Armin Schikorra

Dr. rer. nat. habil.

University of Pittsburgh

I work on partial differential equations which are often motivated from the geometric calculus of variations, one example being harmonic maps between manifolds and various generalizations thereof. In particular I am interested in regularity theory of such local or nonlocal equations. The techniques are usually combinations of geometric considerations and harmonic analysis, e.g. commutator estimates and compensation effects, which also have applications in quantitative estimates in Topology.

Currently, I am an Assistant Professor at the University of Pittsburgh.

Current Seminars

Positions held


2017-	Assistant Professor, University of Pittsburgh
2016-2017	DFG Heisenberg Fellow, University of Freiburg
2014-2016	Postdoc, Group of Enno Lenzmann, University of Basel
2011-2014	Postdoc, Group of Jürgen Jost, Max-Planck Institute MIS Leipzig
2011	Postdoc, FIM ETH Zürich

Interests

Geometric Analysis
Harmonic Analysis
Nonlinear Partial Differential Equations

Education

Habilitation in Mathematics, 2016

University of Freiburg
PhD in Mathematics, 2010

RWTH Aachen
Diplom in Mathematics, 2007

RWTH Aachen

Selected Publications

On O'hara knot energies I: Regularity for critical knots

May, 2019

Simon Blatt, Philipp Reiter, Armin Schikorra

Journal Differential Geometry (accepted)

Details arXiv Journal

An estimate of the Hopf degree of fractional Sobolev mappings

April, 2019

Armin Schikorra, Jean Van Schaftingen

Proc.AMS 148 (2020), 2877–2891

Details arXiv Journal

Boundary equations and regularity theory for geometric variational systems with Neumann data

June, 2017

Armin Schikorra

Arch. Rat. Mech. Anal 229(2), pp. 709-788, 2018

Details arXiv Journal

Fractional div-curl quantities and applications to nonlocal geometric equations

May, 2017

Katarzyna Mazowiecka, Armin Schikorra

J. Funct. Anal. 275 (2018), no. 1, 1–44.

Details arXiv Journal

On energy-critical half-wave maps into S^2

March, 2017

Enno Lenzmann, Armin Schikorra

Invent. Math. 213 (2018), no. 1, 1–82

Details arXiv Journal

Sharp commutator estimates via harmonic extensions

December, 2016

Enno Lenzmann, Armin Schikorra

Nonlinear Analysis, 193, April 2020

Details PDF arXiv Journal

Nonlinear commutators for the fractional p-Laplacian and applications

June, 2015

Armin Schikorra

Math. Ann. 366(1), 695–720, (2016)

Details arXiv Journal

Integro-differential harmonic maps into spheres

January, 2014

Armin Schikorra

Comm.PDE 40(3), 506-539 (2015)

Details PDF

Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups

January, 2013

Piotr Hajłasz, Jeremy T. Tyson, Armin Schikorra

Geom. Funct. Anal. 24 (2014), pp.245-268

Details arXiv Journal

epsilon-regularity for systems involving non-local, antisymmetric operators

January, 2012

Armin Schikorra

Calc. Var. P.D.E. 54(4),3531-3570, (2015)

Details PDF

Harmonic analysis meets critical knots (Stationary points of the Moebius energy are smooth)

November, 2011

Simon Blatt, Philipp Reiter, Armin Schikorra

Trans. Amer. Math. Soc. 368 (2016), 6391-6438

Details PDF arXiv Journal

Regularity of n/2 harmonic maps into spheres

September, 2010

Armin Schikorra

Journal of Differential Equations 252 (2012) 1862–1911

Details PDF

A Remark on Gauge Transformations and the Moving Frame Method

September, 2008

Armin Schikorra

Ann.Institute H.Poincare ( C ), 27 (2010), pp. 503-515

Details PDF Journal

Recent Publications

More Publications

A fractional version of Riviere's GL(N)-gauge

January, 2021

Francesca Da Lio, Katarzyna Mazowiecka, Armin Schikorra, Lifeng Wang

preprint

Details arXiv

Non-blowup at critical exponent for a semilinear nonlocal diffusion equation

December, 2020

Sujin Khomrutai, Auttawitch Manui, Armin Schikorra

Preprint

Details

Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note

November, 2020

Armin Schikorra, James M. Scott

preprint

Details arXiv

On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations

July, 2020

Sasikarn Yeepo, Wicharn Lewkeeratiyutkul, Sujin Khomrutai, Armin Schikorra

Preprint

Details arXiv

Minimal $W^{s,n/s}$-harmonic maps in homotopy classes

June, 2020

Katarzyna Mazowiecka, Armin Schikorra

preprint

Details arXiv

On a Fractional Version of a Murat Compactness Result and Applications

April, 2020

Harbir Antil, Carlos N. Rautenberg, Armin Schikorra

Preprint

Details arXiv

Calderon-Zygmund type estimates for nonlocal PDE with Hoelder continuous kernel

February, 2020

Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo

Preprint

Details arXiv

Partial Regularity for fractional harmonic maps into spheres

September, 2019

Vincent Millot, Marc Pegon, Armin Schikorra

Preprint

Details arXiv

On symmetry of traveling solitary waves for dispersion generalized NLS

August, 2019

Lars Bugiera, Enno Lenzmann, Armin Schikorra, Jérémy Sok

Nonlinearity 33 (2020), no. 6, 2797–2819

Details arXiv Journal

W(s,n/s)-maps with positive distributional Jacobians

May, 2019

Siran Li, Armin Schikorra

Pot.A. (accepted)

Details PDF arXiv Journal

Teaching

Advanced Calculus I and II (Math 1530/1540)

Math 1530: Advanced Calculus I and II, ²⁰²⁰⁄₂₁.

Introduction to Analysis (Math420)

Math 420: Introduction to Analysis, Spring 2020.

Partial Differential Equations 2

Partial Differential Equations 2, Fall 2019.

Partial Differential Equations 1

Partial Differential Equations 1, Spring 2019.

Calculus of Variations

Calculus of Variations, Spring 2018.

Calculus 2

Calculus 2, Fall 2017.

Nash embedding theorem

Seminar on Nash Embedding theorem, SS 2017, University of Freiburg.

Partielle Differentialgleichungen II

Partielle Differentialgleichungen II, WS 2016/ 2017, University of Freiburg.

Reelle Anlaysis

Reelle Anlaysis, HS 2015, University of Basel.

Funktionalanalysis

Funktionalanalysis, FS 2015, University of Basel.

Virtual Reality in Mathematics

Heisenberg group in Virtual Reality

Heisenberg group

Menger Sponge in VR

MengerSponge flythrough in Virtual Reality

Curvature flows for knots

Visualization of curvature flow

Funding

Currently I receive research funding as the P.I. from the following sources - Simons foundation grant no 579261 (2018-2023)

Previously I received research funding as the P.I. from the following sources - German Research Foundation (DFG), Grant SCHI-1257-3-1 (2016-2018) - Daimler-Benz foundation (2017-2018)

Moreover I was P.I. in the following education-related projects (together with my co-PIs: Ryan Alvarado, Dana Miller-Cotto, Tom Everest)

Provost’s Personalized Education Grant, Seed funding, (2018-2019)
dB-Serc, Course Tansformation Award, (2018-2019)

grants and fellowships


2018	Provost’s Personalized Education Seed Funding (USD 26306)
2018	dB-Serc Course Tansformation Award (USD 9999)
2017	Daimler und Benz Stiftung Grant (40000 Euro)
2016	VolkswagenStiftung-Grant for Summerschool 2017 “Modern Knot Theory” (82200 Euro)
2015	DFG-Grant “Nichtlokale Differentialgleichungen in Analysis und Geometrie” (36 month, 186200 Euro)
	DFG-Heisenberg Fellowship
	SNF-Ambizione Fellowship, 3 years, (402813 CHF, declined in favor of Heisenberg)
2014	SNF (19800 CHF): International Exploratory Workshop: Workshop on Knots in Theory and the Sciences
2012	DAAD PostDoc Program (D/12/40670) to University of Pittsburgh (Sep. 2012 - Aug. 2013)
2011	DAAD PostDoc Program (D/10/50763) to ETH Zürich (Mar 2011 - Aug 2011)
2008	Studienstiftung des Deutschen Volkes (PhD program, Jul 2008 - Sep 2010)
	Stipendium nach Richtlinien zur Förderung des wissenschaftlichen Nachwuchses an der RWTH Aachen (Apr - May 2008)
2007	Graduiertenkolleg Hierarchie und Symmetrie in mathematischen Modellen (Dec 2007 - Mar 2008)
2003	Studienstiftung des Deutschen Volkes (student program, Apr. 2003 - Sep. 2007)

Research Group

Katarzyna Mazowiecka via DFG-Grant SCHI-1257-3-1 (2016-2018)
James Scott (MRC Postdoc) (2020-2022)

Conferences

future conferences (organizer)


2021	Minimal surfaces and geometric flows: interaction between the local and the nonlocal worlds (Matrix, Australia)

links to past conferences


2019	Local and Nonlocal Trends in Analysis and Geometry (U Pitt)
2019	Bagel19 (Summerschool and Workshop)
2018	Geometric PDEs in Freiburg 2018 (U Freiburg)
2017	Summer School on modern knot theory (U Freiburg)
2016	Analysis and Numerics In Curvature Energies-Meeting (U Freiburg)
2015	Geometric Energies with Links to Applications, Topology and Open problems (U Basel)
2014	Curvature - Applications - Knots - Energies (MPI MIS Leipzig 2014)

Curriculum

a short curriculum:


2017	Assistant Professor, University of Pittsburgh
	01. September 2017
2016	Habilitation, Universität Freiburg
	01. July 2016
2016	Heisenberg Fellow, Universität Freiburg
	February 2016 - August 2017
2014	Postdoctoral Lecturer, Universität Basel
	August 2014 - January 2016
2013	Postdoc, Max-Planck Institute for Mathematics Leipzig
	August 2013 - July 2014
2012	Postdoc, University of Pittsburgh
	September 2012 - July 2013
2011	Postdoc, Max-Planck Institute for Mathematics Leipzig. Research group: Geometry, Analysis and Theoretical Physics, VARIOGEO of Prof. J. Jost
	December 2011 - August 2012
2011	Japanese Language Student in Fukuoka, Japan
	October 2011 - November 2011
2011	Postdoc, FIM, ETH Zürich
	financed by ETH Zürich, DAAD
	February 2011 - September 2011
2010	Teaching Assistant at Institut für Mathematik, RWTH Aachen
	October 2010 - February 2011
2010	PhD in Mathematics
	supervisor: Prof. Dr. H. von der Mosel
	22. September 2010
2007	Graduate Student at Institut für Mathematik, RWTH Aachen
	December 2007 - September 2010
2007	Diploma in Mathematics
	supervisor: Prof. Dr. H. von der Mosel
	30th November 2007
2004	Student at RWTH Aachen
	October 2005 - November 2007
2005	Visiting student at Universidad Autononoma de Madrid
	October 2004 - September 2005
2002	Student at RWTH Aachen
	April 2002 - September 2004
2002	Abitur at Westerwaldgymnasium Altenkirchen
	March 2002

Contact

armin@pitt.edu
412-624-8375
Thackeray Hall, Room 410, University of Pittsburgh, PA 15260, USA
email for appointment