ROLAND VAN DER VEEN

### RESEARCH ROLAND VAN DER VEEN

My research focuses on knot theory and its interactions with low-dimensional topology, representation theory, geometry and physics.

PREPRINTS:
• with J. Murakami, Quantized SL(2) representations of knot groups, arxiv 1812.09539
• with S. Gauroufalidis, C.R.S. Lee, The Slope Conjecture for Montesinos knots arxiv 1807.00957
• with C.R.S. Lee, Colored Jones polynomials without tails, arxiv 1806.04565
PUBLICATIONS:
• with Bar-Natan, D., A polynomial time knot polynomial, 2018 to appear in Proceedings of the AMS.
• 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:
• 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
$\hat{f}(\chi) = \sum_{g\in G}f(g)\bar{\chi}(g)$
$\mathbb{C}[G] = \bigoplus_\rho \rho\ \mathrm{dim}(\rho)$
$\det X_G = \prod_{j=1}^r P_j(x)^{\mathrm{deg} P_j}$
$V_i\otimes V_j = \bigoplus_{k = |i-j|}^{i+j}V_k$
OUTREACH

Upcoming: Leids Kampioenschap Kamertjeverhuren (Leiden Dots&Boxes Championship)

PUBLICATIONS ON POPULARIZATION OF MATHEMATICS
• with J. van de Craats, the Riemann hypothesis, Mathematical Association of America, 2016. (Winner of the 2018 MAA Beckenbach prize)
• Het vormen van ruimte: van Poincare tot Perelman, Nieuw Archief v. Wiskunde 5/15 1 (2014), p.51-65.
• with A. van den Brandhof, B. Koren. J. van de Craats, De zeven grootste raadsels van de wiskunde, Bert Bakker, 2012.
• with J. van de Craats, de Riemann hypothese, Epsilon, 2011.
TEACHING

• Roland van der Veen, Bernoulli Institute, Mathematics, University of Groningen
• Visiting address: Bernoulliborg 468, Nijenborgh 9 Groningen, Netherlands.
• Mailing address: University of Groningen, Bernoulli Institute, P.O. Box 407, 9700 AK Groningen, The Netherlands.
• email: r.i.van.der.veenATrug.nl