RESEARCH ROLAND VAN DER VEEN
CONFERENCES:
- Rencontres GDR Tresses:
Topologie géométrique et quantique Dijon, September 10-17-2021
- Modular forms and quantum knot invariants, Banff, March 10-17
- Workshop on Jones polynomials using solvable Lie algebras Toulouse, April 23-27
- Geometry, Quantum Topology and Asymptotics 2018, school: Geneva July 2-6, conference: Aarhus July 9-13
- 60th Birthday conference Jun and Hitoshi Murakami, Tokyo University, August 22-25
- Classical and Quantum 3-Manifold Topology, Monash University, Melbourne, December 17-21
- "Quantum Topology and hyperbolic geometry, Da Nang, Vietnam, May 27-31 2019
- Expansions, Lie Algebras and Invariants, CRM Montreal, July 1-31 2019
My research focuses on knot theory and its interactions with low-dimensional topology, representation theory, geometry and physics.
PREPRINTS:
- with D. Bar-Natan, Perturbed Gaussian generating functions for universal knot invariants, Arxiv.
- with D. Bar-Natan, Z. Dancso, Over then Under tangles, Arxiv.
- with D. Bar-Natan, An Unexpected Cyclic Symmetry of Iun, Arxiv.
- with J. Murakami, Quantized SL(2) representations of knot groups, arxiv 1812.09539
PUBLICATIONS:
- with A. Mashaghi, Polynomial invariant of molecular circuit topology , JKTR Special issue, arxiv 2006.01303
- with C.R.S. Lee, Cancellations in the degree of the colored Jones polynomial , JKTR Special issue, arxiv 2006.01303
- with S. Garoufalidis, The FKB invariant is the 3d index
- with C.R.S. Lee, Colored Jones polynomials without tails, arxiv 1806.04565
- with S. Garoufalidis, C.R.S. Lee, The Slope Conjecture for Montesinos knots arxiv 1807.00957
- with D. Bar-Natan, A polynomial time knot polynomial, PAMS.
- with A. de Klerk, J. Dalhuisen, D. Bouwmeester, Knotted optical vortices in exact solutions to Maxwell's equations, Phys. Rev. A 95 (2017), 053820.
- with C.R.S. Lee, Slopes for pretzel knots, New York J. Mathematics 22 (2016), p. 1339–1364.
- with S. Garoufalidis, Quadratic integer programming and the slope conjecture, New York J. Mathematics, 22 (2016) 907-932.
- A slope conjecture for links, J. Knot Theory Ramifications, 24, 1550077 (2015).
- with F. Costantino, F. Gueritaud, On the volume conjecture for polyhedra, Geometriae Dedicata (2015), Volume 179, Issue 1, 385–409.
- with T. Dimofte, D. Gaiotto, RG Domain Walls and Hybrid Triangulations, Advances in Theoretical Physics, 19 (2015) 135–274.
- with S. Garoufalidis, A generating series for Murakami-Ohtsuki-Yamada graph evaluations, Acta Mathematica Vietnamica, 39 (2014) 529-539.
- with S. Garoufalidis and D. Zagier, Asymptotics of classical spin networks, Geometry & Topology, 17, (2013) 1-37.
- with S. Garoufalidis, Asymptotics of quantum spin networks at a fixed root of unity, Mathematische Annalen (2011), 1-26.
- The volume conjecture for augmented knotted trivalent graphs, Algebraic and Geometric Topology, 9, 2, (2009), 691-722.
- Proof of the volume conjecture for Whitehead chains, Acta. Math. Vietnammica, 3, 33 (2008), 47-60.
PROCEEDINGS:
- One step beyond the Alexander polynomial, Oberwolfach Low-Dimensional Topology and Number Theory, (2017).
- Lecture notes on quantum knot invariants, MATRIX Book 2016, proceedings Workshop Interactions between topological recursion, modularity, quantum invariants and low-dimensional topology, MATRIX, Melbourne, Australia.
- A new MOY state sum for the colored HOMFLY polynomial, Oberwolfach Reports: Low-Dimensional Topology and Number Theory, 2014.
- q-Difference Equations for the Jones polynomial of planar graphs, Proceedings of Geometry and Analysis of Discrete Groups and Hyperbolic Spaces, Kyoto, 2011.
- Asymptotics of spin networks, Proceedings Intelligence of Low-dimensional topology, Kyoto, 2010.
- A cabling formula for the colored Jones polynomial, Oberwolfach Low-Dimensional Topology and Number Theory, (2010), p. 2101–2163.
PhD thesis, Asymptotics of quantum spin networks 2010, advisors Eric Opdam, Stavros Garoufalidis.
Interview about my thesis work, Nieuw Archief voor Wiskunde (Dutch)
Presentation and dance performance.
TALKS:
- Quick quantum invariants of rotational tangles, Columbia Topology seminar
- Algebra quantization of the SL(2) character variety, Indiana University seminar.
- Tangle and Tensors, LSU Topology seminar.
- Gaussians and Tangles: Construction of fast, strong and natural knot invariants, Monash University, Melbourne Dec 18.
- Polynomial time knot polynomial, PPICTA Busan South-Korea 2017
$\hat{f}(\chi) = \sum_{g\in G}f(g)\bar{\chi}(g)$
$\mathbb{C}[G] = \bigoplus_\rho \rho\ \mathrm{dim}(\rho)$
$\det X_G = \prod_{j=1}^r P_j(x)^{\mathrm{deg} P_j}$
$V_i\otimes V_j = \bigoplus_{k = |i-j|}^{i+j}V_k$