Publication List

Researchgate Link

Google Scholar Profile

Preprints on arXiv.org

## Invariant Theory

**Book: **H. Derksen and G. Kemper, “Computational Invariant Theory”, *Encyclopaedia of Mathematical Sciences* 130, Springer, Heidelberg, second edition, 2015 (first edition 2002).

H. Derksen and V. Makam, “Polynomial degree bounds for matrix semi-invariants”, Adv. Math. 310, p 44-63, 2017.

H. Derksen and V. Makam, “Generating invariant rings of quivers in arbitrary characteristic”, J. Algebra 489, p. 435-445, 2017.

H. Derksen and V. Makam, “Degree bounds for semi-invariant rings of quivers”, J. Pure Appl. Algebra 222 (10), p. 3282-3298, 2018.

H. Derksen and G. Kemper, “Computing invariants of algebraic groups in arbitrary characteristic”, Adv. Math.217 (5), p. 2089-2129, 2008.

H. Derksen, E. Jeandel and P. Koiran, “Quantum automata and algebraic groups”, J. Symbolic Comput. 39 (3-4), 357-371, 2005.

H. Derksen, “Degree bounds for syzygies of invariants”, Adv. Math. 185 (2), p. 207-214, 2004.

H. Derksen and G. Kemper, “On global degree bounds for invariants”, In Invariant Theory in all characteristics, CRM Proc. Lecture Notes 35, p. 37-41, Amer. Math. Soc., Providence, RI, 2004.

H. Derksen, “Constructive invariant theory”, In Invariant Theory in all characteristics, CRM Proc. Lecture Notes 35, p. 11-36, Amer. Math. Soc., Providence, RI, 2004.

H. Derksen, “Restrictions of algebraic group representations to finite subgroups”, Bull. London Math. Soc. 34 (2), p. 165-173, 2002.

H. Derksen, “Polynomial bounds for rings of invariants”, Proc. Amer. Math. Soc. 129 (4), p. 955-963, 2001.

H. Derksen, “Computation of invariants for reductive groups”, Adv. Math. 141 (2), p. 366-384, 1999.

H. Derksen and H. Kraft, “Constructive invariant theory”, In Algèbre non-commutative, groups quantiques et invariants (Reims 19995), Sémin. Congr. 2, p. 221-244, Soc. Math. France, Paris, 1997.

## Quiver Representations

**Book: **H. Derksen and J. Weyman, “An Introduction to Quiver Representations”, *Graduate Studies in Mathematics* 184, American Mathematical Society, 2007.

H. Derksen and J. Fei, “General presentations of algebras”, Adv. Math. 278, p. 210-237, 2015.

H. Derksen, B. Huisgen-Zimmermann and J. Weyman, “Top-stable degenerations of finite-dimensional algebras II”, Adv. Math. 259, p. 730-765, 2014.

H. Derksen and J. Weyman, “The combinatorics of quiver representations”, Ann. Inst. Fourier (Grenoble) 61 (3), p. 1061-1131, 2011.

H. Derksen, J. Weyman and A. Zelevinsky, “Quivers with potentials and their representations II: applications to cluster algebras”, J. Amer. Math. Soc. 23 (3), p. 749-790, 2010.

H. Derksen, J. Weyman and A. Zelevinsky, “Quivers with potentials and their representations I: Mutations”, Selecta Math. (N.S.) 14 (1), p. 59-119, 2008.

H. Derksen and T. Owen, “New graphs of finite mutation type”, Electron. J. Combin. 15 (1): Research Paper 139, 15, 2008.

H. Derksen, A. Schofield and J. Weyman, “On the number of subrepresentations of a general quiver representation”, J. London Math. Soc. (2) 76 (1), p. 135-147, 2007.

C. Chindris, H. Derksen and J. Weyman, “Counterexamples to Okounkov’s log-concavity conjecture”, Compos. Math. 143 (6), p. 1545-1557, 2007.

H. Derksen and J. Weyman, “Quiver representations”, Notices Amer. Math. Soc. 52 (2), p. 200-206, 2005.

H. Derksen and J. Weyman, “Semi-invariants for quivers with relations”, J. Algebra 258 (1), p. 216-227, 2002.

H. Derksen and J. Weyman, “On the Littlewood-Richardson polynomials”, J. Algebra 255 (2), p. 247-257, 2002.

H. Derksen and J. Weyman, “On the canonical decomposition of quiver representations”, Compositio Math. 133 (3), p. 245-265, 2002.

H. Derksen and J. Weyman, “Generalized quivers associated to reductive groups”, Colloq. Math. 94 (2), p. 151-183, 2002.

H. Derksen and J. Weyman, “Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients”, J. Amer. Math. Soc. 13(3), p. 457-479, 2000.

## Tensors

H. Derksen, “A general theory of singular values with applications to signal denoising“, SIAM J. on Applied Algebra and Geometry, to appear, 2018.

H. Derksen, V. Makam, “Explicit tensors of border rank 2d-2 in K^{2}oK^{2}oK^{2} in arbitrary characteristic“, Linear and Multilinear Algebra, p. 1-13, 2018.

H. Derksen and V. Makam, “On non-commutative rank and tensor rank”, Linear and Multilinear Algebra 66 (6), p. 1069–1084, 2018.

H. Derksen, “On the equivalence between low-rank matrix completion and tensor rank”, Linear and Multilinear Algebra 66 (4), p. 645-667, 2018.

H. Derksen, “On the nuclear norm and the singular value decomposition of tensors”, Found. Comput. Math. 16 (3), p. 779-811, 2016.

H. Derksen, “Matrix completion and tensor rank”, Linear and Multilinear Algebra 64 (4), p. 680-685, 2016.

H. Derksen and Z. Teitler, “Lower bound for ranks of invariant forms”, J. Pure Appl. Algebra 219 (12), p. 5429-5441, 2015.

H. Derksen, “Kruskal’s uniqueness inequality is sharp”, Linear Algebra Appl. 438 (2), p. 708-712, 2013.

## Commutative Algebra

H. Derksen, R. Eggermont and A. Snowden, “Topological Noetherianity for cubic polynomials”, Algebra & Number Theory 11 (9), p. 2197-2212, 2017.

H. Derksen, “Hilbert series of subspace arrangements”, J. Pure Appl. Algebra 209 (1), p. 91-98, 2007.

H. Derksen, “Universal denominators of Hilbert series”, J. Algebra 285 (2), p. 586-607, 2005.

H. Derksen and J. Sidman, “Castelnuovo-Mumford regularity by approximation”, Adv. Math 188 (1), p. 104-123, 2004.

H. Derksen, “The fundamental theorem of algebra and linear algebra”, Amer. Math. Monthly 110 (7), p. 620-623, 2003.

H. Derksen and J. Sidman, ”A sharp bound for the Castelnuovo-Mumford regularity of subspace arrangements”, Adv. Math. 172 (2), p. 151-157, 2002.

**Automorphisms of Affine Space**

H. Derksen, A. van den Essen and W. Zhao, “The Gaussian moments conjecture and the Jacobian conjecture”, Israel J. Math. 219 (2), p. 917-928, 2017.

H. Derksen, A. van den Essen, D. R. Finston and S. Maubach, “Unipotent group actions on affine varieties”, J. Algebra 336, p. 200-208, 2011.

H. Derksen. O. Hadas and L. Makar-Limanov, “Newton polytopes of invariants of additive group actions”, J. Pure Appl. Algebra 156 (2-3), p. 187-197, 2001.

H. Derksen, F. Kutzschebauch and J. Winkelmann, “Subvarieties of C^{n} with non-extendable automorphisms”, J. Reine Angew. Math. 509, p. 213-235, 1999.

Derksen and F. Kutzschebauch, “Global holomorphic linearization of actions of compact Lie groups on Cn”, In Complex geometric analysis in Pohang (1997), Contemp. Math. 22, p. 201-210, Amer. Math. Soc., Providence, RI, 1999.

H. Derksen and F. Kutzschebauch, “Nonlinearizable holomorphic group actions”, Math. Ann. 311 (1), p. 41-53, 1998.

H. Derksen, “Quotients of algebraic group actions”, In Automorphisms of affine spaces (Curaçao, 1994), p. 191-200, Kluwer Acad. Publ., Dordrecht, 1995.

H. Derksen, “Inverse degrees and the Jacobian conjecture”, Comm. Algebra 22 (12), p. 4793-4794, 1994.

H. Derksen, “The kernel of a derivation”, J. Pure Appl. Algebra 84 (1), p. 13-16, 1993.

## Combinatorics

H. Derksen and A. Fink, “Valuative invariants for polymatroids”, In 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), Nancy, 2010.

H. Derksen, “The graph isomorphism problem and approximate categories”, J. Symbolic Comput. 59, p. 81-112, 2013.

H. Derksen and A. Fink, “Valuative invariants for polymatroids”, Adv. Math. 225 (4), p. 1840-1892, 2010.

H. Derksen, “Symmetric and quasi-symmetric functions associated to polymatroids”, J. Algebraic Combin. 30 (1), p. 43-86, 2009.

H. Derksen, “Error-correcting codes and B_{h}–sequences”, IEEE Trans. Inform. Theory 50 (3), p. 476-485, 2004.

H. Derksen, C. Eggermont and A. van den Essen, “Multimagic squares”, Amer. Math. Monthly 114 (8), p. 703-713, 2007.

## Number Theory

H. Derksen and D. Masser, “Linear equations over multiplicative groups, recurrences, and mixing III”, Ergodic Th. Of Dyn. Systems, p. 1-19, 2017, online.

H. Derksen and D. Masser, “Linear equations over multiplicative groups, recurrences, and mixing II”, Indag. Math. (N.S.) 26 (11), p. 113-136, 2015.

H. Derksen and D. Masser, “Linear equations over multiplicative groups, recurrences, and mixing I”, Proc. London Math. Soc. (3), 104 (5), p. 1045-1083, 2012.

H. Derksen, “A Skolem-Mahler-Lech theorem in positive characteristic and finite automata”, Invent. Math. 168 (1), p. 175-224, 2007.

## Applied Mathematics

S. Ansari, N. Farzaneh, M. Heung, K. Oldham, H. Derksen K. R. Ward and K. Najarian, “Real-time detection of intradialytic hypotension using a novel polyvinylidene fluoride based sensor”, In IEEE-EMBS International Conference on Biomedical and Health Informatics (BHI), 2016.

R. Fazlali, N. Karimi, S.M. R. Soroushmehr, S. Samavi, B. Nallamothu, H. Derksen and K. Najarian, “Robust catheter identification and tracking in X-ray angiographic sequences”, Engineering in Medicine and Biology (EMBC), 37^{th} Annual International Conference of the IEEE, p. 7901-7904, 2015.

S. Kazeminia, N. Karimi, S.M.R. Soroushmehr, S. Samavi, H.Derksen and K. Najarian, “Region of interest for lossless compression of bone X-ray images”, Engineering in Medicine and Biology (EMBC), 37^{th} Annual International Conference of the IEEE, p. 3061-3064, 2015.

S.M.R. Soroushmehr, A. Bafna, S. Schlosser, K. Ward, H. Derksen and K. Najarian, “CT image segmentation in traumatic brain injury”, Engineering in Medicine and Biology (EMBC), 37^{th} Annual International Conference of the IEEE, p. 2973-2976, 2015.

C. Biwer, A. Rothberg, H. IglayReger, H. Derksen, C. F. Burant and K. Najarian, “Windowed persistent homology: a topological signal processing algorithm applied to clinical obesity data”, PLOS one 12 (5): e0177696, 2017.

M. Nejati, S. Samavi, H. Derksen and K. Najarian, “Denoising by low-rank and sparse representation”, J. Vis. Commun. Imag. R. 36, p 28-39, 2016.

A. Belle, S. Ansari, M. Spadafore, V. Convertino, K. R. Ward, H. Derksen and K. Najarian, “A signal processing approach for detection of hemodynamic instability before decompensation”, PLOS one 11 (2):e014544, 2016.

Y. Ma, A. Y. Yang, H. Derksen and R. Fossum, “Estimation of subspace arrangements with applications in modeling and segmenting mixed data”, SIAM Review 50 (3), p. 413-458, 2008.

Y. Ma, H. Derksen, W. Hong and J. Wright, “Segmentation of multivariate mixed data via lossy coding and compression”, IEEE Trans. On Pattern Analysis and Machine Intelligence (PAMI) 29 (9), p. 1546-1562, 2007.

Rao, H. Derksen, R. Fossum, Y. Ma, A. Wagner and A. Yang, “The algebra and statistics of generalized principal component analysis”, In SPIE conference on Visual Communications and Image Processing (VCIP), 2007

J. Wright, W. Hong, Y. Ma and H. Derksen, “Segmentation of multivariate mixed data via lossy coding and compression”, In SPIE conference on Visual Communications and Image Processing (VCIP), 2007.