Mathematics
PhD in Mathematics, Max Planck Institute / University of Bonn, Germany
PhD in Mathematics, Max Planck Institute / University of Bonn, Germany
Some of the linked documents available below are the original manuscripts that may differ from their published counterparts slightly (especially in layout and page or section numbering).
C*-algebraic drawings of dendroidal sets, Algebr. Geom. Topol., 19 (3), 1171-1206, 2019; DOI: 10.2140/agt.2019.19.1171; arXiv:1501.05799. [PDF]
This is my dream project that presents a conjectural roadmap to a unified perspective on noncommutative geometry. It combines the best of both worlds (algebraic and analytic) leading to synergies.
Model structure on projective systems of C*-algebras and bivariant homology theories (with I. Barnea and M. Joachim), New York J. Math., 23, 383-439, 2017; ISSN: 1076-9803/2017; arXiv:1508.04283. [Published version]
Symmetric monoidal noncommutative spectra, strongly self-absorbing C*-algebras, and bivariant homology, J. Noncommut. Geom., 10 (4), 1269-1301, 2016; DOI: 10.4171/JNCG/260; arXiv:1403.4130. [PDF]
Colocalizations of noncommutative spectra and bootstrap categories, Adv. Math., 285, 72-100, 2015; DOI: 10.1016/j.aim.2015.07.029; arXiv:1412.8370. [PDF]
Noncommutative stable homotopy and stable infinity categories, J. Topol. Anal., 7 (1), 135-165, 2015; DOI: 10.1142/S1793525315500077; arXiv:1211.6576. [PDF]
G-theory of F1-algebras I: the equivariant Nishida problem, J. Homotopy Relat. Struct. 12 (4), 901-930, 2017; DOI: 10.1007/s40062-017-0168-0; arXiv:1110.6001. [PDF] [Published version]
On the Generating Hypothesis in Noncommutative Stable Homotopy, Math. Scand., 116 (2), 301-308, 2015; DOI: 10.7146/math.scand.a-21164; arXiv:1302.2051. [PDF]
Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture, J. Homotopy Relat. Struct., 9 (2), 299-315, 2014; DOI: 10.1007/s40062-013-0027-6; arXiv:1107.2191. [PDF] [Published version]
Algebraic K-theory, K-regularity, and T-duality of O∞-stable C*-algebras, Math. Phys. Anal. Geom., 18 (1), 21 pages, 2015; DOI: 10.1007/s11040-015-9182-9; arXiv:1311.4720. [PDF]
Twisted K-theory, K-homology and bivariant Chern-Connes type character of some infinite dimensional spaces, Kyoto J. Math., 54 (3), 597-640, 2014; DOI: 10.1215/21562261-2693460; arXiv:1104.4835. [PDF]
Higher nonunital Quillen K'-theory, KK-dualities and applications to topological T-dualities, J. Geom. Phys., 61 (5), 875-889, 2011; DOI: 10.1016/j.geomphys.2010.12.011; arXiv:1503.06404. [PDF] [Erratum]
Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups (with V. Mathai), Lett. Math. Phys., 97 (3), 263-277, 2011; DOI: 10.1007/s11005-011-0492-y; arXiv:1012.5893. [PDF] [Erratum]
Noncommutative Geometry in the Framework of Differential Graded Categories, Arithmetic and Geometry Around Quantization, Progr. Math., 279, 253-275, 2010; DOI: 10.1007/978-0-8176-4831-2_9; arXiv:0805.1628.
Noncommutative tori and the Riemann-Hilbert correspondence (with W. D. van Suijlekom), J. Noncommut. Geom., 3 (2), 261-287, 2009; DOI: 10.4171/JNCG/37; arXiv:0705.1076. [PDF] [Download published version]
Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori, An Invitation to Noncommutative Geometry, World Sci. Publ., Hackensack, NJ, 355-382, 2008; DOI: 10.1142/9789812814333_0005; arXiv:math/0610043.
Continuous homotopy invariance of bivariant local cyclic homology for σ-C*-algebras, arXiv:1202.1333. [PDF]
This manuscript was an attempt to extend the theory of local cyclic homology to σ-C*-algebras. The modern approach of our article should supplant the methods in the above manuscript. Some form of Adams representability should be used to construct bivariant local cyclic homology in the general setting of projective systems of separable C*-algebras.
Noncommutative correspondence categories, simplicial sets and pro C*-algebras, arXiv:0906.5400.
This manuscript represents my first attempt to harmonize the two paradigms of noncommutative geometry (algebraic and analytic). Eventually I changed the underlying technology stack to achieve the desired result. This manuscript is superseded by C*-algebraic drawings of dendroidal sets.
Algebraic Aspects of Noncommutative Tori: the Riemann-Hilbert Correspondence, PhD Thesis, Max Planck Institute for Mathematics / University of Bonn, 2007.
On some approaches towards non-commutative algebraic geometry (survey), arXiv:math/0501166. [PDF]
This manuscript presents a snapshot of the status quo in 2004. For the current state of affairs interested readers are advised to do their own research.
Lecture notes: Clifford Johnson on Perturbative and Nonperturbative String Theory (with S. Chen and P. McLachlan). [PDF]
Algebraic and rational points on cubic surfaces (after D. F. Coray). [PDF]
This manuscript is my undergraduate thesis that was written in 2003 as a visiting student at École Normale Supérieure, Paris.
YouTube Video of my lecture on Bivariant homology theories for noncommutative spaces at Hausdorff Center for Mathematics, Bonn
Dendroidal sets and noncommutative spaces: a bridge between two paradigms of noncommutative geometry
A planned bachelor seminar on Bott Periodicity.
Winter semester 2015/16, University of Regensburg, Germany - Morse Theory (with Prof. Dr. Bernd Ammann)
Winter semester 2015/16, University of Regensburg, Germany - Calabi Conjecture and Special Holonomy (with Prof. Dr. Bernd Ammann)
Summer semester 2015, University of Regensburg, Germany - CDH-Descent for Homotopy Algebraic K-Theory Higher Invariants Oberseminar Talk
Summer semester 2014, University of Münster, Germany - Topology in Euclidean Spaces (with Dr. Filipp Levikov und Prof. Dr. Michael Weiss)
Winter semester 2013/14, University of Münster, Germany - Topology 1 (Instructor - Prof. Dr. Michael Weiss)
Summer semester 2013, University of Münster, Germany - Infinite Dimensional Lie Theory (with apl. Prof. Dr. Wend Werner)
Winter semester 2012/13, University of Münster, Germany - Mathematics for Physicists 1 (Instructor - apl. Prof. Dr. Wend Werner)
Spring 2010, Johns Hopkins University, USA - Advanced Algebra II Math 402
Fall 2009, Johns Hopkins University, USA - Calculus I (Eng) Math 108 (2 courses)
Spring 2009, Johns Hopkins University, USA - Calculus II (Bio) Math 107
Spring 2008, University of Toronto, Canada - Calculus I MAT135Y (Part 2)
Fall 2007, University of Toronto, Canada - Calculus I MAT135Y (Part 1)
Spring School on Algebraic K-theory of Topological Algebras (with Prof. Dr. Ulrich Bunke and Dr. Alexander Engel), March 2015 in Regensburg, Germany
Methods of Noncommutative Geometry in Analysis and Topology (with Dr. Robin Deeley, Dr. Magnus Goffeng, and Dr. Bram Mesland), October 2014 in Hannover, Germany
SFB Miniworkshop on C*-Algebras, C*-Bundles, and Group Actions (with Dr. Hannes Thiel), November 2013 in Münster, Germany
IGA / AMSI Workshop on Dualities in Field Theories and the Role of K-Theory (with Prof. Peter Bouwknegt, Dr. Pedram Hekmati, and Prof. Mathai Varghese), March 2012 in Adelaide, Australia
IGA / AMSI Workshop on The Mathematical Implications of Gauge-String Dualities (with Prof. Peter Bouwknegt, Dr. Pedram Hekmati, and Prof. Mathai Varghese), March 2012 in Adelaide, Australia
IGA / AMSI Workshop on Group-valued moment maps with applications to mathematics and physics (with Dr. Pedram Hekmati, Prof. Mathai Varghese, and Prof. Craig Westerland), September 2011 in Adelaide, Australia
IGA / AMSI Workshop on Dirac Operators in Geometry, Topology, Representation Theory, and Physics (with Prof. Peter Bouwknegt, Dr. Pedram Hekmati, and Prof. Mathai Varghese), October 2010 in Adelaide, Australia
Noncommutative Geometry, Arithmetic and Related Topics (as an internal coordinator), March 2009 in Baltimore, USA