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# Martin Schlichenmaier

### Professor

Research Topics Algebraic Geometry, Complex Analysis, Differential Geometry, Symplectic Geometry and Theoretical and Mathematical Physics, Algebraic Structures
Faculty or Centre Faculté des Sciences, de la Technologie et de la Communication
Research Unit Mathématiques
Maison du Nombre
6, Avenue de la Fonte
L-4364 Esch-sur-Alzette
Campus Office MNO, E06 0625-060
Email
Telephone (+352) 46 66 44 6236
Fax (+352) 46 66 44 6237
Social Media & Blogs
Speaks English, French, German
Research Stays in Denmark, Germany, France, Luxembourg, Austria, Poland, Sweden, USA

The main part of my research topics are concentrated at the interface between Algebraic Geometry, Complex Analysis, Differential Geometry, Symplectic Geometry and Theoretical and Mathematical Physics.  An incomplete link is here

Beside other topics, I am interested in problems of algebraic geometry and algebra related to Computer-Algebra and its applications.

But also other fields of mathematics and its applications are not excluded.

To personal Homepage: http://math.uni.lu/schlichenmaier

Last updated on: Tuesday January 16 2018

# 2017

The Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra
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E-print/Working paper (2017)

An elementary proof of the formal rigidity of the Witt and Virasoro algebra

Scientific Conference (2017, December 19)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2017, November 27)

Introduction to Berezin-Toeplitz quantization

Presentation (2017, July 05)

Canonically defined star products for Kaehler manifolds

Scientific Conference (2017, February 07)

Algebraic Curves

Learning material (2017)

N-point Virasoro algebras are multipoint Krichever-Novikov-type algebras

in Communications in Algebra (2017), 45

Introduction to Berezin-Toeplitz quantization (3 Lectures)

Presentation (2017)

Basic Algebraic Structures - Lecture notes for the MICS

Learning material (2017)

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# 2016

N-point Virasoro algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2016, December 14)

N-point Virasoro algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2016, December 12)

Mathematik als universeller Schluessel komplexer Systeme

Speeches/Talks (2016)

Travaux mathematiques, Geoquant 2015

N-point Virasoro algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2016, July 25)

N-point Virasoro algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2016, July 11)

Canonical ways to quantize Kaehler manifolds

Scientific Conference (2016, June 20)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2016, May 19)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2016, April 30)

Some naturally defined star products for K\"ahler manifolds

Scientific Conference (2016, February 18)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2016, January 05)

Berezin-Toeplitz quantization - a lecture course of 5 lectures

Presentation (2016, January)

Krichever-Novikov type algebras. An introduction

in Misra, Kailish; Nakano, Daniel; Parsall, Brian (Eds.) Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topis (2016)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2016)

N-point Virasoro algebras considered as Krichever-Novikov type algebras

in Schlichenmaier, Martin; kielianowski, Piotr; Bieliavsky, Piere; Odzzijewicz, Anatol; Voronov, Theodore; Ali, S.T. (Eds.) Goemetric Methods in Physics (2016)

Geometric Methods in Physics, Bialowieza 2015
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# 2015

Krichever-Novikov type algebras and Wess-Zumino-Witten models

E-print/Working paper (2015)

N point Virasoro algebras considered as Krichever-Novikov type algebras

E-print/Working paper (2015)

N point Virasoro Algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2015, October 23)

Some naturally defined star products on Kaehler manifolds

Scientific Conference (2015, October 01)

Multi-point Krichever-Novikov type algebras

Scientific Conference (2015, July 16)

N-point Virasoro algebras are multi-point Krichever-Novikov type algebras

Scientific Conference (2015, June 28)

Some naturally defined star products on Kaehler manifolds

Presentation (2015, June 04)

N-point Virasoro algebras are multi-point Krichever--Novikov type algebras

E-print/Working paper (2015)

Lie Superalgebras of Krichever-Novikov type

in KIelanowski, Piotr; Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore (Eds.) Geometric Methods in Physics, Bialowieza XXXIII (2015)

Geometric Methods in Physics, XXXIII workshop Bialowieza, Poland
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# 2014

Lie superalgebras of Krichever-Novikov type

Scientific Conference (2014, December 02)

Lie superalgebras of Krichever-Novikov type

E-print/Working paper (2014)

Krichever-Novikov type algebras. An Introduction

E-print/Working paper (2014)

Lie superalgebras of Krichever-Novikov type

Scientific Conference (2014, June 29)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2014, April 02)

Quasikristalle - 10 zaehlige Symmetrien gibt es nicht - oder doch

Conference given outside the academic context (2014)

Some naturally defined star products for Kaehler manifolds

Scientific Conference (2014, March 10)

Krichever-Novikov type algebras. Theory and Applications

From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond

in Vasil'ev, Alexander (Ed.) Harmonic and Complex Analysis and its Applications (2014)

Multipoint Lax operator algebras. Almost-graded structure and central extensions

in Sbornik: Mathematics (2014), 205(5), 117-160

Daniel Sternheimer
;

in Goemetric Methods in Physics, XXXII workshop (2014)

Geometric Methods in Physics, XXXII Workshop Bialowieza, Poland, Jnue 30 - July 6, 2-13
; ; ; ;

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# 2013

Geometric methods in physics. XXXI workshop, Biaowieza, Poland June 24--30, 2012. Selected papers based on the presentations at the workshop.
; ; ; ; ;

Geometric methods in physics. XXX workshop, Bialowieza, Poland June 26 --July 2, 2011. Selected papers based on the presentations at the workshop.
; ; ; ;

Some naturally defined star products on K\"ahler manifolds

Scientific Conference (2013, October 17)

Some naturally defined star products on K\"ahler manifolds

Scientific Conference (2013, September 10)

Some naturally defined star products on K\"ahler manifolds

Scientific Conference (2013, July 02)

A global operator approach to WZNW models via KN type algebras

Presentation (2013, March 07)

From the Virasoro Algebra to Krichever--Novikov Type Algebras and Beyond

E-print/Working paper (2013)

Lie superalgebras of Krichever-Novikov type and their central extensions

in Analysis and Mathematical Physics (2013), 3(3), 235--261

Symmetries and infinite dimensional Lie algebras

in Bartholmé, C.; Connor, T.; Dominicy, Y.; Kidzinski, L.; Richard, N.; Swan, Yvik (Eds.) Notes de la cinquième BSSM (2013)

Berezin's coherent states, symbols and transform for compact Kähler manifolds.

in Geometric Methods in Physics, XXX Workshop 2011 (2013)

An elementary proof of the formal rigidity of the WItt and Virasoro Algebra

in Kielanowski, Piotr; Ali, Twareque; Odesskii, A;examder; Odzzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore (Eds.) Geometric Methods in Physics, XXXI Workshop 2012 (2013)

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# 2012

Nikolai Neumaier
; ; ; ;

Berezin-Toeplitz quantization of compact Kaehler manifolds and its application

Scientific Conference (2012, September 19)

Toeplitz operators and TQFT

Scientific Conference (2012, July 18)

Some naturally defined star products for Kähler manifolds

in Travaux Mathématiques (2012)

Krichever-Novikov type algebras - personal recollections of Julius Wess

in International Journal of Modern Physics: Conference Series (2012), 13

Berezin-Toeplitz quantization and star products for compact Kähler manifolds

in Contemporary Mathematics 583. Mathematical aspects of quantization (2012)

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# 2011

Berezin's coherent states, symbols and transform revisited

Scientific Conference (2011, October)

Berezin-Toeplitz quantization for compact Kähler manifolds. An introduction (3 Lectures)

Scientific Conference (2011, September)

Berezin's coherent states, symbols and transform revisited

Scientific Conference (2011, September)

Presentation (2011, April 20)

Presentation (2011, April 19)

Berezin-Toeplitz quantization of moduli spaces

Presentation (2011, April 18)

Berezin-Toeplitz quantization of moduli spaces

Scientific Conference (2011, February 22)

Almost-graded central extensions of Lax operator algebras

Scientific Conference (2011, January 11)

Almost-graded central extensions of Lax operator algebras

Scientific Conference (2011, January 07)

Almost-Graded Central Extensions of Lax Operator Algebras

in Banach Center Publications (2011), 93

Berezin - Toeplitz quantization for compact Kähler manifolds. An introduction

in Travaux Mathématiques (2011), 19

Geometry and quantization. Lectures presented at the 3rd international school and conference, Geoquant, Luxembourg City, Luxembourg, August 31--September 5, 2009.
; ;

Book published by Travaux Mathématiques 19. Luxembourg: University of Luxembourg Faculty of Science, Technology and Communication. 277~p. (2011)

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# 2010

Deformation methods in mathematics and physics. Abstracts from the workshop held September 25th--October 1st, 2010.
; ;

in Oberwolfach Rep. (2010), 7(3), 2503-2560

XXIX workshop on geometric methods in physics, Bia\lowie\Dza Poland, June 27 -- July 3, 2010. Selected papers based on the presentations at the workshop.
; ; ; ;

Book published by AIP Conference Proceedings 1307. Melville, NY: American Institute of Physics (AIP). ix, 220~p. EUR~129.95/net; SFR~151.00; \sterling~95.00 \$~142.00 (2010) Berezin symbols and Berezin transform revisited Scientific Conference (2010, December 14) Berezin-Toeplitz quantization of moduli spaces Scientific Conference (2010, October 21) Berezin-Toeplitz quantization of moduli spaces Scientific Conference (2010, June 08) An introduction to Krichever-Novikov type algebras Presentation (2010, June 01) Berezin-Toeplitz quantization of compact Kähler manifolds Presentation (2010, January 14) Berezin-Toeplitz quantization of moduli space Presentation (2010, January) Quantisierung - 3 Vortraege Presentation (2010, January) Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results in Advances in Mathematical Physics (2010), 1(203), 38 Top of Page # 2009 XXVIII Workshop on Geometrical Methods in Physics, Bialowieza, Poland, 28 June - 4 July 2009 ; ; Book published by AIP (2009) Abel-Preis für Mathematiker Mischa Gromov ; Article for general public (2009) Berezin-Toeplitz quantization of moduli spaces Presentation (2009, December 03) Berezin-Toeplitz quantization of moduli spaces Presentation (2009, November 06) Berezin-Toeplitz quantization of moduli spaces Scientific Conference (2009, October) Symmetrien in der Natur. Was sagt uns die Mathematik hierzu Conference given outside the academic context (2009) Almost-graded extensions of Lax operator algebras Scientific Conference (2009, May) Berezin-Toeplitz quantization of moduli spaces Scientific Conference (2009, March) Deformations of the Witt, Virasoro, and Current Algebra in Silvestrov, Sergei; Paal, Eugen; Abramov, Viktor; Stolin, Alexander (Eds.) Generalized Lie Theory in Mathematics, Physics and Beyond (2009) Classification of central extensions of Lax operator algebras in Proceedings of the XXVII Workshop on Geometric Methods in Physics (2009) Top of Page # 2008 Bahnbrechende Leistungen. "Nobelpreis in Mathematik": Abelpreis an Thompson und Tits ; Article for general public (2008) Classification of central extensions of Lax operator algebras in Geometric methods in physics (2008) Proceedings of the XXVII Workshop on Geometric Methods in Physics, Bialowieza July 2008 ; ; ; Book published by AIP (2008) Central extensions of Lax operator algebras ; in Russian Mathematical Surveys (2008), 63(4), 131-172 Top of Page # 2007 Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras ; in Communications in Mathematical Physics (2007), 46(11), 2708-2724 Proceedings of the XXVI Workshop on Geometrical Methods in Physics AIP Conference Proceedings / Mathematical and Statistical Phsyics ; ; ; Book published by American Institute of Physics (2007) A global operator approach to Wess-Zumino-Novikov-Witten models in Proceedings of the XXVI Workshop on Geometrical Methods in Physics (2007) Higher genus affine Lie algebras of Krichever-Novikov type in Proceedings of the International Conference “Difference Equations, special functions and orthogonal polynomials” (2007) Berezin-Toeplitz quantization of the moduli space of flat SU(N) connections in Journal of Geometry and Symmetry in Physics (2007), 9 Global Deformations of the Virasoro algebra, current and affine algebra by Krichever-Novikov type algebras ; in International Journal of Theoretical Physics (2007), 46 Proceedings of the XXV Workshop on Geometric Methods in Physics, Bialowieza July 2006 ; ; ; ; ; Book published by Bulgarian Academy of Science (2007) Top of Page # 2006 XXIV Workshop on Geometric Methods in Physics, Bialowieza, Poland, June 26 - July 2, 2005, Proceedings Special issue of the Journal of Geometry and Symmetry in Physics, containting vol. 5 and 6 ; ; ; ; ; Book published by Institute of Biophysics, Bulgarian Academy of Sciences (2006) Higher genus affine Lie algebras of Krichever-Novikov type in Journal of Geometry and Symmetry in Physics (2006), 5 Deformations of the Virasoro algebra of Krichever-Novikov type in Journal of Geometry and Symmetry in Physics (2006), 5 Deformations and contractions in mathematics and physics ; ; ; in Oberwolfach Reports (2006), 3(1), 119--186 Top of Page # 2005 Twenty Years of Bialowieza: A Mathematical Anthology Aspects of differential geometric methods in physics ; ; ; ; Book published by World Scientific (2005) Global geometric deformations of current algebras as Krichever-Novikov type algebras ; in Communications in Mathematical Physics (2005), 260(3), 579-612 Proceedings of the 4th Conference on Poisson Geometry 2004 Travaux mathématiques, Vol. XVI ; ; Book published by University of Luxembourg (2005) Top of Page # 2004 Deformation quantization for almost-Kähler manifolds in Journal of Nonlinear Mathematical Physics (2004), 11(Supplement), 49-54 Recent Developments in Quantuzation. Proceedings of the XXI Workhsop on Geometric Methods in Physics, Bialowieza June 2002 ; ; ; Book published by JNLS (2004) Knizhnik-Zamolodchikov equations for positive genus and Krichever-Novikov algebras ; in Russian Mathematical Surveys (2004), 59(4), 737-770 Top of Page # 2003 Global deformations of the Witt algebra of Krichever-Novikov type ; in Communications in Contemporary Mathematics (2003), 5(6), 921-946 Higher genus affine Lie algebras of Krichever-Novikov type in Moscow Mathematical Journal (2003), 3 Local cocycles and central extensions for multi-point algebras of Krichever-Novikov type in Journal für die Reine und Angewandte Mathematik (2003), 559 Algebra in Walz (Ed.) Faszination Mathematik (2003) Several entries in Bagger, J.; Duplij, S.; Siegel, W. (Eds.) Concise Encyclopedia on supersymmetry and non-commutative structures in mathematics and physics (2003) several entries in the field algebra, algebraic topology, homological algebra, categories in Walz (Ed.) Lexikon der Mathematik (2003) Top of Page # 2001 Almost Kähler deformation quantization ; in Letters in Mathematical Physics (2001), 57(2), 135-148 Identification of Berezin-Toeplitz deformation quantization, ; in Journal für die Reine und Angewandte Mathematik (2001), 540 Quantization of singular symplectic quotients ; ; Book published by Birkhäuser (2001) Berezin-Toeplitz Quantization and Berezin Transform in Long Time Behaviour of Classical Quantum Systems. Proceedings of the Bologna APTEX International Conference (2001) Berezin-Toeplitz quantization of compact Kähler manifolds in Coherent States, Quantization and Gravity, Proceedings of the XVII Workshop on Geometric Methods in Physics (2001) Coherent states, quantization and Gravity, Proceedings of Bialowieza workshop on Geometric Methods in Physics XVII, July, 1998 ; ; ; Book published by Warsaw University Press (2001) Top of Page # 2000 Coherent state embeddings, polar divisors and Cauchy formulas ; in Journal of Geometry & Physics (2000), 34 Deformation quantization of compact Kähler manifolds by Berezin-Toeplitz quantization in Conférence Moshé Flato 1999: Quantization, Deformations, and Symmetries (2000) Elements of a Global Operator Approach to Wess-Zumino-Novikov-Witten Models in Lie Theory and its Applications in Physics III: Proceedings of the Third International Workshop, Clausthal, Germany, 11-14 July 1999 (2000) W_(1+\infty) algebras in Hazewinkel (Ed.) Encycloppedia of Mathematics, Suppl. II (2000) Top of Page # 1999 Sugawara operators for higher genus Riemann surfaces in Reports on Mathematical Physics (1999), 43 Wess-Zumino-Witten-Novikov theory, Knizhnik-Zamolodchikov equations, and Krichever-Novikov algebras, I ; in Russian Mathematical Surveys (1999), 54(1), 213-250 Coherent states, differential and quantum goemetry, Proceedings of Bialowieza workshop on Geometric Methods in Physics, June 30-Jly6, 1997 ; ; ; Book published by Polish Scientific Publisher (1999) Top of Page # 1998 Berezin-Toeplitz quantization and Berezin symbols for arbitrary compact Kähler manifolds in Quantization, Coherent States and Poisson Structures. Proceedings of the XIV’th Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995 (1998) Sugawara construction and Casimir operators for Krichever-Novikov algebras ; in Journal of Mathematical Sciences (1998), 92(2), 3807-3834 Top of Page # 1997 Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators in Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras: Proceedings of the XXI International Colloquium on Group Theoretical Methods in Physics (1997) Operaden und Vertexalgebren Learning material (1997) Vertexalgebren eine Einführung Learning material (1997) Top of Page # 1996 Top of Page # 1994 Toeplitz quantization of Kähler manifolds and gl(N), N to infinity, limits ; ; in Communications in Mathematical Physics (1994), 165 Differential operator algebras on compact Riemann surfaces in Generalized Symmetries in Physics, Clausthal 1993 (1994) Top of Page # 1993 Degenerations of generalized Krichever-Novikov algebras on tori in Journal of Mathematical Physics (1993), 34 Top of Page # 1992 String branchings on complex tori and algebraic representations of generalized Krichever-Novikov algebras ; ; in Letters in Mathematical Physics (1992), 26(1), 23-32 Top of Page # 1991 gl(infinity) and geometry quantization ; ; ; in Communications in Mathematical Physics (1991), 138$ gl(\infty)\$ and geometric quantization
; ; ;

in Communications in Mathematical Physics (1991), 138(2), 209--244

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# 1990

Krichever-Novikov algebras for more than two points: explicit generators

in Letters in Mathematical Physics (1990), 19(4), 327-336

Krichever-Novikov algebras for more than two points

in Lett. Math. Phys. (1990), 19(2), 151--165

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# 1989

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces