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An Introduction to Conformal Field Theory for Mathematicians

Lecture Series delivered at the Introductory Workshop of the MATRIX Program:
Interactions between topological recursion, modularity, quantum
invariants and low-dimensional topology
November 28 - December 2, 2016,
Melbourne University, Australia

Reflecting a special K3 theory

Moonshine and K3 surfacesNovember 7 - 11, 2016,
Nagoya University, Japan

Vertex operator algebras for K3

Automorphic forms,
Mock modular forms and string theory,
August 29 - September 2, 2016,
Simons Center for Geometry and Physics, Stony Brook, USA

Can singularities govern conformal field theory?

Differential Geometry and its Applications,
July 11 - 15, 2016, Brno, Czech Republic

From catastrophes to conformal field theory

June 30, 2016, Vortragsreihe des
Graduiertenkolleg 1493 "Mathematische Strukturen in der modernen
Quantenphysik",

University of Göttingen, Germany

University of Göttingen, Germany

Konforme Feldtheorie und ihr Einsatz in der
Geometrie

June 2, 2016, Antrittsvorlesung, University of Freiburg, Germany

Moduli and modular forms in conformal
field theory

Moduli and Automorphic Forms:
A Meeting for Women in Mathematics,
March 12 - 14, 2016, Berlin, Germany

Complex Geometry and Mathematical Physics

March 5 - 7, 2016, DFG-AIMS Workshop,
Dakar, Senegal

Simple singularities have an ADE-classification - what's next?

January 9 - 13, 2016, Moduli spaces, integrable systems,
and topological recursions,
CRM Montreal, Canada

An application of singularity theory in conformal field theory

August 31 - September 4, 2015, The 17th EWM General Meeting, in Cortona, Italy

Towards vertex operator algebras of K3

August 14-18, 2015, Lie Algebras, Vertex Operator Algebras and Related Topics, A Conference in honor of J. Lepowsky and R. Wilson, at the University of Notre Dame, South Bend, USA

The elliptic genus - a view from conformal field theory

July 27-31, 2015, Symposium on Metric and analytic aspects of moduli spaces, at the Newton Institute in Cambridge, UK

Supersymmetry decomposes the virtual bundle that underlies the elliptic genus

June 10-13, 2015, 2015 International AMS-EMS-SPM Meeting, Session 25 on "Geometrical and enumerative structures in supersymmetry", at Porto, Portugal

Symmetrien und die Kunst, sie anzuwenden

May 12, 2015, Freiburger Kolloquium der Studienstiftung des deutschen Volkes, at Freiburg, Germany

How does extended supersymmetry affect the elliptic genus?

April 13-17, 2015, (Mock) Modularity, Moonshine and String Theory, at the Perimeter Institute for Theoretical Physics, Waterloo, Canada

The elliptic genus revisited

October 27-31, 2014, Higher Structures in Geometry and Physics 2014, Geneva, Switzerland

Mathieu Moonshine: Facts and Fantasies

September 22-26, 2014, The String Theory Universe, Mainz, Germany

The elliptic genus in conformal field theory

September 1-5, 2014, VBAC 2014 - Algebraic varieties: Bundles, Topology, Physics, Berlin, Germany

On Mathieu Moonshine

July 14-18, 2014, 30th International Colloquium on Group Theoretical Methods in Physics, Ghent, Belgium

An instance of mirror symmetry on K3

June 15-20, 2014, Workshop on Quantum Curves and Quantum Knot Invariants, Banff, Canada

Mathieu Moonshine on K3

June 14, 2014, Workshop on Calabi-Yau Manifolds and their Moduli, Satellite Meeting to the StringMath 2014, Edmonton, Canada

The elliptic genus of K3: From index theory to conformal field theory I and II

May 29-30, 2014, Workshop on Recent Developments in Moonshine, Gothenburg, Sweden

The elliptic genus of K3 and how it comes in useful in quantum field theory

May 24, 2014, Felix Klein Colloquium, Leipzig University, Germany

The elliptic genus of K3 and CFT

April 14-18, 2014, International Workshop on Mock Modular Forms and Physics, IMSc, Chennai, India

From conformal geometry to conformal field theory

January 29, 2014, Mathematics Colloquium, University of Potsdam, Germany

Moonshine - or how to distill geometry from conformal field theory

January 14, 2014, Mathematics Colloquium, University of Erlangen, Germany

Symmetry-surfing the moduli space of Kummer K3s II

September 6, 2013, Program in Mock Modular Forms, Moonshine, and String Theory, Simons Center for Geometry and Physics, Stony Brook, USA

Lecture Course: K3 Surfaces: Geometry, conformal field theory and number theory

August 19-23, 2013, GEOQUANT 2013 School on Geometry and Quantization, ESI Vienna, Austria

Lecture Course: Algebraic Geometry and Conformal Field Theory

July 15-31, 2013, Summer School on Geometric, Algebraic and Topological Methods for Quantum Field Theory, Villa de Leyva, Colombia

Moonshine in Mathematics and String Theory

July 4, 2013, Bethe Colloquium, Physics Institute, Bonn, Germany

The elliptic genus of K3

May 24-27, 2013, Bayrischzell Workshop 2013 Quantization, topological models and generalized geometries, Bayrischzell, Germany

Mathieu Moonshine for K3

April 23, 2013, Integrable Systems and Mathematical Physics Seminar, University of Glasgow, Scotland

A twist in the Mathieu Moonshine Story

April 7, 2013, Southeast Regional Math/Strings Meeting, Duke University, USA

A binary view on Kummer K3s and Mathieu-Moonshine

January 21, 2013, Mathematics Colloquium, University of Stuttgart, Germany

A constructive approach to Mathieu Moonshine

November 23, 2012, Heilbronn Day: Modular Forms, Geometry and Physics, ICMS Edinburgh, UK

A binary view on Kummer K3s and M_{24}-Moonshine

November 15, 2012, Mathematics Colloquium, University of Geneva, Switzerland

Mathematical foundations of conformal field theory and applications

(lecture series), October 26 - November 4, 2012, COPROMAPH International School, Cotonou, Benin

Geometric aspects of Mathieu moonshine

September 3-7, 2012, Heilbronn Workshop on String Theory and Arithmetic Geometry, Bristol, UK

Large subgroups of M_{24} form overarching symmetry groups of K3

July 16-21, 2012, StringMath 2012, Bonn, Germany

Singularitätentheorie als geometrischer Zugang zur topologischen Quantenfeldtheorie

July 10, 2012, Augsburger Mathematisches Kolloquium, Augsburg, Germany

A geometric approach to topological quantum field theory

July 1, 2012, Joint EMS/EWM Survey Lectures, European Women in Mathematics at the 6ECM, Krakow, Poland

Singularities and topological quantum field theories

June 28, 2012, Mathematisches Kolloquium, Universität Münster, Germany

On symplectic automorphisms of K3 surfaces and their associated conformal field theories

June 4-8, 2012, Conference on Symplectic Geometry and Mathematical Physics, Beijing Center for Mathematical Physics, Beijing, China

Von Singularitätentheorie zur topologischen Quantenfeldtheorie

May 31, 2012, Gemeinsames Kolloquium der Mathematik und Physik, Universität Heidelberg, Germany

The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_{24}

May 23, 2012, Köln-Bonn Oberseminar Zahlentheorie und Physik, MPI Bonn, Germany

A geometric approach to topological quantum field theories

April 4, 2012, Hausdorff-Kolloquium, Mathematics Institute, Universität Bonn, Germany

On symmetries of K3, its associated CFTs and the Mathieu group M_{24}

February 27, 2012, Oberseminar Algebraische Geometrie, Universität Zürich, Switzerland

Von Katastrophen und anderen Singularitäten

January 17, 2012, Didaktisches Seminar, Freiburg, Germany

On K3 surfaces in physics and geometry

December 9, 2011, Mathematisch-Physikalisches Kolloquium, Freiburg, Germany

Singularitäten und topologische Quantenfeldtheorien

December 7, 2011, Mathematisches Kolluquium, TU München, Germany

Symmetries of K3 and the automorphisms of the Golay code

November 28, 2011, Oberseminar Differentialgeometrie, Münster, Germany

Kummer K3 surfaces and the automorphism group of the Golay code

November 14-15, 2011, Trends and Perspectives in Mathematics, Tel Aviv, Israel

K3 surfaces and the Mathieu group M_{24}

October 30-November 4, 2011, Chern Centennial Conference, MSRI Berkeley, USA

On catastrophes and related singularities

October 6-8, 2011, International SimTech Symposium Partial Differential Equations: Theory, Applications, Simulations, Stuttgart, Germany

Topological field theories and integrable systems

July 25-29, 2011, The 4th International Workshop on Nonlinear Mathematical Physics and The 11th National Conference on Integrable Systems, Wuhan, China

K3 Flächen, deren Symmetrien und was sie mit Codes zu tun haben

July 13, 2011, Mathematisches Kolloquium, Eberhard-Karls-Universität Tübingen, Germany

From the K3-lattice to the (A_{1})^{24}-Niemeier lattice

July 7-9, 2011, Mathieu Moonshine Meeting, ETH Zurich, Switzerland

K3 Flächen, deren Symmetrien und was sie mit Codes zu tun haben

June 17, 2011, Mathematisches Kolloquium, Goethe-Universität Frankfurt, Germany

From the Golay Code to K3-surfaces and their associated conformal field theories

April 28, 2011, Maths and Appications Sussex Seminar at the University of Sussex, UK

Die Geometrie von Singularitäten und Quantenfeldtheorien

April 1-2, 2011, Tagung deutschsprachiger Mathematikerinnen 2011 at the RWTH Aachen, Germany

Symmetries of K3 in M_{24}: I Geometry

February 28 - March 18, 2011, School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics at the ICTP, Trieste, Italy

Von K3 bis M_{24}

January 20, 2011, Mathematics Colloquium, University of Mainz, Germany

Lattices, their symmetries, and how they affect conformal field theories on K3

December 20, 2010, Theoretical Physics Seminar, Londrina University, Brazil

The symmetries of K3 surfaces and their implementation in conformal field theory

December 13-17, 2010, Second Latin Congress on Symmetries in Geometry and Physics in Curitiba, Brazil

What is a K3 surface - and how can it be used in physics?

December 3, 2010, Deutsches Haus für Wissenschaft und Innovation des DAAD, Moscow, Russia

>On Kummer surfaces, the Mathieu group M_{24}, and conformal field theory

November 24, 2010, Algebraic and Geometry Seminar, University of Bristol, UK

On Kummer surfaces, the Golay code, and conformal field theory

November 9, 2010, Algebraic Geometry Seminar, Università di Milano, Italy

On the symmetries of K3 surfaces

September 13 - 16, 2010, Courant Colloquium 2010, Göttingen, Germany

On the geometry of singularities in quantum field theory

August 19 - 27, 2010, International Congress of Mathematicians 2010, Hyderabad, India

Quantum field theories and the geometry of singularities

July 26 - 30, 2010, The XXVIII International Colloquium on Group-Theoretical Methods in Physics, Newcastle, UK

Von Singularitäten zu topologischen Quantenfeldtheorien

July 13, 2010, Fakultätskolloquium der Fakultät Mathematik und Physik, Leibniz-Universität Hannover, Germany

On K3 surfaces and their applications in physics

June 27 - July 3, 2010, XXIX Workshop on Geometric Methods in Physics, Bialowieza, Poland

K3 erklimmen? Von der Basis in der klassischen Optik bis zum Gipfelpanorama in Geometrie und Quantenfeldtheorie

May 7, 2010, Lecture series "frauen, die forschen", University of Kiel, Germany

TQFT & singularities from a conformal field theorist's point of view

April 15, 2010, COW seminar in Cardiff, Wales

On singularities and conformal field theory

April 12, 2010, Mathematics Colloquium, University of Durham, UK

On singularities and modularity

March 14-19, 2010, Global Analysis and Automorphic Forms - On the Occasion of the 60th Birthday of Werner Müller in Jerusalem, Israel

Conformal field theories on Borcea-Voisin 3-folds

December 17-18, 2009, Workshop on Algebraic and Topological Aspects of D-branes in Würzburg, Germany

Eine mathematische Entdeckungsreise zu K3

November 25, 2009, Kolloquium des Fachbereiches Mathematik, TU Darmstadt, Germany

Encounters with conformal field theory

November 20-21, 2009, Advances in Theoretical Physics - A conference in honour of Professor Werner Nahm in Dublin, Ireland

A Hiker's Guide to K3

November 4, 2009, Dresdener Mathematisches Seminar, Dresden, Germany

How to attach gauge theory data to elliptic fibrations

September 14-18, 2009, Workshop on Algebraic Geometry and Physics (WAGP 2009) Representations, Lie Theory and Physics in Maresias, Brazil

Asymptotic analysis for unitary conformal field theories

September 7-11, 2009, Third International Conference on Geometry and Quantization GEOQUANT at the University of Luxembourg, Luxembourg

(0,4) lessons for (0,2)

August 17-21, 2009, (0,2) Mirror Symmetry and Quantum Sheaf Cohomology, Potsdam, Germany

A discovery tour to K3

August 5, 2009, Mathematics Colloquium, St. Patrick's college, Dublin, Ireland

The symmetries of K3, and how to build conformal field theories from them

July 19-24, 2009, Symmetries in science, Bregenz, Austria

An explicit construction of superconformal field theories on certain Calabi-Yau 3-folds

July 6-9, 2009, XIII International Conference Symmetry Methods in Physics, Dubna, Russia

Geometrische Aspekte von Quantenfeldtheorien

June 27, 2009, Mathematics Institute, TU Munich, Germany

Geometrische Anwendungen von Quantenfeldtheorien

June 19, 2009, Mathematics Institute, Freiburg i.Br., Germany

The geometry of conformal field theory

June 8-20, 2009, RTG Graduate Summer School Geometry of Quantum Fields and Strings, University of Pennsylvania, Philadelphia, USA

Lecture series on K3 surfaces and CFT

April 6-8, 2009, Graduate workshop: K3 surfaces and multigraded rings, University of Warwick, UK

A classification of a family of free fermionic orbifold models

March 30, 2009, Duke-UNC String theory seminar, UNC Chapel Hill, USA

How are intersection numbers governed by representation theory?

January 20, 2009, Oberseminar Geometrie, LMU München, Germany

From dualities to intersection theory

January 16, 2009, Scottish topology colloquium, University of Edinburgh, Scotland

Applications of a string-string duality

December 15-22, 2008, First Cuban Congress on Symmetries in Geometry and Physics, Havana, Cuba

Symmetrien und die Kunst, sie anzuwenden

October 23, 2008, public lecture for the Year of Mathematics, Zeughaus Augsburg, Germany

On explicit SCFT constructions for certain Calabi-Yau varieties

September 17, 2008, Korean Institute of Advanced Studies, Seoul, South Korea

On orbifolds and free fermion constructions

September 8-12, 2008, International Workshop From integrable structures to topological strings and back, SISSA, Trieste, Italy

How are intersection numbers governed by representations of Lie algebras?

August 13-19, 2008, XXVII Intl. Colloquium on Group Theoretical Methods in Physics, Yerevan, Armenia

Die Geometrie topologischer Quantenfeldtheorien

July 4, 2008, Honorary speech at the annual celebration of the University of Augsburg, Germany

On some implications of string-string dualities

June 30 - July 4, 2008, The manifold geometries of quantum field theory, Hausdorff Center for Mathematics, Bonn, Germany

Extending the geometry of certain Calabi-Yau varieties

May 12-13, 2008, Irish Geometry Conference 2008, IT Tralee, Ireland

Conformal field theory: From physics to mathematics

April 29, 2008, Seminar zur Theorie der kondensierten Materie, Physikalisches Institut, Augsburg, Germany

From dualities to geometry

March 14-20, 2008, International Conference on Geometry and Analysis on Manifolds, Santa Barbara, USA

How to implement special properties of K3 surfaces in conformal field theory

February 15, 2008, Algebraic and complex geometry seminar, Osaka, Japan

How to lift a construction by Hiroshi Inose to Conformal Field Theory

February 12, 2008, IPMU Seminar, University of Tokyo, Japan

Eine mathematische (Ein-)führung zu K3

February 1, 2008, Bonner Mathematisches Kolloquium, Bonn, Germany

Geometry and beyond for K3 and one of its higher dimensional cousins

January 17, 2008, ZMP Kolloquium, University of Hamburg, Germany

On K3-surfaces and beyond - from a geometer's and a conformal field theorist's point of view

November 22, 2007, Oberseminar Algebraische Geometrie, Hanover, Germany

How do twisted indices on K3 relate to intersection numbers in Calabi-Yau threefolds?

October 26, 2007, Workshop in memory of Andrei Tyurin, Steklov Institute, Moscow, Russia

Schritt für Schritt auf dem Weg zu K3

October 23, 2007, Antrittsvorlesung, University of Augsburg, Germany

Quantum field theory as an aid to geometers

September 24, 2007, Mathematics seminar, IISc Bangalore, India

Quantum field theory as an aid to geometers

September 19, 2007, Mathematics seminar, IIT Bombay, India

Quantum field theory as an aid to geometers

August 29 - September 2, 2007, ICTAMI07, Alba Iulia, Romania

On the relation between Conformal Field Theory and Geometry

August 26-31, 2007, International Conference on Symmetries in String Theory, Ascona, Switzerland

The topology and geometry of certain quotient singularities - some new techniques

August 19-25, 2007, The Eighth International Workshop on Differential Geometry and its Applications, Cluj, Romania

What do quartic K3 surfaces have in common with orbifold limits of K3?

July 3, 2007, Oberseminar Geometrie, LMU München, Germany

A reversal of sigma model constructions

June 24-30, 2007, Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine

A reversal of sigma model constructions

June 18-24, 2007, VII. International Workshop Lie Theory and its Applications in Physics, Varna, Bulgaria

'Nearly attractive' K3-surfaces - describing and generalizing Kähler-Einstein metrics on them

June 6, 2007, Oberseminar Globale Analysis, Bonn, Germany

Eine elementare Diskussion von T-Dualität und Spiegelsymmetrie

May 5, 2007, Mathematisches Kolloquium, Regensburg, Germany

From dualities to geometry

April 16-19, 2007, British Mathematical Colloquium 2007, Swansea, Wales

From index theory to intersection numbers

April 8-14, 2007, International Conference on Geometry and Analysis on Manifolds, Tianjin, China

The imprint of dualities in complex geometry

March 25-30, 2007, Minisymposium Globale Analysis, DMV Jahrestagung 2007, HU Berlin, Germany

How to construct deformations of the (2)^{4} Gepner model on smooth K3 surfaces

March 5, 2007, Theory Seminar, CEA Saclay, France

K3 surfaces, and how to construct associated conformal field theories

January 24, 2007, Forschungsseminar "Geometrische Analysis und Spektraltheorie'', HU Berlin, Germany

Spezielle quartische K3-Flächen und assoziierte 'metageometrische' Strukturen

December 14, 2006, Kolloquium des GK ατμγ, Münster, Germany

Approaching Geometry from Conformal Field Theory

November 16, 2006, Mathematical Physics Seminar, Zürich University, Switzerland

Verallgemeinerte Laplace-Operatoren als Schlüssel zur geometrischen Dekodierung konformer Feldtheorien

October 7, 2006, Workshop "Anwendbare Analysis", Stuttgart, Germany

Towards the boundary of spaces of conformal field theories

July 27, 2006, IGA satellite workshop to Mathematics of String Theory, Adelaide, Australia

A family of superconformal field theories hosting all "very attractive" relatives of the (2)^{4} Gepner model

July 21, 2006, Workshop on Mathematics of String Theory, Canberra, Australia

Anomaly cancellation in the light of heterotic - type IIA string duality

July 14-17, 2006, minicourse at the Instructional Program of Mathematics of String Theory, Canberra, Australia

The Monster and String Theory

May 24, 2006, LIMS Evening lecture, Lighthill Insitute of Mathematical Sciences, London, UK

A scenic view of K3

May 19, 2006, Mathematics Colloquium, University of Kent, UK

"Nearly attractive" K3 surfaces and associating SCFTs to them

May 4, 2006, Algebra Seminar, Kansas State University, USA

Z_{4} orbifold limits of K3 and a family of smooth quartic K3s: A nonclassical duality

December 1, 2005, Duke-UNC String theory seminar, Duke University, USA

A duality between "nearly attractive" quartic K3s and Z_{4} orbifold limits of K3

November 16, 2005, Geometry Seminar, Boston University, USA

On some quartic K3 surfaces, their natural metrics, and their natural associated SCFTs

August 20-26, 2005, XXIII Int. Conf. on Differential Geometric Methods in Theoretical Physics, Tianjin, China

Anomalien - eine Anwendung klassischer Indexsätze im Rahmen nichtklassischer Dualitäten

July 8, 2005, Mathematics Institute, Augsburg, Germany

On a family of smooth algebraic K3 surfaces and their associated CFTs

May 18-20, 2005, Journées de géométrie algébrique, Lille, France

How to construct SCFTs associated to a family of smooth quartic K3 surfaces

May 4, 2005, Triangle Seminar London, UK

A survey of K3 from a conformal field theorist's point of view

February 7, 2005, Dublin Theoretical Physics Colloquium, School of Mathematics, Trinity College Dublin, Ireland

Approaching geometry through conformal field theory

January 27, 2005, Warwick theory group seminar, Department of Physics, University of Warwick, UK

On the "very attractive" relatives of the Fermat quartic and conformal field theories associated to them

December 1, 2004, Deformation theory seminar, Department of Mathematics, University of Pennsylvania, Philadelphia, USA

Endliche Spiegelungsgruppen und die Allgegenwart von ADE-Klassifikationen

November 19, 2004, Kolloquiumsreihe der Mathematischen Gesellschaft Göttingen, Germany

K3: Eine mathematische Wanderung von Geometrie zu konformer Feldtheorie und zurück

October 21, 2004, Kolloquiumsreihe der Mathematischen Gesellschaft Göttingen, Germany

Conformal field theories, their limits and their geometric interpretations

October 1, 2004, Math/Physics seminar, University of Pennsylvania, Philadelphia, USA

From large level to large volume limits and their geometric interpretations

September 22-25, 2004, 6th Bologna Workshop on CFT and Integrable Models, Bologna, Italy

On a family of SCFTs associated to quartic K3 surfaces

September 6-10, 2004, Workshop on Complex Geometry in Physics, ICMS Edinburgh, Scotland

Friendly giant meets pointlike instantons? On a new conjecture by John McKay

July 5-13, 2004, Moonshine- the first quarter centry and beyond, ICMS Edinburgh, Scotland

The 'very attractive' relatives of the (2)^{4} Gepner model

June 9, 2004, 9th meeting of the North British Mathematical Physics Seminar, York, UK

On degenerating sequences of CFTs and their geometric interpretation

May 20, 2004, Workshop on Geometry and duality in string theory, Oberwolfach, Germany

On degeneration phenomena in geometry and conformal field theory

April 29 - May 3, 2004, lecture series presented at the ESI workshop Mathematical and physical aspects of branes in Calabi-Yau spaces, Vienna, Austria

From geometry to CFT and back to geometry

March 18, 2004, Theoretical Particle Physics Seminar, DIAS Dublin, Ireland

On conformal field theories associated to "very attractive'' K3 surfaces

November 3, 2003, Geometry/topology seminar, Glasgow, Scotland

Orbifold constructions of K3

Geometric interpretations of conformal field theories associated to K3

September 17 and 18, 2003, Math-Physics Joint Seminar, University of Pennsylvania, Philadelphia, USA

The many routes to K3

September 16, 2003, Math/Physics Colloquium, University of Pennsylvania, Philadelphia, USA

Decoding the geometry of conformal field theories

September 11, 2003, Mathematics Colloquium, UNC Chapel Hill, USA

September 8, 2003, Physics Colloquium, UNC Chapel Hill, USA

Conformal field theory and geometry of strings: Some introductory remarks

Conformal field theories and their geometric interpretations

June 16 and 19, 2003, Dipartimento di Fisica, Università di Pisa, Italy

Conformal field theory on K3: The Fermat quartic

May 14, 2003, Geometry Seminar, Bath, UK

Geometric interpretation of conformal field theories: A (degenerate) example

May 1, 2003, Geometry Seminar, University of Edinburgh, Scotland

CFT on K3 and an application of Shioda-Inose structures

March 9-21, 2003, Frontiers in Number Theory, Physics and Geometry, École de physique des Houches, Les Houches, France

Ascent to K3 by CFT

November 22-25, 2002, London Mathematical Society Regional Meeting - Wales 2002, Gregynog, Wales

Conformal field theory on K3: A status report

November 18, 2002, String theory seminar, Mathematical Institute, Oxford, UK

Aspects of mirror symmetry on K3

June 24-28, 2002, EuroConference on Higher dimensional complex geometry, Cambridge, UK

A hiker's view of K3: Geometric aspects of conformal field theory

June 10, 2002, Isaac Newton Institute Seminar, Cambridge, UK

Orbifold constructions of K3: SCFT vs. geometry

May 24, 2002, The Third ABC-KLM Network Meeting, Cambridge, UK

Geometric aspects of CFT on K3

April 8-12, 2002, Workshop on String Theory and Complex Geometry, Bad Honnef, Germany

Strings on low-dimensional Calabi-Yau manifolds: A geometric approach

Strings on K3: Orbifold constructions

March 19 and April 19, 2002, series of talks presented at the "Algebraic Geometry" and "Physically inspired Mathematics" Seminars at the Department of Mathematics, UNC Chapel Hill, USA

Geometry and conformal field theory for orbifold limits of K3

February 13 and 14, 2002, Theory group seminar at the Enrico Fermi Institute, University of Chicago, and BCDE Seminar at the University of Illinois at Urbana-Champaign, USA

January 24, 2002, Duke-UNC String Theory Seminar, UNC Chapel Hill, USA

Mirror symmetry on Kummer type K3 surfaces. An overview

November 15, 2001, Seminar on Topological Quantum Field Theory, MPI für Mathematik, Bonn, Germany

Aspects of mirror symmetry for orbifold limits of K3

November 7, 2001, Theoretical Physics Seminar at the Mathematics Department, King's College, London, UK

Aspects of N=(4,4) SCFT on K3, I and II: Mirror symmetry on Kummer type K3 surfaces

October 31 and November 1, 2001, Workshop on Mathematical Aspects of String Theory, Erwin Schrödinger Institut, Vienna, Austria

Orbifold CFT on K3 and applications to mirror symmetry

July 20, 2001, AG Darstellungstheorie, Mathematics Institute, Freiburg i.Br., Germany

Geometric aspects of conformal field theory

July 16, 2001, Mathematisches Kolloquium für Analysis, Stuttgart, Germany

Mirror symmetry on Kummer type K3 surfaces

July 12, 2001, Special Seminar in the Maths Department, Durham, UK

Orbifold conformal field theories on K3

May 4-8, 2001, Workshop on "Mathematical Aspects of Orbifold String Theory", Madison, Wisconsin, USA

October 12, 2000, Duke-UNC String Theory Seminar, UNC Chapel Hill, USA

From the torus to K3: Orbifold conformal field theories

August 17, 2000, Seminar on Topological Quantum Field Theory, MPI für Mathematik, Bonn, Germany

Conformal field theory: Z_{M} Orbifolds in the moduli space of conformal field theories with c=6

July 20, 2000, Oberseminar zur Algebra, Stuttgart, Germany

Moduli of CFT on K3. II: Superconformal field theories

June 29, 2000, Seminar on Topological Quantum Field Theory, MPI für Mathematik, Bonn, Germany

(Crystallographic) orbifold conformal field theories

March 6, 2000, Specialist Mathematical Physics Monday's Seminar, York, UK

Z_{2} Orbifolds in the moduli space of N=(4,4) superconformal field theories with central charge c=6

March 3, 2000, Friday Lunchtime Seminar in the Maths Department, Durham, UK

A Hiker's guide to K3 - Aspects of N=(4,4) superconformal field theory with central charge c=6

January 7-11, 2000, Workshop on "Recent developments in string theories, conformal field theories and integrable models from the previous millennium", Tel Aviv, Israel

Aspects of conformal field theory on K3

April 18-24, 1999, Conference on Mathematical Aspects of String Theory, Oberwolfach, Germany

Kritische Metriken bzgl. analytischer Ray-Singer Torsion und Quillenmetrik

February 13, 1997, Forschungsseminar "Geometrische Analysis und Spektraltheorie'', HU Berlin, Germany

Regularized determinants of Laplacians and Ray-Singer analytic torsion

October 9-11, 1996, Conference on "Analysis, Numerics and Applications of Differential and Integral Equations", Stuttgart, Germany