter groups, Advances in Mathematics 184 (2004), 161–176. arXiv:math.CO/0309259

• The Alexander duality functors and local duality with monomial support, Journal of Algebra 231 (2000), 180–234.

4.5 Synergistic activities

• Organizer of:

– MSRI program on Commutative Algebra (2012–2013, with D. Eisenbud, S. Iyengar, A. Singh, and K. Smith); – BIRS workshop on Combinatorial Game Theory (2008, with M. Albert, E. Berlekamp,

M. Mueller, R. Nowakowski, and D. Wolfe);

– AIM workshop on Rigidity and Polyhedra (2007, with R. Connelly and I. Pak);

– 15th Romanian National School of Algebra (2006, with M. Becheanu, V. Ene, C. Ionescu, D. Popescu, M. Ştefǎnescu);

– Algebraic Geometry and Combinatorics session at the Summer Institute in Algebraic Geometry (2005, with W. Fulton);

– IAS/PCMI Research Program & Summer School (2004, with V. Reiner and B. Sturmfels)

– multiple AMS special sessions Program or scientific committee member for conferences on combinatorics and commutative algebra in Austria (2009) and Romania (2008)

• Volunteer judge for the Minnesota Academy of Sciences State Science Fair (2004)

• Associate Editor, Discrete Mathematics (since 2007); Editorial Board Member: Beiträge zur Algebra und Geometrie (since 2008), Advances in Math (since 2009), and SIAM J. Discrete Math (since 2009); Referee activities: item(s) for 38 journals and AMS publications; 6 conferences; 3 national granting agencies; various countries’ national level prizes or awards

• Author of two graduate-level textbooks in the areas of algebra and combinatorics

• Participant in – IMA 2007–2008: Mathematics of Molecular and Cellular Biology

– IAS/Park City 2001: Quantum Field Theory, Supersymmetry, Enumerative Geometry – Clay Math Institute 2000: Mathematics and Physics

4.6 Recent collaborators

• Collaborator 1 (Institution 1)

• Collaborator 2 (Institution 2)

• Collaborator 3 (Institution 3)

• Collaborator 4 (Institution 4)

4.7 Advisees. Postdoc (8): Sonja Mapes (Duke), Megan Owen (SAMSI), Stephen Griffeth (Edinburgh), Drew Armstrong (Miami), Milena Hering (Connecticut), Alexander Yong (Urbana-Champaign), Calin Chindris (Iowa), Jeremy Martin (Kansas); Grad (2): Patrick Byrnes and Robert Edman (Minnesota); Undergrad (4): Alan Guo (Duke), Nathaniel Born (Minnesota), Matthew Coudron (Minnesota), David Molitor (Minnesota)

4.8 Graduate advisor: Bernd Sturmfels, UC Berkeley

4.9 Postdoctoral advisor: Richard Stanley, MIT

Part G. Budget

Budget justification goes here; your institution might have a standard template for this, to which you add items or justifications specific to your proposal.

Part J. Special information & supplementary documentation

This is where the letters from collaborators go, for example.

Postdoctoral Researcher Mentoring Plan

If your budget specifies funding for postdoctoral researchers, then you must have a Postdoctoral Researcher Mentoring Plan; see the Grant Proposal Guide.

Part K. List of suggested reviewers

• This kind of information can be helpful ...

• ...to the program officers assembling panels of reviewers.

Part L. Appendices

Inlcude only if approved in advance of proposal submission, or by proposal solicitation.