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Personal profile

Quote

In systems with a great deal of symmetry, dealing with a million variables can be as easy as dealing with ten.

Research profile

Rob Eggermont is an assistant professor with the research group Discrete Mathematics at the TU/e department of Mathematics and Computer Science. He is a member of the group for Discrete Algebra and Geometry, which plays a leading role in algebraic graph theory, finite and incidence geometry, and discrete Lie theory. His research focuses on finiteness properties in settings of variable or infinite dimension with symmetry, as well as the general theory and structure of these settings, as well as algorithms and their practical applications.

No matter the number of coefficients in a matrix, one can state whether or not the matrix has rank at most one. In the same way, in the setting of algebraic geometry many varieties can be described independent of the number of variables. It turns out that many of these varieties can be described by finitely many equations up to symmetry, again independent of the number of variables. If said equations can be found, this allows for algorithms that test membership of such a variety in polynomial time. This has applications in many fields, such as phylogenetics, chemistry, and algebraic statistics.

Academic background

Rob Eggermont received his MSc in Mathematics from Leiden University (The Netherlands) in 2011, with the distinction cum laude. He did his PhD at Eindhoven University of Technology (TU/e, the Netherlands) where he graduated cum laude in August 2015. After being a postdoctoral researcher at the University of Michigan until July 2017, he returned to TU/e to become an assistant professor (tenure track) in the research group Discrete Mathematics at the department of Mathematics and Computer Science.

Rob Eggermont has published in a wide selection leading journals, such as Algebra Number Theory and Linear Algebra Appl. He has given talks at multiple editions of the DIAMANT symposium, Intercity Number Theory Seminar and at the Summer School 'An Interdisciplinary Approach to Tensor Decomposition'. He has also participated in a wide range of schools and workshops, including AIM workshop on 'Representation stability' (San Jose, 2016), BIRS workshop on 'Free Resolutions, Representations, and Asymptotic Algebra' (Banff, 2016), Summer School on 'An Interdisciplinary Approach to Tensor Decomposition' (Trento, 2014) and CIME-CIRM Course on Combinatorial Algebraic Geometry (Levico Terme, 2013). Rob was awarded the Jong Talent Aanmoedigingsprijs, 2007, an award for the best first year student in mathematics in Leiden.

External positions

University of Michigan

Fingerprint Dive into the research topics where Rob H. Eggermont is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

Finiteness Mathematics
Symmetry Mathematics
Infinite Matrices Mathematics
Toric Ideal Mathematics
Equivariant Mathematics
Noetherian Mathematics
Toric Varieties Mathematics
Grassmannian Mathematics

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Research Output 2012 2018

  • 20 Citations
  • 7 Article
  • 6 Report
  • 1 Conference contribution
  • 1 Phd Thesis 1 (Research TU/e / Graduation TU/e)
2 Citations (Scopus)

Plücker varieties and higher secants of Sato's Grassmannian

Draisma, J. & Eggermont, R. H., 4 Jan 2018, In : Journal für die reine und angewandte Mathematik (Crelle's Journal). 737, p. 189-215 27 p.

Research output: Contribution to journalArticleAcademicpeer-review

Open Access
File
Grassmannian
Chord or secant line
Polynomials
Vector spaces
Natural number

Polynomials and tensors of bounded strength

Bik, A., Draisma, J. & Eggermont, R. H., 2 Aug 2018, (Accepted/In press) In : Communications in Contemporary Mathematics.

Research output: Contribution to journalArticleAcademicpeer-review

Tensors
Tensor
Polynomials
Polynomial
Tensor Decomposition
3 Citations (Scopus)

Topological noetherianity for cubic polynomials

Derksen, H., Eggermont, R. H. & Snowden, A., 1 Jan 2017, In : Algebra & Number Theory. 11, 9, p. 2197-2212 16 p.

Research output: Contribution to journalArticleAcademicpeer-review

Commutative Algebra
Polynomial
Veins
Noetherian
Algebraically closed

Algebraic boundary of matrices of nonnegative rank at most three

Eggermont, R. H., Horobeţ, E. & Kubjas, K., 1 Nov 2016, In : Linear Algebra and Its Applications. 508, p. 62-80 19 p.

Research output: Contribution to journalArticleAcademicpeer-review

Generating Set
Non-negative
Lexicographic Order
Nonconvex Optimization
Irreducible Components
6 Citations (Scopus)

Finiteness properties of congruence classes of infinite-by-infinite matrices

Eggermont, R. H., 2015, In : Linear Algebra and Its Applications. 484, p. 290-303

Research output: Contribution to journalArticleAcademicpeer-review

Infinite Matrices
General Linear Group
Affine Space
Finiteness
Congruence

Prizes

Stability and structure in infinite-dimensional spaces

Rob Eggermont (Recipient), 2018

Recognition: NWOVeniScientific

Infinite-dimensional Spaces
Data Structures

Courses

Linear algebra 1

1/09/12 → …

Course

Set theory and algebra

1/09/12 → …

Course