Pekka Pankka

Professor

Contact information

Room: D325
Address: Department of Mathemetics and Statisfics, P.O. Box 68 (Pietari Kalmin katu 5), FI-00014 University of Helsinki, Finland
Email: pekka.pankka 'at' helsinki.fi

Teaching

Spring 2025: Introduction to algebraic topology
Fall 2024: Topology II
Spring 2024: De Rham theory
Fall 2023: Topology II
Spring 2023: De Rham theory
Fall 2022 (Period II) Lineaarialgebra ja matrisiilaskenta I
Fall 2022 (Period I): Raja-arvot
Fall 2021 (Period II): Lineaarialgebra ja matriisilaskenta I [Lecture notes for Lineaarialgebra ja metriisilaskenta I-III]
Fall 2021 (Period I): Raja-arvot
Spring 2021 (Period IV): Lineaarialgebra ja matriisilaskenta III
Spring 2021 (Period III): Lineaarialgebra ja matriisilaskenta II
Fall 2020 (Period II): Lineaarialgebra ja matriisilaskenta I
Spring 2020 (Period IV): Lineaarialgebra ja matriisilaskenta III
Spring 2020 (Period III): Integraalilaskenta
Spring 2019: Topologia Ia & Ib
Spring 2018: Topologia Ia & Ib

Fall 2016: Topologia Ia and Topologia Ib

Fall 2015 (Jyväskylä): Degree theory and Branched covers [Lecture notes from 2017]
Fall 2014 (Jyväskylä): Perusryhmä ja peiteavaruus
Fall 2013 (Jyväskylä): Introduction to de Rham cohomology

Preprints

Liouville's theorem in calibrated geometries (with Toni Ikonen) [arXiv:2410.02722]
Deep Invertible Approximation of Topologically Rich Maps between Manifolds (with Michael Puthawala, Matti Lassas, Ivan Dokmanic, and Maarten de Hoop) [arXiv:2210.00577]
Ahlfors reflection theorem for p-morphisms (with Pekka Koskela and Yi Zhang). [arXiv:1912.09200]
Vertical quasi-isometries and branched quasisymmetries (with Jeff Lindquist). [arXiv:1911.12680]
Deformation and quasiregular extension of cubical Alexander maps (with Jang-Mei Wu). [arXiv:1904.09095] [slides]

Publications

De Rham algebras of closed quasiregularly elliptic manifolds are Euclidean (with Susanna Heikkilä) Ann. Math. 201(2), 2025. [arXiv:2302.11440]
Harmonic extensions of quasiregular maps (with Juan Souto). Jour. Diff. Geom. (to appear) [arXiv:1711.08287]
TILT: topological interface recovery in limited-angle tomography (with Elli Karvonen, Matti Lassas, and Samuli Siltanen) SIAM J. Imaging. Sci. 17(3), 2024.
Bubbling of quasiregular maps (with Juan Souto). Math. Ann. 385(3-4), 2023. [arXiv:1904.00885]
Quasiregular Curves of Small Distortion in Product Manifolds (with Susanna Heikkilä and Eden Prywes ) J. Geom. Anal. 33(1), 2023. [arXiv:2106.11871]
Invisibility cloaking and transformation optics for three dimensional manifolds and applications in cosmology (with Tracey Balehowsky, Matti Lassas, and Ville Sirviö) SIAM J. Math. Anal. 54(3), 2022. [arXiv:2011.09547]
Quasiregular curves: Hölder continuity and higher integrability (with Jani Onninen). Complex Anal. Synerg. 7(3), 2021 [arXiv:2006.09340]
A Neohookean model of plates (with Tadeusz Iwaniec, Jani Onninen, and Teresa Radice). SIAM J. Math. Anal. 53(1), 2021 [arXiv:2004.03381]
Bing meets Sobolev (with Jani Onninen). Rev. Mat. Iberoameracana 37(5), 2021 [arXiv:1908.09193]
Entropy in uniformly quasiregular dynamics (with Ilmari Kangasniemi, Yûsuke Okuyama, and Tuomas Sahlsten). Ergodic Theory Dynam. Systems 41(8), 2021 [arXiv:1903.10183]
Metric currents and polylipschitz forms (with Elefterios Soultanis). Calc. Var. Partial Differential Equations 59(2), 2020. [arXiv:1902.06106]
Quasiregular curves. Ann. Acad. Sci. Fenn. 45(2), 2020. [arXiv:1909.08221] [slides]
Stoilow's theorem revisited (with Rami Luisto). Expos. Math. 38(3), 2020 [arXiv:1701.05726]
Pull-back of metric currents and homological boundedness of BLD-elliptic spaces (with Elefterios Soultanis). Anal. Geom. Metr. Spaces 7(1), 2019 [arXiv:1809.03009]
Uniform cohomological expansion of uniformly quasiregular mappings (with Ilmari Kangasniemi). Proc. London Math. Soc. 118(3), 2019. [arXiv:1708.01451]
Free vs. Locally Free Kleinian Groups (with Juan Souto). J. Reine Angew. Math. 746, 2019. [arXiv:1506.00156]
Topologically nontrivial counterexamples to Sard's theorem (with Paweł Goldstein and Piotr Hajłasz ). IMRN, rny179, 2018. [arXiv:1804.07658]
Local monodromy of branched covers and dimension of the branch set (with Martina Aaltonen). Ann. Acad. Sci. Fenn. 42, 2017. [arXiv:1509.06617]
Quasiconformal non-parametrizability of almost smooth spheres (with Vyron Vellis). Selecta Math. 23(2), 2017. [arXiv:1505.05293]
Rigidity of extremal quasiregularly elliptic manifolds (with Rami Luisto). Groups Geom. Dyn. 10(2), 2016. [arXiv:1307.7940]
Sharpness of Rickman's Picard theorem in all dimensions (with David Drasin). Acta Math. 214(2), 2015. [arXiv:1304.6998] [slides]
Rescaling principle for isolated essential singularities of quasiregular mappings (with Yûsuke Okuyama). Proc. Amer. Math. Soc. 143, 2015. [arXiv:1211.2977]
Quasiregular ellipticity of open and generalized manifolds (with Kai Rajala and Jang-Mei Wu). Comput. Methods Funct. Theory 14, 2-3 (Gehring Memorial Volume), 2014. [arXiv:1310.8595]
Geometry and quasisymmetric parametrization of Semmes spaces (with Jang-Mei Wu). Rev. Mat. Iberoameracana 30(3), 2014. [arXiv:1111.2197]
Equilibrium measures for uniformly quasiregular dynamics (with Yûsuke Okuyama). J. London Math. Soc. 89(2), 2014. [arXiv:1204.6503]
Distributional limits of Riemannian manifolds and graphs with sublinear genus growth (with Hossein Namazi and Juan Souto). Geom. Funct. Anal. 24(1), 2014. [arXiv:1208.2130]
Closed BLD-elliptic manifolds have virtually Abelian fundamental groups (with Enrico Le Donne). New York J. Math. 20, 2014. [arXiv:1312.1308]
Accumulation of periodic points for local uniformly quasiregular mappings (with Yûsuke Okuyama). In RIMS Kôkyûroku Bessatsu B43, 2013. [arXiv:1306.3298]
Slow mappings of finite distortion (with Jani Onninen). Math. Ann. 354 (2), 2012. PDF
Quasiregularly elliptic link complements (with Kai Rajala). Geom. Dedicata 154 (1), 2011. PDF
Quasiconformal extension fields (with Kai Rajala). Calc. Var. Partial Differential Equations 42(1-2), 2011. [arXiv:1006.2259] PDF
Mappings of bounded mean distortion and cohomology. Geom. Funct. Anal. 20(1), 2010. PDF
Quasiconformal frames (with Juha Heinonen and Kai Rajala). Arch. Rat. Mech. Anal. 196(3), 2010. PDF
Sharp exponential integrability for traces of monotone Sobolev functions (with Pietro Poggi-Corradini and Kai Rajala). Nagoya Math. Jour. 192, 2009. [arXiv:math.AP/072332]
Slow quasiregular mappings and universal coverings. Duke Math. J. 141(2), 2008.
p-Laplace operator, quasiregular mappings, and Picard-type theorems (with Ilkka Holopainen). In Quasiconformal Mappings and their Applications, 2007, pp. 117-150. PS PDF
Quasiregular mappings from a punctured ball into compact manifolds. Conform. Geom. Dyn. 10, 2006.
A big Picard theorem for quasiregular mappings into manifolds with many ends (with Ilkka Holopainen). Proc. Amer. Math. Soc. 133, 2005.
Mappings of finite distortion: Global homeomorphism theorem (with Ilkka Holopainen). Ann. Acad. Sci. Fenn. Ser. A I Math. 29, 2004.
Mappings of finite distortion and weighted parabolicity. In Future trends in geometric function theory (D. Herron, eds.), Rep. Univ. Jyväskylä Dept. Math. Stat. 92, 2003. PS PDF

Other

Global behavior of quasiregular mappings and mappings of finite distortion under parabolic assumptions on spaces. Dissertation, University of Helsinki, 2005. PDF
Six hours on quasiregular mappings. Lecture notes, April 2014. PDF
Erään esimerkin tarina. Arkhimedes (in Finnish, to appear). PDF