CV

Academic degrees

Oct. 2021 Habilitation University of Warsaw - Mathematics.
Achievement: series of articles around the topic “elliptic geometric variational problems”
May 2012 Ph.D. University of Warsaw - Mathematics - advisor: prof. Paweł Strzelecki.
Thesis: “Integral Menger curvature for sets of arbitrary dimension and codimension”
Feb. 2008 M.Sc. University of Warsaw - Mathematics - advisor: dr hab. Andrzej Weber.
Thesis: “CW-structure of a Space of Loops on a Lie Group”
June 2006 M.Sc. University of Warsaw - Computer Science - advisor: prof. Paweł Urzyczyn.
Thesis: “Wajsberg-Ben-Yelles Algorithm for Intuitionistic Propositional Logic”

Employment

Oct. 2016 – present: Adiunkt (assistant professor) at University of Warsaw (Poland)
Oct. 2012 – Sept. 2016: Junior scientist at MPI Albert-Einstein-Institute (Potsdam, Germany)
Oct. 2011 – Sept. 2014: Research and teaching assistant at the University of Warsaw (Poland)
Sept. 2009 – Feb. 2010: Early Stage Researcher at University of Helsinki (Finland) within the EU RTN “CODY”

Awards

2013 Nomination to participate in the first Heidelberg Laureate Forum
2013 “START” stipend awarded by the Foundation for Polish Science
2013 Nomination in the $5^{t h}$ edition of “International Banach Prize” awarded by the Polish Mathematical Society and Ericpol Sp. z o.o.
2012 Distinguished PhD thesis at University of Warsaw.
2006 Honorable mention in the contest for the best M.Sc. thesis in logic and its applications awarded by the Polish Association for Logic and Philosophy of Science.

Grants

Elliptic geometric variational problems

Pointwise regularity theory for sets, measures, and varifolds

Curvature energies for non-smooth subsets of Euclidean spaces

Całkowa krzywizna Mengera dla powierzchni dowolnego kowymiaru

Nieliniowe równania cząstkowe: zagadnienia wariacyjne i geometryczne

Outreach

Author and co-author of two popular articles in the Polish magazine Delta targeted at high-school students; volumes 02/2015 and 10/2008
Popular talk on nonstandard analysis at a workshop XLVI Szkoła matematyki poglądowej (School on Synoptic Mathematics) held in Warsaw targeted at high-school teachers; Jan. 2011
Co-author of an educational portal for high-school students; 2009 – 2012

Publications

Regularity of distance functions from arbitrary closed sets

Kolasiński, Sławomir and Santilli, Mario, "Regularity of the distance function from arbitrary closed sets.", 2023, Math. Ann. , Vol. 386, No. 1-2, p. 735-777

Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets

Sławomir Kolasiński, Antonio De Rosa, and Mario Santilli, Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets, 2020, Arch. Ration. Mech. Anal., p. 1157--1198

Equivalence of the ellipticity conditions for geometric variational problems

Sławomir Kolasiński and Antonio De Rosa, Equivalence of the ellipticity conditions for geometric variational problems, Comm. Pure Appl. Math. no. 11, 2020, p. 2473--2515

Compactness and isotopy finiteness for submanifolds with uniformly bounded geometric curvature energies

Sławomir Kolasiński, Paweł Strzelecki, and Heiko von der Mosel, Compactness and isotopy finiteness for submanifolds with uniformly bounded geometric curvature energies, Comm. Anal. Geom., Vol. 26, No. 6 (2018), pp. 1251-1316

Existence of solutions to a general geometric elliptic variational problem

Sławomir Kolasiński and 方扬钦 (Yangqin Fang), Existence of solutions to a general geometric elliptic variational problem, Calc. Var. PDE, Vol. 57(3), 2018

Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds

Sławomir Kolasiński and Ulrich Menne, Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds, Nonlinear Differ. Equ. Appl. (NoDEA), Vol. 24(2), 2017

Higher order rectifiability of measures via averaged discrete curvatures

Sławomir Kolasiński, Higher order rectifiability of measures via averaged discrete curvatures, Rev. Mat. Iberoamericana, Vol. 33, 861-884, 2017

Estimating discrete curvatures in terms of beta numbers

Sławomir Kolasiński, Estimating discrete curvatures in terms of beta numbers, 2016, arXiv:1605.00939

Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

Sławomir Kolasiński, Geometric Sobolev-like embedding using high-dimensional Menger-like curvature, Trans. Amer. Math. Soc., Vol. 367, 775-811, 2015

Characterizing $W^{2, p}$ submanifolds by $p$ -integrability of global curvatures

Sławomir Kolasiński, Paweł Strzelecki, and Heiko von der Mosel, Characterizing $W^{2,p}$ submanifolds by $p$-integrability of global curvatures, Geom. Funct. Anal., Vol. 23(3), 937–984, 2013

Minimal Hölder regularity implying finiteness of integral Menger curvature

Sławomir Kolasiński and Marta Szumańska, Minimal Hölder regularity implying finiteness of integral Menger curvature, Manuscripta Math., Vol. 141, Issue 1, 125–147, 2013

Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds

Sławomir Kolasiński and Simon Blatt, Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds, Adv. Math., Vol. 230(3), 839–852, 2012

Integral Menger curvature for sets of arbitrary dimension and codimension

Sławomir Kolasiński, Integral Menger curvature for sets of arbitrary dimension and codimension, Ph.D. Thesis

Regularity of weak solutions of $n$ -dimensional H-systems

Sławomir Kolasiński, Regularity of weak solutions of $n$-dimensional H-systems, Differential and Integral Equations, Vol. 23, Num. 11-12, 1073-1090, 2010