Ezra Miller
Professor of Mathematics
Professor Miller's research centers around problems in geometry, algebra, topology, combinatorics, statistics, probability, and computation originating in mathematics and the sciences, including biology, chemistry, computer science, and imaging.
The techniques range, for example, from abstract algebraic geometry or commutative algebra of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces; from deep topological constructions such as equivariant Ktheory and stratified Morse theory to elementary simplicial and persistent homology; from functorial perspectives on homological algebra in the derived category to specific constructions of complexes based on combinatorics of cell decompositions; from geodesic contraction applied to central limit theorems for samples from stratified spaces to dynamics of explicit polynomial vector fields on polyhedra.
Beyond motivations from within mathematics, the sources of these problems lie in, for example, graphs and trees in evolutionary biology and medical imaging; massaction kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; Lie theory; and geometric statistics of data sampled from highly nonEuclidean spaces. Examples of datasets under consideration include MRI images of blood vessels in human brains and lungs, 3D folded protein structures, and photographs of fruit fly wings for developmental morphological studies.
The techniques range, for example, from abstract algebraic geometry or commutative algebra of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces; from deep topological constructions such as equivariant Ktheory and stratified Morse theory to elementary simplicial and persistent homology; from functorial perspectives on homological algebra in the derived category to specific constructions of complexes based on combinatorics of cell decompositions; from geodesic contraction applied to central limit theorems for samples from stratified spaces to dynamics of explicit polynomial vector fields on polyhedra.
Beyond motivations from within mathematics, the sources of these problems lie in, for example, graphs and trees in evolutionary biology and medical imaging; massaction kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; Lie theory; and geometric statistics of data sampled from highly nonEuclidean spaces. Examples of datasets under consideration include MRI images of blood vessels in human brains and lungs, 3D folded protein structures, and photographs of fruit fly wings for developmental morphological studies.
Office Hours
Office hours: Monday, 16:15 – 17:15 on Zoom
Thursday, 13:15 – 14:30 on Zoom from Physics 209 or outside
Current Appointments & Affiliations
 Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2009
 Professor of Statistical Science, Statistical Science, Trinity College of Arts & Sciences 2015
Contact Information
 209 Physics Bldg, 120 Science Drive, Durham, NC 27708
 Box 90320, Durham, NC 277080320
 (919) 6602846
 # homepage
 CV (Curriculum Vitae)
 Talks, seminars, and lecture series
 Background

Education, Training, & Certifications
 Ph.D., University of California  Berkeley 2000
 B.S., Brown University 1995

Leadership & Clinical Positions at Duke
 Liaison to MA Teaching Program. Duke Mathematics Department, August 2019

Academic Positions Outside Duke
 Associate Director, Statistical and Applied Mathematical Sciences Institute (SAMSI). 2011  2014
 Associate Professor, University of Minnesota. 2006  2008
 Assistant Professor, University of Minnesota. 2002  2006
 Recognition

In the News

APR 24, 2015 Duke Research Blog 
MAR 20, 2014 Fox8 News 
MAR 17, 2014 News & Observer 
MAR 12, 2014 
JAN 24, 2014 
JAN 22, 2014 Los Angeles Times


Awards & Honors
 Fellow. American Mathematical Society. 2012
 Institute of Technology Guillermo E. Borja Award. University of Minnesota. 2007
 McKnight Presidential Fellow. University of Minnesota. 2007
 Faculty Early Career Development (CAREER) Program. National Science Foundation. 2005
 McKnight LandGrant Professorship. University of Minnesota. 2005
 "Thank a Teacher" award. University of Minnesota. 2004
 Alfred P. Sloan Doctoral Dissertation Fellowship. Alfred P. Sloan Foundation. 1999
 Expertise

Subject Headings
 Research

Selected Grants
 R2 [Reciprocal Relationships]: Mentorships to Strengthen and Sustain STEM Teachers awarded by National Science Foundation 2020  2025
 HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation 2019  2022
 Algebraic and Geometric Methods In Data Analysis awarded by National Science Foundation 2017  2020
 Integrative Middle School STEM Teacher Preparation: A Collaborative Capacity Building Project at Duke University awarded by National Science Foundation 2014  2017

Fellowships, Supported Research, & Other Grants
 Algebraic and geometric methods in data analysis awarded by National Science Foundation 2017  2020
 Integrative Middle School STEM Teacher Preparation: A Collaborative Capacity Building Project at Duke University awarded by National Science Foundation 2014  2017
 Combinatorics in geometry and algebra with applications to the natural sciences awarded by National Science Foundation 2010  2016
 CAREER: Discrete structures in continuous contexts awarded by National Science Foundation 2005  2010
 Publications & Artistic Works

Selected Publications

Academic Articles

Katthän, L., Michałek, M., & Miller, E. (2019). When is a Polynomial Ideal Binomial After an Ambient Automorphism? Foundations of Computational Mathematics, 19(6), 1363–1385. https://doi.org/10.1007/s1020801894050Full Text

Berenstein, A., Braverman, M., Miller, E., Retakh, V., & Weitsman, J. (2016). Andrei Zelevinsky, 1953–2013. Advances in Mathematics, 300, 1–4. https://doi.org/10.1016/j.aim.2016.06.006Full Text

Kahle, T., Miller, E., & O’Neill, C. (2016). Irreducible decomposition of binomial ideals. Compositio Mathematica, 152(6), 1319–1332. https://doi.org/10.1112/S0010437X16007272Full Text

Bendich, P., Marron, J. S., Miller, E., Pieloch, A., & Skwerer, S. (2016). Persistent homology analysis of brain artery trees. Annals of Applied Statistics, 10(1), 198–218.Open Access Copy Link to Item

Huckemann, S., Mattingly, J. C., Miller, E., & Nolen, J. (2015). Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability, 20. https://doi.org/10.1214/EJP.v203887Full Text Open Access Copy

Miller, E. (2015). Fruit flies and moduli: Interactions between biology and mathematics. Notices of the American Mathematical Society, 62(10), 1178–1184. https://doi.org/10.1090/noti1290Full Text

Miller, E., Owen, M., & Provan, J. S. (2015). Polyhedral computational geometry for averaging metric phylogenetic trees. Advances in Applied Mathematics, 68, 51–91. https://doi.org/10.1016/j.aam.2015.04.002Full Text

Zamaere, C. B., Griffeth, S., & Miller, E. (2015). Systems of parameters and holonomicity of Ahypergeometric systems. Pacific Journal of Mathematics, 276(2), 281–286. https://doi.org/10.2140/pjm.2015.276.281Full Text

Gopalkrishnan, M., Miller, E., & Shiu, A. (2014). A geometric approach to the global attractor conjecture. Siam Journal on Applied Dynamical Systems, 13(2), 758–797. https://doi.org/10.1137/130928170Full Text

Kahle, T., & Miller, E. (2014). Decompositions of commutative monoid congruences and binomial ideals. Algebra and Number Theory, 8(6), 1297–1364. https://doi.org/10.2140/ant.2014.8.1297Full Text

Skwerer, S., Bullitt, E., Huckemann, S., Miller, E., Oguz, I., Owen, M., … Marron, J. S. (2014). Treeoriented analysis of brain artery structure. Journal of Mathematical Imaging and Vision, 50(1), 126–143. https://doi.org/10.1007/s1085101304730Full Text

Gopalkrishnan, M., Miller, E., & Shiu, A. (2013). A projection argument for differential inclusions, with applications to persistence of massaction kinetics. Symmetry, Integrability and Geometry: Methods and Applications (Sigma), 9. https://doi.org/10.3842/SIGMA.2013.025Full Text

Miller, E. (2013). Affine stratifications from finite misère quotients. Journal of Algebraic Combinatorics, 37(1), 1–9. https://doi.org/10.1007/s1080101203553Full Text

Hotz, T., Huckemann, S., Le, H., Marron, J. S., Mattingly, J. C., Miller, E., … Skwerer, S. (2013). Sticky central limit theorems on open books (null). The Annals of Applied Probability, 23, 2238–2258. https://doi.org/10.1214/12AAP899Full Text Open Access Copy

Guo, A., & Miller, E. (2012). Erratum: Lattice point methods for combinatorial games (Advances in Applied Mathematics (2011) 46:1 (363378)). Advances in Applied Mathematics, 48(1), 269–271. https://doi.org/10.1016/j.aam.2011.09.001Full Text

Miller, E., Novik, I., & Swartz, E. (2011). Face rings of simplicial complexes with singularities. Mathematische Annalen, 351(4), 857–875. https://doi.org/10.1007/s0020801006205Full Text

Anderson, D., Griffeth, S., & Miller, E. (2011). Positivity and Kleiman transversality in equivariant Ktheory of homogeneous spaces. Journal of the European Mathematical Society, 13(1), 57–84. https://doi.org/10.4171/JEMS/244Full Text

Guo, A., & Miller, E. (2011). Lattice point methods for combinatorial games. Advances in Applied Mathematics, 46(1–4), 363–378. https://doi.org/10.1016/j.aam.2010.10.004Full Text

Dickenstein, A., Matusevich, L. F., & Miller, E. (2010). Combinatorics of binomial primary decomposition. Mathematische Zeitschrift, 264(4), 745–763. https://doi.org/10.1007/s002090090487xFull Text

Dickenstein, A., Felicia Matusevich, L., & Miller, E. (2010). Binomial dmodules. Duke Mathematical Journal, 151(3), 385–429. https://doi.org/10.1215/001270942010002Full Text

Dickenstein, A., Matusevich, L. F., & Miller, E. (2010). Binomial Dmodules. Duke Mathematical Journal, 151(3), 1–13.

Knutson, A., Miller, E., & Yong, A. (2009). Gröbner geometry of vertex decompositions and of flagged tableaux. Journal Fur Die Reine Und Angewandte Mathematik, (630), 1–31. https://doi.org/10.1515/CRELLE.2009.033Full Text

Miller, E. (2008). What is... a toric variety? Notices of the American Mathematical Society, 55(5), 586–587.

Ezra, M., & Speyer, D. E. (2008). A kleimanbertini theorem for sheaf tensor products. Journal of Algebraic Geometry, 17(2), 335–340. https://doi.org/10.1090/s1056391107004791Full Text

Jow, S. Y., & Miller, E. (2008). Multiplier ideals of sums via cellular resolutions. Mathematical Research Letters, 15(2–3), 359–373. https://doi.org/10.4310/MRL.2008.v15.n2.a13Full Text

Jow, S. Y., & Miller, E. (2008). Multiplier ideals of sums via cellular resolutions. Mathematical Research Letters, 15(2–3), 359–373.

Knutson, A., Miller, E., & Yong, A. (2008). Tableau complexes. Israel Journal of Mathematics, 163, 317–343. https://doi.org/10.1007/s1185600800145Full Text

Miller, E., & Pak, I. (2008). Metric combinatorics of convex polyhedra: Cut loci and nonoverlapping unfoldings. Discrete and Computational Geometry, 39(1–3), 339–388. https://doi.org/10.1007/s0045400890523Full Text

Shin Yao Jow, . (2008). Multiplier ideals of sums via cellular resolutions. Mathematical Research Letters, 15(2), 359–373.

Ning Jia, . (2007). Duality of antidiagonals and pipe dreams. SÉMinaire Lotharingien De Combinatoire, 58.

Knutson, A., Miller, E., & Shimozono, M. (2006). Four positive formulae for type A quiver polynomials. Inventiones Mathematicae, 166(2), 229–325. https://doi.org/10.1007/s0022200605050Full Text

Matusevich, L. F., & Miller, E. (2006). Combinatorics of rank jumps in simplicial hypergeometric systems. Proceedings of the American Mathematical Society, 134(5), 1375–1381. https://doi.org/10.1090/S0002993905082456Full Text

Miller, E., & Reiner, V. (2006). Stanley's simplicial poset conjecture, after M. Masuda. Communications in Algebra, 34(3), 1049–1053. https://doi.org/10.1080/00927870500442005Full Text

Matusevich, L. F., Miller, E., & Walther, U. (2005). Homological methods for hypergeometric families. Journal of the American Mathematical Society, 18(4), 919–941. https://doi.org/10.1090/S0894034705004881Full Text

Miller, E. (2005). Alternating formulas for Ktheoretic quiver polynomials. Duke Mathematical Journal, 128(1), 1–17. https://doi.org/10.1215/S0012709404128118Full Text

Kogan, M., & Miller, E. (2005). Toric degeneration of Schubert varieties and GelfandTsetlin polytopes. Advances in Mathematics, 193(1), 1–17. https://doi.org/10.1016/j.aim.2004.03.017Full Text

Helm, D., & Miller, E. (2005). Algorithms for graded injective resolutions and local cohomology over semigroup rings. Journal of Symbolic Computation, 39(34 SPEC. ISS.), 373–395. https://doi.org/10.1016/j.jsc.2004.11.009Full Text

Miller, E., & Reiner, V. (2005). Reciprocal domains and CohenMacaulay dcomplexes in ℝ^{d}. Electronic Journal of Combinatorics, 11(2 N), 1–9.

Knutson, A., & Miller, E. (2005). Gröbner geometry of Schubert polynomials. Annals of Mathematics, 161(3), 1245–1318. https://doi.org/10.4007/annals.2005.161.1245Full Text

Knutson, A., & Miller, E. (2004). Subword complexes in Coxeter groups. Advances in Mathematics, 184(1), 161–176. https://doi.org/10.1016/S00018708(03)001427Full Text

Victor Reiner, . (2004). Reciprocal domains and CohenMacaulay dcomplexes in R^d. Electronic Journal of Combinatorics, 11(2), Note1,9pp.

Helm, D., & Miller, E. (2003). Bass numbers of semigroupgraded local cohomology. Pacific Journal of Mathematics, 209(1), 41–66. https://doi.org/10.2140/pjm.2003.209.41Full Text

Miller, E. (2003). Mitosis recursion for coefficients of Schubert polynomials. Journal of Combinatorial Theory. Series A, 103(2), 223–235. https://doi.org/10.1016/S00973165(03)000207Full Text

Miller, E. (2002). Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Mathematica, 7(1), 43–90.

Miller, E. (2002). CohenMacaulay quotients of normal semioroup rings via irreducible resolutions. Mathematical Research Letters, 9(1), 117–128. https://doi.org/10.4310/MRL.2002.v9.n1.a9Full Text

David Perkinson, . (2001). Eight lectures on monomial ideals. Queen’S Papers in Pure and Applied Mathematics, 120, 3–105.

Miller, E. (2000). The Alexander duality functors and local duality with monomial support. Journal of Algebra, 231(1), 180–234. https://doi.org/10.1006/jabr.2000.8359Full Text

Miller, E. N. (2000). Icosahedra constructed from congruent triangles. Discrete and Computational Geometry, 24(2–3), 437–451. https://doi.org/10.1007/s004540010047Full Text

Miller, E., Sturmfels, B., & Yanagawa, K. (2000). Generic and cogeneric monomial ideals. Journal of Symbolic Computation, 29(4–5), 691–708. https://doi.org/10.1006/jsco.1999.0290Full Text

Ezra Miller, . (1998). Multiplicities of ideals in Noetherian rings. BeitrÄGe Zur Algebra Und Geometrie, 39(1), 47–51.


Book Sections

Miller, E. (2001). Graded greenleesmay duality and the cech hull. In Local Cohomology and its Applications (pp. 233–253).


Other Articles

Miller, E., & Sturmfels, B. (1999). Monomial ideals and planar graphs. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). https://doi.org/10.1007/3540467963_3Full Text


Conference Papers

Ene, V., & Miller, E. (2018). Preface. In Springer Proceedings in Mathematics and Statistics (Vol. 238, pp. v–viii).

Miller, E. (2011). Theory and applications of lattice point methods for binomial ideals. In Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: the Abel Symposium 2009 (pp. 99–154). https://doi.org/10.1007/9783642194924_8Full Text

Miller, E. (2009). Topological CohenMacaulay criteria for monomial ideals. In V. Ene & E. Miller (Eds.), Combinatorial Aspects of Commutative Algebra (Vol. 502, pp. 137–155). Mangalia, ROMANIA: AMER MATHEMATICAL SOC.Link to Item


 Teaching & Mentoring

Recent Courses
 MATH 403: Advanced Linear Algebra 2021
 MATH 494: Research Independent Study 2021
 MATH 703: Advanced Linear Algebra 2021
 MATH 221D: Linear Algebra and Applications 2020
 MATH 391: Independent Study 2020
 MATH 493: Research Independent Study 2020
 MATH 627: Algebraic Geometry 2020
 MATH 721D: Linear Algebra and Applications 2020
 MATH 221: Linear Algebra and Applications 2019
 MATH 721: Linear Algebra and Applications 2019

Advising & Mentoring

Undergraduate students advised
 2020 Zizai Cui: Classifying group actions on Abelian surfaces preserving symplectic structure
 2020–2021 Phoebe Klett: Computing sylvan minimal resolutions of monomial ideals
 2020 Joey Li: Indecomposable multipersistence modules and QR codes
 2019–2021 Nathan Geist: Experiments in probabilistic homology
_{ } Homological algebra of real multipersistence  2018–2019 Cheryl Wang: Algorithms for unfolding polyhedra
 2016–2019 David Geng: Topology and geometry of piano music and performance
 2016–2018 Surabhi Beriwal: Computation of fruit fly wing vein topology
 Fulbright semifinalist
 2014 Aaron Park: Geometry of lung arteries (Biomed Engineering/Math, summer research)
 2013 Victoria Cheng: Mathematical biology
 2012–2015 Rowena (Jingxing) Gan: Geometry of harmony in Impressionist music (PRUV)
 PhD candidate, UPenn Wharton School: Operations, Information, and Decisions
 2010 Ezgi Kantarcι: Combinatorial Game Theory (summer research)
 PhD, USC Math
 visited from undergrad institution Bogaziçi University
 2009–2011 Alan Guo: Lattice point methods for combinatorial games (PRUV)
 Analyst, Weiss Asset Management
 PhD, MIT CS AIL
 Duke Faculty Scholar
 Goldwater honorable mention
 2008–2009 Nathaniel Born: Implementing a nonoverlapping unfolding algorithm (UROP)
 Associate Engineer, Natural Resource Group, LLC
 advised at Minnesota
 2007–2008 Matthew Coudron: Visualizing flows on polyhedra
 PhD candidate, MIT CS AIL
 Goldwater Scholar
 advised at Minnesota
 2003–2007 David Molitor: (Math and Economics major with Physics minor)
 Assistant Professor of Finance, UIUC
 Goldwater scholar
 advised at Minnesota
 2019– Yupeng Li: combinatorial algebraic geometry and commutative algebra
 2019– Shreya Arya: applied algebra, geometry, and topology
 2015–2020 Do Tran: Sampling from stratified spaces
 Postdoc, Göttingen
 2015–2020 Erika Ordog: Minimal resolutions of monomial ideals
 Postoc, Texas A&M
 2014–2019 Dmitry Vagner: Diagrammatics in categorification and compositionality
 Simulation scientist, Imbellus Inc.
 2013–2019 Ashleigh Thomas: Invariants and metrics for multiparameter persistent homology
 Postdoc, Florida State University
 2011–2015 Kangkang Wang: Determinant, wall monodromy, and spherical functor
 jointly advised with Paul Aspinwall
 Software Engineer, Google
 2009–2014 Christopher O'Neill: Monoid congruences, binomial ideals, and their decompositions
 Assistant Professor, San Diego State University
 2004–2012 Patrick Byrnes: Structural aspects of differential posets
 advised at Minnesota
 jointly advised with Vic Reiner, UMN
 2005–2015 Robert Edman: Diameter and coherence of monotone path graphs in low corank
 advised at Minnesota
 jointly advised with Vic Reiner, UMN
 2020– Xiaojun Zheng
 Duke Statistical Science
 2006–2008 Dumitru Stamate
 Asistent Universitar, University of Bucharest, Romania
 2009 PhD, University of Bucharest
 Fullbright scholar at UMN
 mentored at Minnesota
 2007–2008 Susan Sierra
 Senior Lecturer at University of Edinburgh
 2008 PhD, University of Michigan
 mentored at Michigan
 2007 Raman Sanyal
 Professor, GoetheUniversität Frankfurt
 2008 PhD, TU Berlin
 mentored at Minnesota
 2020– Margaret Regan
 Duke Math
 2020– Woojin Kim
 Duke Math
 2017–2020 Greg Malen
 Duke Math
 Visiting Assistant Professor, Union College
 2016–2017 Justin Curry
 Duke Math
 Assistant Professor, University at Albany
 2015–2017 Adam Jaeger
 Duke Stat and SAMSI
 Assistant Professor, Statistics, Wichita State Univ.
 2015–2016 Justin Allman
 Duke Math
 Assistant Professor, US Naval Academy
 2011–2013 Christine Berkesch
 Duke Math
 Assistant Professor, U. Minnesota
 2010–2011 Anne Shiu
 NSF Postdoc, Duke Math
 Assistant Professor, Texas A&M
 2010, Fall Manoj Gopalkrishnan
 visitor to Duke Math
 Associate Prof., Elec. Engin., IIT Bombay
 2009–2011 Sonja Mapes
 Duke Math
 Assistant Professor of the Practice, Notre Dame
 2009–2010 Megan Owen
 SAMSI/NCSU Math
 Assistant Professor of CS, Lehman College
 2006–2009 Stephen Griffeth
 Minnesota Math
 Associate Professor, U. Talca, Chile
 2006–2009 Drew Armstrong
 Minnesota Math
 Associate Professor, U. Miami
 2006–2008 Milena Hering
 Minnesota Math
 Lecturer, U. Edinburgh
 2005–2008 Alex Yong
 Minnesota Math
 Associate Professor, U. Illinois, UrbanaChampaign
 2005–2008 Calin Chindris
 Minnesota Math
 Associate Professor, U. Missouri
 2003–2005 Jeremy Martin
 Minnesota Math
 Professor, U. Kansas

Undergraduate students advised
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Algebra over polynomial rings with real exponents. University of Talca. December 16, 2020 2020
 Minimal resolutions of monomial ideals. Indian Institute of Technology. December 3, 2020 2020
 Noninteger multigraded algebra. Max Planck Institute. November 17, 2020 2020
 Minimal resolutions of monomial ideals. September 13, 2020 2020
 Minimal resolutions of monomial ideals. Dalhousie University. January 25, 2020 2020
 Sampling from stratified spaces (5 hours of lectures). September 2, 2019  September 3, 2019 2019
 Mathematics of phenotype variation. August 17, 2019 2019
 Primary distance for multipersistence. July 11, 2019 2019
 Topology for statistical analysis of brain artery images. June 25, 2019 2019
 Topological brain statistics. June 20, 2019 2019
 Spanning trees and lattice paths for monomial resolutions. June 10, 2019 2019
 Algebraic structures for topological summaries of data. June 7, 2019 2019
 Primary distance for multipersistence. May 22, 2019 2019
 Multigraded algebra over polynomial rings with real exponents. February 23, 2019 2019
 Algebra for geometric data. February 22, 2019 2019
 Real multiparameter persistent homology. December 4, 2018 2018
 Resolving persistent homology (4.5 hours of lectures). November 19, 2018  November 20, 2018 2018
 Subword complexes as fibers of totally nonnegative parametrizations. September 26, 2018 2018
 From representations of quivers and posets to applied real commutative algebra (3 hours of lectures). September 17, 2018  September 21, 2018 2018
 What makes primary decomposition minimal?. August 6, 2018 2018
 Algebraic structures for topological summaries of data. July 24, 2018 2018
 Topological brain statistics. July 9, 2018 2018
 Homological and geometric finiteness for realexponent multigraded commutative algebra. July 3, 2018 2018
 Real multiparameter persistent homology. June 26, 2018 2018
 Real multiparameter persistent homology. May 22, 2018 2018
 Data structures for real multiparameter persistence modules. April 22, 2018 2018
 Algebra for geometric data. April 18, 2018 2018
 Stratified spaces, fly wings, and multiparameter persistent homology. January 25, 2018 2018
 Topology for statistical analysis of brain artery images. August 12, 2017 2017
 What is a QR code?. August 1, 2017 2017
 What is a barcode for persistent homology with multiple parameters?. July 31, 2017 2017
 Algebraic data structures for topological summaries. July 27, 2017 2017
 Topology for statistical analysis of brain artery images. June 23, 2017 2017
 Fruit fly wing veins as embedded planar graphs. June 13, 2017 2017
 Algebra for topology in biology and statistics. May 27, 2017 2017
 Algebraic data structures for topological summaries. January 26, 2017 2017
 Data structures for real multiparameter persistence. November 12, 2016 2016
 Lessons in topology from statistics of brain arteries. November 10, 2016 2016
 Algebraic data structures for topological summaries. November 9, 2016 2016
 Data structures for real multiparameter persistence. September 12, 2016 2016
 Real applied multigraded commutative algebra. August 18, 2016  August 24, 2016 2016
 Poset encodings of modules with actions of real cones. July 14, 2016 2016
 Topology for statistical analysis of brain artery images. June 14, 2016 2016
 Homological algebra for real multigraded modules. June 2, 2016 2016
 Effective algebra and geometry for images with varied topology. May 24, 2016 2016
 Data structures for real multiparameter persistence. May 1, 2016 2016
 Interactions between topology, biology, and imaging. December 3, 2015 2015
 Irreducible decomposition of binomial ideals. December 3, 2015 2015
 Multigraded modules from fruit flies. November 23, 2015 2015
 Multigraded modules from fruit flies. November 20, 2015 2015
 Lessons in topology from statistics of brain arteries. November 19, 2015 2015
 Multigraded moduli from fruit flies. November 3, 2015 2015
 Topology for statistical analysis of brain artery images. October 20, 2015 2015
 Persistent homology for biological images. September 28, 2015 2015
 Biological applications of persistent homology: interactions with statistics, geometry, and algebra. September 11, 2015 2015
 Multigraded moduli from fruit flies via stratified space statistics. July 7, 2015 2015
 Persistent interactions between biology, topology, and statistics. June 9, 2015 2015
 Applying persistent homology to brain artery and vein imaging. March 21, 2015 2015
 Applying persistent homology to brain artery and vein imaging. January 30, 2015 2015
 Persistent homology analysis of brain artery trees. January 11, 2015 2015
 Applying persistent homology to brain artery and vein imaging. November 12, 2014 2014
 Topological definition of sticky means in arbitrary metric spaces. October 3, 2014 2014
 Topology for statistical analysis of brain artery images. June 27, 2014 2014
 Applying persistent homology to brain artery and vein imaging. May 20, 2014 2014
 Topology for statistical analysis of brain artery images. May 15, 2014 2014
 Topological analysis of geometrically stratified data. May 12, 2014 2014
 Topology for statistical analysis of brain artery images. April 11, 2014 2014
 Applying persistent homology to brain artery imaging. March 10, 2014 2014
 Asymptotics of sampling from topologically stratified spaces. March 4, 2014 2014
 Binomial irreducible decomposition. January 25, 2014 2014
 Binomial irreducible decomposition. November 9, 2013 2013
 Binomial irreducible decomposition. October 12, 2013 2013
 Binomial irreducible decomposition. July 9, 2013 2013
 How do quivers and stratifications apply to biology?. April 27, 2013 2013
 Geometric statistics on stratified spaces. March 7, 2013 2013
 Sticky central limit theorems at singularities. March 6, 2013 2013
 Biological applications of geometric statistics on stratified spaces. February 14, 2013 2013
 Statistics without addition or division. February 6, 2013 2013
 Alexander duality and total positivity: a cluster/commutative algebra connection. December 7, 2012 2012
 Geometry for samples of metric branched structures. October 11, 2012 2012
 NSF funding from the inside. September 25, 2012 2012
 Combinatorics and topology of fibers in total positivity. May 25, 2012 2012
 Sticky central limit theorems at singularities. May 23, 2012 2012
 Sticky central limit theorems at singularities. April 24, 2012 2012
 Subword complexes and fibers of totally nonnegative parametrizations. September 24, 2011 2011
 Sticky central limit theorems at singularities. August 15, 2011 2011
 Sticky central limit theorems at singularities. August 4, 2011 2011
 How primary decomposition in commutative monoids is wrong. June 9, 2011 2011
 Stratified statistics for evolutionary biology. April 30, 2011 2011
 Contractibility via subword complexes in the context of homogeneous spaces. April 23, 2011 2011
 Geometric statistics: sampling from singular spaces. March 26, 2011 2011
 How primary decomposition in commutative monoids is wrong. March 19, 2011 2011
 Sticky central limit theorems on polyhedral spaces. March 12, 2011 2011
 Unfolding polyhedra. February 18, 2011 2011
 Statistics on data sampled from stratified spaces. January 14, 2011 2011
 Statistics on spaces of phylogenetic trees. December 3, 2010 2010
 Combinatorics of phylogenetic trees. December 2, 2010 2010
 Decompositions of commutative monoid congruences and binomial ideals. November 2, 2010 2010
 Decompositions of monoids and binomial ideals (5 hours of lectures). September 1, 2010 2010
 Unfolding convex polyhedra. July 1, 2010 2010
 Face rings of simplicial complexes with singularities. June 1, 2010 2010
 Lattice point methods for combinatorial games. May 1, 2010 2010
 Unfolding convex polyhedra. May 1, 2010 2010
 Lattice point methods for combinatorial games. April 1, 2010 2010
 Lattice point methods for combinatorial games. March 1, 2010 2010
 Unfolding convex polyhedra. February 1, 2010 2010
 Primary decomposition of binomial ideals (8 hours of lectures). January 1, 2010 2010
 Ktheory of toric varieties. December 1, 2009 2009
 Biological and chemical applications of polyhedral geometry and algebra. October 1, 2009 2009
 Equivariant transversality and Ktheoretic positivity. October 1, 2009 2009
 Combinatorics in cohomology of toric varieties. September 1, 2009 2009
 Unfolding polyhedra. September 1, 2009 2009
 What is a toric variety?. September 1, 2009 2009
 Lattice games. July 1, 2009 2009
 Applications of binomial commutative algebra. June 1, 2009 2009
 Binomial ideals. June 1, 2009 2009
 Combinatorial primary decomposition of binomial ideals. April 1, 2009 2009
 Equivariant positivity via transversality in Ktheory of G/P. April 1, 2009 2009
 Potential applications of commutative algebra to combinatorial game theory. April 1, 2009 2009
 Topological CohenMacaulay criteria for monomial ideals. April 1, 2009 2009
 Equivariant transversality and Ktheoretic positivity. March 1, 2009 2009
 Geometry of flags and permutations. March 1, 2009 2009
 Unfolding polyhedra. March 1, 2009 2009
 Unfolding polyhedra. March 1, 2009 2009
 Positivity from transversality and transitivity. January 1, 2009 2009
 Transversality in homogeneous spaces. December 1, 2008 2008
 Cohomology rings of flag and toric varieties. October 1, 2008 2008
 Topological CohenMacaulay criteria for monomial ideals. September 1, 2008 2008
 Cellular resolutions of multiplier ideals of sums. May 1, 2008 2008
 Combinatorics of Horn hypergeometric series. April 1, 2008 2008
 Gröbner geometry of Schubert polynomials. February 1, 2008 2008
 Metric geometry and unfoldings of polyhedra. February 1, 2008 2008
 Unfolding polyhedra. February 1, 2008 2008
 Metric geometry and unfoldings of polyhedra. January 1, 2008 2008

Outreach & Engaged Scholarship

Service to the Profession
 Organizer, IMS Singapore Workshop: Interactions of Statistics and Geometry [ISAG] (with Stephan Huckemann and Zhigang Yao). February 2022 2022
 AMS Nominating Committee. 2021  2023 2021  2023
 Editorial Board Member. Journal of Machine Learning Research. 2020 2020
 Editorial Board Member. Journal of Applied and Computational Topology. 2018 2018
 Organizer, Oberwolfach Workshop: Statistics for data with geometric structure (with Aasa Feragen, Thomas Hotz, and Stephan Huckemann). January 2018 2018
 Technical Program Committee: IEEE International Conference on Big Data, Workshop on HighDimensional Big Data. December 2016 2016
 Director (with Viviana Ene): Summer school on Applicable Combinatorial Commutative Algebra, Romania. August 2016 2016
 Scientific Committee Member: Conference on algebraic combinatorics and group actions, Herstmonceux Castle, England. July 2016 2016
 Local Scientific Coordinator, SAMSI yearlong program on Challenges in Computational Neuroscience. 2015  2016 2015  2016
 Advisory Board, Meeting on Combinatorial Commutative Algebra (MOCCA 2014), Trentino, Italy. September 2014 2014
 Organizer, Oberwolfach miniworkshop: Asymptotic statistics on stratified spaces (with (with Aasa Feragen, Stephan Huckemann, J.S. Marron). September 2014 2014
 Organizer, Fields Institute workshop: Geometric topological and graphical model methods in statistics (with Peter Kim and Hélène Massam). May 2014 2014
 Editorial Board Member. Journal of Combinatorial Theory, Series A. 2014 2014
 Organizer, SAMSI Public Lecture by Greg Fishel (WRALTV Chief Meteorologist): ``The changing climate of weather prognostication: the irony of uncertainty leading to better forecasts''. December 2013 2013
 AMS Fellows Selection Committee. 2013  2015 2013  2015
 Directorate Organizer : SAMSI Summer Program on Neuroimaging Data Analysis (NDA). December 15, 2012  July 1, 2013 2012  2013
 Organizer : Oberwolfach miniworkshop: Asymptotic statistics on stratified spaces (29 Sep  3 Oct 2014). February 29, 2012  October 3, 2014 2012  2014
 AMS Short Course Subcommittee. 2012  2015 2012  2015
 AMS Southeast Section Program Committee. 2012  2014 2012  2014
 Lead Organizer : MBI: Workshop on statistics, geometry, and combinatorics on stratified spaces arising from biological problems (May 2012). December 12, 2011  June 1, 2012 2011  2012
 Scientific Committee Member : Experimental and theoretical methods in algebra, geometry, and topology, Mangalia, Romania (June 2013). December 12, 2011  July 1, 2013 2011  2013
 Organizer (with Sonja Mapes and Christine Berkesch) : Triangle Lectures in Combinatorics, 11 February 2012. July 1, 2011  July 1, 2012 2011  2012
 Directorate Organizer : 20132014 SAMSI yearlong program on LowDimensional Structure in HighDimensional Systems (LDHD). 2011  2014 2011  2014
 Editorial Board Member. Discrete Mathematics. 2011 2011
 Organizer : Triangle Lectures in Combinatorics. September 25, 2010 2010
 Working Group leader and administrator : SAMSI Working Group: Analysis of data sampled from stratified spaces. September 2010  June 2011 2010  2011
 Steering Committee Member : Triangle Lectures in Combinatorics. 2010 2010
 Program Committee Member : 2011 Formal Power Series and Algebraic Combinatorics (FPSAC), Reykjavík, Iceland. December 6, 2009  July 1, 2011 2009  2011
 Working group session organizer (with William Graham, UGA) : Combinatorial Lie theory and applications. October 2009 2009
 Program Committee Member : 2009 Formal Power Series and Algebraic Combinatorics (FPSAC), Research Institute for Symbolic Computation (RISC), Linz, Austria. July 2009 2009
 Organizer : Triangle Lectures in Combinatorics. February 6, 2009 2009
 Editorial Board Member. Advances in Mathematics. 2009 2009
 Editorial Board Member. SIAM Journal on Discrete Mathematics. 2009  2017 2009  2017
 Organizer : 20122013 MSRI yearlong program on Commutative Algebra. 2009  2013 2009  2013
 Scientific Committee Member : Exploratory workshop on combinatorial commutative algebra and computer algebra, Mangalia, Romania. May 2008 2008
 Editorial Board Member. Beiträge zur Algebra und Geometrie. 2008 2008
 Organizer : Workshop on Combinatorial Game Theory, Banff International Research Station (BIRS). January 2008 2008
 Associate Editor. Discrete Mathematics. 2007  2010 2007  2010
 Referee for over 80 journals, conferences, and other venues. 2000 2000

Service to Duke
 Liaison to MA Teaching Program. Duke Mathematics Department. August 2019 2019
 Advanced Linear Algebra (Math 403), sole developer. 2016  2017 2016  2017
 Master of Arts in Teaching (MAT) Program: Math Content Advisor. 2014 2014
 Faculty Advisory Board member, Robert Noyce Teacher Fellowship Program. December 21, 2013 2013
 Associate Director, SAMSI. SAMSI Associate Director. May 1, 2011  June 1, 2014 2011  2014
 Math Everywhere (Math 181) codeveloper, with Ingrid Daubechies and Jonathan Mattingly. 2011 2011
Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.