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Dr. M. (Martijn) Kool

Universitair hoofddocent 
Bètawetenschappen
Wiskunde
Mathematisch Instituut
Fundamental Mathematics
Fundamental Mathematics
Hans Freudenthalgebouw
Budapestlaan 6
Kamer -
3584 CD Utrecht

Dr. M. (Martijn) Kool

Universitair hoofddocent
Fundamental Mathematics
030 253 1218
m.kool1@uu.nl
Profiel CV Publicaties Prijzen Onderzoek Onderwijs Contact
Profiel CV Publicaties Prijzen Onderzoek Onderwijs Contact

Publicaties

2022

Wetenschappelijke publicaties

Cao, Y., Kool, M., & Monavari, S. (2022). K-theoretic DT/PT correspondence for toric Calabi–Yau 4-folds. Communications in Mathematical Physics, 396, 225-264. https://doi.org/10.1007/s00220-022-04472-0
Göttsche, L., & Kool, M. (2022). Virtual Segre and Verlinde numbers of projective surfaces. Journal of the London Mathematical Society, 106(3), 2562-2608. https://doi.org/10.1112/jlms.12641
Jiang, Y., & Kool, M. (2022). Twisted sheaves and SU(r)/Z_r Vafa-Witten theory. Mathematische Annalen, 382(1-2), 719-743. https://doi.org/10.1007/s00208-021-02303-6
Cao, Y., Kool, M., & Monavari, S. (2022). Stable pair invariants of local Calabi-Yau 4-folds. International Mathematics Research Notices, 2022(6), 4753-4798. https://doi.org/10.1093/imrn/rnab061

2021

Wetenschappelijke publicaties

Göttsche, L., Kool, M., & Williams, R. (2021). Verlinde formulae on complex surfaces: K-theoretic invariants. Forum of Mathematics, Sigma, 9, 1-31. [e5]. https://doi.org/10.1017/fms.2020.50
https://dspace.library.uu.nl/bitstream/handle/1874/410281/1903.03869.pdf?sequence=1

2020

Wetenschappelijke publicaties

Cao, Y., & Kool, M. (2020). Curve counting and DT/PT correspondence for Calabi-Yau 4-folds. Advances in Mathematics, 375, [107371]. https://doi.org/10.1016/j.aim.2020.107371
https://dspace.library.uu.nl/bitstream/handle/1874/410282/1903.12171.pdf?sequence=2
Göttsche, L., & Kool, M. (2020). Virtual refinements of the Vafa-Witten formula. Communications in Mathematical Physics, 376, 1-49. https://doi.org/10.1007/s00220-020-03748-7

2019

Wetenschappelijke publicaties

Göttsche, L., & Kool, M. (2019). Sheaves on surfaces and virtual invariants. Surveys in Differential Geometry, 24, 67-116. https://doi.org/10.4310/SDG.2019.v24.n1.a3
Göttsche, L., & Kool, M. (2019). Refined SU(3) Vafa-Witten invariants and modularity. Pure and Applied Mathematics Quarterly, 14(3-4), 467-513. https://doi.org/10.4310/PAMQ.2018.v14.n3.a3
Gholampour, A., & Kool, M. (2019). Higher rank sheaves on threefolds and functional equations. Épijournal de Géométrie Algébrique, 3, 1-29. [17]. https://doi.org/10.46298/epiga.2019.volume3.4375
Cao, Y., & Kool, M. (2019). Counting zero-dimensional subschemes in higher dimensions. Journal of Geometry and Physics, 136, 119-137. https://doi.org/10.1016/j.geomphys.2018.11.004
https://dspace.library.uu.nl/bitstream/handle/1874/386659/1805.04746.pdf?sequence=2
Göttsche, L., & Kool, M. (2019). A rank 2 Dijkgraaf-Moore-Verlinde-Verlinde formula. Communications in Number Theory and Physics, 13(1), 165 – 201. https://doi.org/10.4310/CNTP.2019.v13.n1.a6
Bryan, J., & Kool, M. (2019). Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex. Forum of Mathematics, Sigma, 7, [e7]. https://doi.org/10.1017/fms.2019.1

2018

Wetenschappelijke publicaties

Cao, Y., & Kool, M. (2018). Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds. Advances in Mathematics, 338, 601-648. https://doi.org/10.1016/j.aim.2018.09.011
https://dspace.library.uu.nl/bitstream/handle/1874/373040/1712.07347.pdf?sequence=2
Bryan, J., Kool, M., & Young, B. (2018). Trace identities for the topological vertex. Selecta Mathematica, New Series, 24(2), 1527-1548. https://doi.org/10.1007/s00029-017-0302-1
https://dspace.library.uu.nl/bitstream/handle/1874/367844/1603.05271.pdf?sequence=2
Gholampour, A., Kool, M., & Young, B. (2018). Rank 2 sheaves on toric 3-folds: classical and virtual counts. International Mathematics Research Notices, 2018(10), 2981-3069. https://doi.org/10.1093/imrn/rnw302
https://dspace.library.uu.nl/bitstream/handle/1874/367843/1509.03536.pdf?sequence=2

2017

Wetenschappelijke publicaties

Kool, M., & Thomas, R. (2017). Stable pairs with descendents on local surfaces I: the vertical component. Pure and Applied Mathematics Quarterly, 13(4), 581-638. https://doi.org/10.4310/PAMQ.2017.v13.n4.a2
Gholampour, A., Jiang, Y., & Kool, M. (2017). Sheaves on weighted projective planes and modular forms. Advances in Theoretical and Mathematical Physics, 21(6), 1455-1524. https://doi.org/10.4310/ATMP.2017.v21.n6.a2
https://dspace.library.uu.nl/bitstream/handle/1874/367849/1209.3922.pdf?sequence=1
Gholampour, A., & Kool, M. (2017). Rank 2 wall-crossing and the Serre correspondence. Selecta Mathematica, 23(2), 1599-1617. https://doi.org/10.1007/s00029-016-0293-3
https://dspace.library.uu.nl/bitstream/handle/1874/369734/1602.03113.pdf?sequence=2
Gholampour, A., & Kool, M. (2017). Stable reflexive sheaves and localization. Journal of Pure and Applied Algebra, 221(8), 1934–1954. https://doi.org/10.1016/j.jpaa.2016.10.018
https://dspace.library.uu.nl/bitstream/handle/1874/350518/1308.3688.pdf?sequence=2

2016

Wetenschappelijke publicaties

Kool, M. (2016). Stable pair invariants of surfaces and Seiberg-Witten invariants. The Quarterly Journal of Mathematics, 67(3), 365-386. https://doi.org/10.1093/qmath/haw012
https://dspace.library.uu.nl/bitstream/handle/1874/344086/1303.5340.pdf?sequence=2

2015

Wetenschappelijke publicaties

Kool, M. (2015). Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces. Geometriae Dedicata, 241-269. https://doi.org/10.1007/s10711-014-9966-2

2014

Wetenschappelijke publicaties

Kool, M., & Thomas, R. (2014). Reduced classes and curve counting on surfaces II: calculations. Algebraic Geometry, 1(3), 384-399. http://algebraicgeometry.nl/2014-3/2014-3-018.pdf
https://dspace.library.uu.nl/bitstream/handle/1874/407343/1112.3070.pdf?sequence=1
Kool, M., & Thomas, R. (2014). Reduced classes and curve counting on surfaces I: theory. Algebraic Geometry, 1(3), 334-383. https://doi.org/10.14231/AG-2014-017
https://dspace.library.uu.nl/bitstream/handle/1874/407342/1112.3069.pdf?sequence=1

2011

Wetenschappelijke publicaties

Kool, M., Shende, V., & Thomas, R. (2011). A short proof of the Göttsche conjecture. Geometry and Topology, 15(1), 397–406. https://doi.org/10.2140/gt.2011.15.397
Kool, M. (2011). Fixed point loci of moduli spaces of sheaves on toric varieties. Advances in Mathematics, 227(4), 1700-1755. https://doi.org/10.1016/j.aim.2011.04.002
https://dspace.library.uu.nl/bitstream/handle/1874/407340/0810.0418.pdf?sequence=1
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