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 K-theory 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; mass-action kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; Lie theory; and geometric statistics of data sampled from highly non-Euclidean 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 K-theory 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; mass-action kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; Lie theory; and geometric statistics of data sampled from highly non-Euclidean 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 in Physics 209 or outside
Thursday, 13:15 – 14:30 in 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 27708-0320
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(919) 660-2846
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# homepage
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CV (Curriculum Vitae)
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Talks, seminars, and lecture series
- Background
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Education, Training, & Certifications
- Ph.D., University of California - Berkeley 2000
- B.S., Brown University 1995
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Leadership & Clinical Positions at Duke
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Lead PI, NSF/Simons proposal: National Institute for Theory and Mathematics in Biology ($50M cross-departmental endeavor; declined), Fall 2021
Liaison to MA Teaching Program. Duke Mathematics Department, August 2019
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Lead PI, NSF/Simons proposal: National Institute for Theory and Mathematics in Biology ($50M cross-departmental endeavor; declined), Fall 2021
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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
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In the News
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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
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Awards & Honors
- Simons CRM Professor. Centre de Recherches Mathématiques (CRM), Montréal. 2018
- 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 Land-Grant 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
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Subject Headings
- Research
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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 - 2023
- 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
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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
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External Relationships
- University of Goettingen
- University of Leipzig
- Publications & Artistic Works
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Selected Publications
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Academic Articles
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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/s10208-018-9405-0Full Text
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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
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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
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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
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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
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Zamaere, C. B., Griffeth, S., & Miller, E. (2015). Systems of parameters and holonomicity of A-hypergeometric systems. Pacific Journal of Mathematics, 276(2), 281–286. https://doi.org/10.2140/pjm.2015.276.281Full Text
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Huckemann, S., Mattingly, J. C., Miller, E., & Nolen, J. (2015). Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability, 20, 1–34. https://doi.org/10.1214/EJP.v20-3887Full Text Open Access Copy
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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
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Skwerer, S., Bullitt, E., Huckemann, S., Miller, E., Oguz, I., Owen, M., … Marron, J. S. (2014). Tree-oriented analysis of brain artery structure. Journal of Mathematical Imaging and Vision, 50(1), 126–143. https://doi.org/10.1007/s10851-013-0473-0Full Text
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Miller, E. (2013). Affine stratifications from finite misère quotients. Journal of Algebraic Combinatorics, 37(1), 1–9. https://doi.org/10.1007/s10801-012-0355-3Full Text
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Hotz, T., Huckemann, S., Le, H., Marron, J. S., Mattingly, J. C., Miller, E., … Skwerer, S. (2013). Sticky central limit theorems on open books. The Annals of Applied Probability, 23, 2238–2258. https://doi.org/10.1214/12-AAP899Full Text Open Access Copy
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Guo, A., & Miller, E. (2012). Erratum: Lattice point methods for combinatorial games (Advances in Applied Mathematics (2011) 46:1 (363-378)). Advances in Applied Mathematics, 48(1), 269–271. https://doi.org/10.1016/j.aam.2011.09.001Full Text
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Gopalkrishnan, M., & Shiu, A. (2012). A projection argument for differential inclusions, with applications to persistence of mass-action kinetics (Accepted). Sigma (Symmetry, Integrability, and Geometry: Methods and Applications).
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Thomas Kahle, . (2012). Decompositions of commutative monoid congruences and binomial ideals (Accepted). Algebra & Number Theory.
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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/s00208-010-0620-5Full Text
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Anderson, D., Griffeth, S., & Miller, E. (2011). Positivity and Kleiman transversality in equivariant K-theory of homogeneous spaces. Journal of the European Mathematical Society, 13(1), 57–84. https://doi.org/10.4171/JEMS/244Full Text
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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
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Dickenstein, A., Matusevich, L. F., & Miller, E. (2010). Combinatorics of binomial primary decomposition. Mathematische Zeitschrift, 264(4), 745–763. https://doi.org/10.1007/s00209-009-0487-xFull Text
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Dickenstein, A., Matusevich, L. F., & Miller, E. (2010). Binomial D-modules. Duke Mathematical Journal, 151(3), 1–13.
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Ezra Miller, . (2010). Binomial D-modules. Duke Mathematical Journal, 151(3), 385–429.Link to Item
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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
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Miller, E. (2008). What is... a toric variety? Notices of the American Mathematical Society, 55(5), 586–587.
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Ezra, M., & Speyer, D. E. (2008). A kleiman-bertini theorem for sheaf tensor products. Journal of Algebraic Geometry, 17(2), 335–340. https://doi.org/10.1090/s1056-3911-07-00479-1Full Text
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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
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Jow, S. Y., & Miller, E. (2008). Multiplier ideals of sums via cellular resolutions. Mathematical Research Letters, 15(2–3), 359–373.
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Knutson, A., Miller, E., & Yong, A. (2008). Tableau complexes. Israel Journal of Mathematics, 163, 317–343. https://doi.org/10.1007/s11856-008-0014-5Full Text
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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/s00454-008-9052-3Full Text
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Shin Yao Jow, . (2008). Multiplier ideals of sums via cellular resolutions. Mathematical Research Letters, 15(2), 359–373.
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Ning Jia, . (2007). Duality of antidiagonals and pipe dreams. SÉMinaire Lotharingien De Combinatoire, 58.
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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/s00222-006-0505-0Full Text
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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/S0002-9939-05-08245-6Full Text
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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
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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/S0894-0347-05-00488-1Full Text
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Miller, E. (2005). Alternating formulas for K-theoretic quiver polynomials. Duke Mathematical Journal, 128(1), 1–17. https://doi.org/10.1215/S0012-7094-04-12811-8Full Text
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Kogan, M., & Miller, E. (2005). Toric degeneration of Schubert varieties and Gelfand-Tsetlin polytopes. Advances in Mathematics, 193(1), 1–17. https://doi.org/10.1016/j.aim.2004.03.017Full Text
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Helm, D., & Miller, E. (2005). Algorithms for graded injective resolutions and local cohomology over semigroup rings. Journal of Symbolic Computation, 39(3-4 SPEC. ISS.), 373–395. https://doi.org/10.1016/j.jsc.2004.11.009Full Text
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Miller, E., & Reiner, V. (2005). Reciprocal domains and Cohen-Macaulay d-complexes in ℝd. Electronic Journal of Combinatorics, 11(2 N), 1–9.
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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
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Knutson, A., & Miller, E. (2004). Subword complexes in Coxeter groups. Advances in Mathematics, 184(1), 161–176. https://doi.org/10.1016/S0001-8708(03)00142-7Full Text
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Victor Reiner, . (2004). Reciprocal domains and Cohen-Macaulay d-complexes in R^d. Electronic Journal of Combinatorics, 11(2), Note1,9pp.
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Helm, D., & Miller, E. (2003). Bass numbers of semigroup-graded local cohomology. Pacific Journal of Mathematics, 209(1), 41–66. https://doi.org/10.2140/pjm.2003.209.41Full Text
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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/S0097-3165(03)00020-7Full Text
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Miller, E. (2002). Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Mathematica, 7(1), 43–90.
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Miller, E. (2002). Cohen-Macaulay 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
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David Perkinson, . (2001). Eight lectures on monomial ideals. Queen’S Papers in Pure and Applied Mathematics, 120, 3–105.
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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
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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
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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
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Ezra Miller, . (1998). Multiplicities of ideals in Noetherian rings. BeitrÄGe Zur Algebra Und Geometrie, 39(1), 47–51.
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Miller, E. (n.d.). Stratifications of real vector spaces from constructible sheaves with conical microsupport. Journal of Applied and Computational Topology.Link to Item
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Miller, E., & Geist, N. (n.d.). Global dimension of real-exponent polynomial rings (Accepted). Algebra and Number Theory.Link to Item
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Miller, E., Kahle, T., & O’Neill, C. (n.d.). Irreducible decomposition of binomial ideals (Accepted). Compositio Mathematica.Link to Item
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Book Sections
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Miller, E. (2001). Graded greenlees-may duality and the cech hull. In Local Cohomology and its Applications (pp. 233–253).
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Other Articles
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Miller, E., & Sturmfels, B. (1998). Monomial ideals and planar graphs. (M. Fossorier, H. Imai, S. Lin, & A. Poli, Eds.), Applied Algebra, Algebraic Algorithms and Error Correcting Codes.
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Conference Papers
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Ene, V., & Miller, E. (2018). Preface. In Springer Proceedings in Mathematics and Statistics (Vol. 238, pp. v–viii).
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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/10.1007/978-3-642-19492-4_8Full Text
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Miller, E. (2009). Topological Cohen-Macaulay 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
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Preprints
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Miller, E., Ordog, E., & Li, Y. (n.d.). Minimal resolutions of lattice ideals. https://arxiv.org/abs/2208.09557.
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- Teaching & Mentoring
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Recent Courses
- MATH 393: Research Independent Study 2023
- MATH 403: Advanced Linear Algebra 2023
- MATH 492: Independent Study 2023
- MATH 501: Introduction to Algebraic Structures I 2023
- MATH 703: Advanced Linear Algebra 2023
- MATH 403: Advanced Linear Algebra 2022
- MATH 493: Research Independent Study 2022
- MATH 627: Algebraic Geometry 2022
- MATH 703: Advanced Linear Algebra 2022
- MATH 221: Linear Algebra and Applications 2021
- MATH 403: Advanced Linear Algebra 2021
- MATH 494: Research Independent Study 2021
- MATH 703: Advanced Linear Algebra 2021
- MATH 721: Linear Algebra and Applications 2021
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Advising & Mentoring
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Undergraduate students advised
- 2022–2023 Jesse Zhang: Geodesic complexity of convex polyhedra
- 2022–2023 Nathan Nguyen: Matroid h-vectors and Stanley's hypothesis
- 2021–2022 William He: Computing presentations of fly wing bipersistence
- 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 (PRUV)
- 2019–2021 Nathan Geist: Experiments in probabilistic homology
Homological algebra of real multipersistence
Global dimension of real-exponent polynomial rings (PRUV) - 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
- Research Engineer, Polygon Zero
- 2013–2019 Ashleigh Thomas: Invariants and metrics for multiparameter persistent homology
- Postdoc, University of Florida / Georgia Tech
- 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: statistical applications of persistent homology
- 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, Goethe-Universität 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, Urbana-Champaign
- 2005–2008 Calin Chindris
- Minnesota Math
- Associate Professor, U. Missouri
- 2003–2005 Jeremy Martin
- Minnesota Math
- Professor, U. Kansas
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Undergraduate students advised
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- Geometric central limit theorems on non-smooth spaces. December 15, 2022 2022
- Concrete representatives for multiparameter derived sheaves. November 8, 2022 2022
- Geometric central limit theorems on non-smooth spaces. September 7, 2022 2022
- Central limit theorems on non-smooth spaces. August 3, 2022 2022
- Multigraded algebra: past, present, future. July 1, 2022 2022
- Homological algebra over partially ordered real vector spaces. June 5, 2022 2022
- Duke Math panel: Networking & Collaborations. April 13, 2022 2022
- Polynomials with real exponents. April 1, 2022 2022
- Computation of persistent homology with real parameters. March 26, 2022 2022
- NCAA bracket probabilities. March 16, 2022 2022
- NCAA bracket probabilities. March 15, 2022 2022
- NCAA bracket probabilities. March 13, 2022 2022
- Computational algebra and geometry of multipersistence. Society for Industrial and Applied Mathematics. August 19, 2021 2021
- Multigraded algebra over polynomial rings with real exponents. IPM. July 29, 2021 2021
- Endpoints for multiparameter persistence. Lorentz Center. July 22, 2021 2021
- Persistent homology with multiple parameters. Mathematical Sciences Research Institute. May 11, 2021 2021
- Endpoints for multiparameter persistence. University of Chicago. April 30, 2021 2021
- Algebra over polynomial rings with real exponents. University of Talca. December 3, 2020 2020
- Minimal resolutions of monomial ideals. Indian Institute of Technology. December 3, 2020 2020
- Non-integer 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 real-exponent 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
- K-theory of toric varieties. December 1, 2009 2009
- Biological and chemical applications of polyhedral geometry and algebra. October 1, 2009 2009
- Equivariant transversality and K-theoretic 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 K-theory of G/P. April 1, 2009 2009
- Potential applications of commutative algebra to combinatorial game theory. April 1, 2009 2009
- Topological Cohen-Macaulay criteria for monomial ideals. April 1, 2009 2009
- Equivariant transversality and K-theoretic 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 Cohen-Macaulay 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
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Outreach & Engaged Scholarship
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Service to the Profession
- Organizer, IMS Singapore Workshop: Interactions of Statistics and Geometry [ISAG II] (with Stephan Huckemann and Zhigang Yao). October 14, 2024 - October 25, 2024 2024
- Organizer, Harvard CMSA Conference: Geometry and Statistics (with Stephan Huckemann and Zhigang Yao). February 27, 2023 - March 1, 2023 2023
- AMS Special Session organizer. Multiparameter persistence in theory and practice. University of Virginia. March 11, 2022 - March 13, 2022 2022
- 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
- Advisory Editor. Combinatorial Theory. 2021 2021
- 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 High-Dimensional 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 year-long 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 mini-workshop: 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 - 2020 2014 - 2020
- Organizer, SAMSI Public Lecture by Greg Fishel (WRAL-TV 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 mini-workshop: 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 : 2013-2014 SAMSI year-long program on Low-Dimensional Structure in High-Dimensional 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 : 2012-2013 MSRI year-long 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
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Service to Duke
- Lead PI, NSF/Simons proposal: National Institute for Theory and Mathematics in Biology (declined). 2021 2021
- 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) co-developer, 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.
