The Eighth BICMR Advanced Seminar in Symplectic Geometry and Topological Field Theory: "Topological recursion in geometry," a series of four 2-hour lectures, Beijing International Center for Mathematical Research, Peking University, October 2018.

2018 ERC Conference in Warsaw, Quantum Fields, Knots, and Strings: "Ribbon graphs, Frobenius-Hopf duality, and CohFT," University of Wassaw, Poland, September 2018.

2018 Summer School of the TRR 195 and the Graduiertenkolleg *Experimental and constructive algebra*, Topological Recursion:
"Magic of Ribbon Graphs," a series of three 90-min lectures,
University of Tübingen, August 2018.

2018 Les Diablerets Winter School in Mathematical Physics: "Quantum Curves," a series of 4 lectures, Les Diablerets, Switzerland, January 2018.

Institute for Basic Science Center for Geometry and Physics Intensive Lecture Series: "Topological Recursion and Quantum Curves," a series of 5 lectures, Pohang, Korea, September 2017.

IHÉS Conference:
*Algebraic Analysis in Honor of Masaki
Kashiwara's 70th Birthday *
Video:
"Quantum Curves."
Institut des Hautes Études Scientifiques,
Bures-sur-Yvette,
June 6, 2017.

LJAD Conference:
*Higgs Bundles and Related Topics *
"An Invitation to Quantum Curves
and 2D TQFT."
Laboratoire J.A. Dieudonné, Nice,
May 31, 2017.

IST Austria:
*Algebraic Geometry Seminar *
"Ribbon graph formulation of CohFT and 2D TQFT."
Institute of Science and Technology, Austria,
March 22, 2017.

IHP Workshop:
*"Enumerative Geometry and Combinatorics of
Moduli Spaces *
"From Cayley to Hurwitz to Hitchin."
Institut Henri Poincaré, Paris,
March 15, 2017.

QUANTMOD:
*Quantization and
Moduli Spaces *
"Holomorphic quantization of Higgs bundles."
Université du Luxembourg,
January 12, 2017.

MATRIX Conference:
*Topological recursion and modularity *
"Category of cell graphs and a new set of axioms for 2D TQFT."
MATRIX, Creswick, Australia,
December 22, 2016.

Kobe 2016 International Conference:
*Algebraic Geometry and Integrable Systems *
"Algebraic geometry of quantum curves and opers."
Kobe University, Japan,
December 8, 2016.

The 15th Oka Symposium: "Quantization of Hitchin spectral curves and holomorphic Lagrangians." Oka Mathematical Institute, Nara, Japan, December 4, 2016.

BIRS Workshop:
*Painlevé Equations and Discrete Dynamics *
"Quantization of Hitchin spectral curves as opers."
Banff International Research Station, Banff, Canada,
October 4, 2016.

RIMS Workshop:
*Studies on Integrable Systems: State of the Art and Perspective for Future *
"Quantization of Higgs bundles and opers."
Research Institute for Mathematical Sciences, Kyoto
University,
September 6, 2016.

OCAMI Meeting:
*Integrable Systems, Moduli Spaces
and Non-linear PDE *
"Quantization of Hitchin spectral curves, opers, and their WKB analysis via topological recursion."
Osaka City University Advanced Mathematical Institute, Osaka,
September 3, 2016.

Infinite Analysis 2016 Summer School:
*Integrable Hierarchies and Beyond*
A series of three 1-hour talks.
1 "World of character varieties."
2 "Quantization of Higgs bundles."
3 "Opers and quantum curves."
Graduate School of Mathematics, Nagoya University,
August 30, 31, September 1, 2016.

SCGP Workshop:
*New perspectives on Higgs bundles, branes and quantization*
"Algebraic geometry of Gaiotto correspondence and quantization of Higgs bundles."
Simons Center for Geometry and Physics,
Stony Brook,
June 17, 2016.

ICTS-TIFR Conference:
*Higgs Bundles*
"Quantum Curves and Gaiotto's Conjecture."
International Center for Theoretical Sciences,
Tata Institute of Fundamental Research Bangalore, India,
March 23, 2016.

IMAR Lecture:
*Algebraic Geometry*
"A family of deformations that connects Higgs
bundles and opers."
Institute de Matematică "Simion Stoilow"
al Academiei Române, Bucharest, Romania,
February 25, 2016.

MFO Workshop:
*Topological Recursion and TQFTs*
"Solution to Gaiotto Conjecture and Quantum Curves."
Mathematisches Forschungsinstitut Oberwolfach, Germany, February 14, 2016.

University of Luxembourg:
*RMATH General Mathematics Seminar*
"A formula for Non-Abelian Hodge theory through Gaiotto's conjecture."
Mathematics Research Unit,
University of Luxembourg, Luxembourg,
February 9, 2016.

Warsaw Advanced School:
*Topological Quantum Field Theory*
A series of four lectures.
Faculty of Physics, University of Warsaw, Poland,
December 7 - 10, 2015.

OCU Workshop:
*Quantization of Spectral Curves*
"Opers and quantum curves."
Osaka City
University Advanced Mathematical Institute,
Osaka, Japan, November 4, 2015.

GEOQUANT 2015:
*School and International Conference on Geometry and Quantization*
"Topological recursion, 2D TQFT, and quantization of Hitchin spectral curves."
Instituto de Ciencias Mathemáticas
(ICMAT), Madrid,
Spain, September 14, 2015.

MPIM-Bonn:
*Mathematische Arbeitstagung 2015 *
"The topological recursion -- an inductive mechanism of counting on the moduli of curves."
Max-Planck-Institut für Mathematik, Bonn,
Germany, June 27, 29, 2015.

Kolloquium des
Graduiertenkollegs 1463:
*Analysis, Geometrie und Stringtheorie *
"The story that a graph on a surface weaves."
Leibniz Universität, Hannover,
Germany, June 8, 2015.

Lorentz Center Workshop: *Geometric Invariants and Spectral Curves *
"2D TQFT from cellular graphs and a TQFT-valued topological recursion."
Lorentz Center, Leiden, the Netherlands, June 5, 2015.

SCGP Program: *Knot homologies, BPS states, and SUSY gauge theories*
"Topological recursion and quantization."
Simons Center for Geometry and Physics,
May 14, 2015.

HKUST Seminar on Geometry (A series of 10 lectures): "I. Introduction to the topological recursion and quantum curves, II. From Catalan numbers to the Witten-Kontsevich theory of intersection numbers, III. The topological recursion of simple Hurwitz numbers, IV. Simple Hurwitz numbers and the topological recursion, V. Simple algebraic geometry proofs of the Witten conjecture and the lambda-g formula via topological recursion, VI. Quantum curves, Part 1, 2, 3, IX: 35 years since the work of Sato on KP equations and the Grassmannians, Part 1, 2." Hong Kong University of Science and Technology, March 24 - April 20, 2015.

WAGS Spring 2015: *Western Algebraic Geometry Symposium* "Topological recursion and quantum curves." University of California, Davis,
March 1, 2015.

MPIM Workshop: *Geometric quantization and topological recursion*
"Quantum curves and Hitchin fibrations."
Max-Planck-Institut für Mathematik, Bonn,
November, 2014.

EIMI International Conference:
*Embedded Graphs *
"Enumeration of embedded surface
graphs and quantum curves."
Euler International Mathematical
Institute, St. Petersburg, Russia, October 2014.

AIM Workshop:
*Quantum curves, Hitchin systems, and the Eynard-Orantin theory *
"An introductory remark on quantum curves."
American Institute of Mathematics, Palo
Alto, California, September 2014.

Advanced Summer School:
*Modern Trends in Gromov-Witten Theory*
"Quantum curves, topological recursion, and Hitchin systems."
A series of three1-hour lectures,
Leibniz
Universität Hannover, September 2014.

Kobe Summer School:
*Advanced Science and Technology Graduate Course 2014 *
"A mathematical theory of quantum curves :
what they are, and what they do."
A series of eight 1.5-hour lectures,
Kobe University, July 2014.

IMS Summer Research Institute:
*The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles *
"Quantization of spectral curves of Higgs bundles via a B-model topological recursion."
(Lecture I, 7/10/2014)
(Lecture II, 7/11/2014)
Institute for Mathematical Sciences,
National University of Singapore, July 2014.

International
Conference: *The Mathematics of Quantum Theory
in Honor of Professor Albert
Schwarz at his 80th Birthday*
"A mathematical approach to quantum curves."
UC Davis, California, May 2014.

MPIM Seminar on Algebra, Geometry and Physics "Algebraic geometry of quantum curves and classical differential equations." Max-Planck-Institut für Mathematik, Bonn, May 2014.

Mathematical Institute Geometry and Analysis Seminar "Quantum curves for Higgs bundles and quantum invariants." Mathematical Institute, University of Oxford, May 2014.

Conference on Mirror Symmetry and Spin Curves "Quantum curves: what they are, and what they do." Palazzone di Cortona, Italy, April 2014.

SMS Spring Conference on Quantization of Moduli Spaces "Construction of quantum spectral curves for Higgs bundles via a new topological recursion." Villa Battelle, University of Geneva, April 2014.

Workshop on Moduli of curves and mathematical physics "Quantum curves for Hitchin fibrations." Korteweg-de Vries Institute, Amsterdam, the Netherlands, January 2014.

Séminaire de Mathématiques (organisé par Mikhail Gromov, Laurent Lafforgue, Maxim Kontsevich) "Quantum curves for Hitchin systems and the Eynard-Orantin theory." l'Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, November 2013.

SISSA Workshop on Hamiltonian PDEs, Frobenius Manifolds, and Deligne-Mumford Moduli Spaces "Quantum curves for Hitchin fibrations." La Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy, September 2013.

BIRS Workshop on Integrable Systems and Moduli Spaces (13w5064) (Video) "Quantum curves and topological recursion." Banff International Research Station, Canada, August 2013.

5th IST Lectures on Algebraic Geometry and Physics -- 2013 "The Eynard-Orantin recursion, algebraic geometry, and quantum invariants (Series of two 1.5 hour lectures)," Instituto Superior Técnico, Lisbon, Portugal. February 2013.

QGM Conference on Topological recursion and quantum algebraic geometry (Video) "Quantum curves for geometric enumeration problems." Center for Quantum Geometry of Moduli Spaces, Aarhus University, Denmark. January-February 2013.

BIRS Workshop on Integrable systems, growth processes and KPZ universality (12w5015) (Video) "The Eynard-Orantin recursion and quantum invariants in geometry." Banff International Research Station, Canada. September 2012.

XXXI Workshop on Geometric Methods in Physics "The Laplace Transform, Mirror Symmetry, and the Topological Recursion of Eynard-Orantin." Białowieża, Poland. June 2012.

BICMR Conference on Symplectic Geometry and Mathematical Physics "The Laplace transform of the Catalan numbers and the Eynard-Orantin recursion." The Beijing International Center for Mathematical Research, Beijing. June 2012.

The Hausdorff Research Institute for Mathematics Workhsop: Integrability in Topological String Theory "Laplace transform of Catalan Numbers and Topological Recursion." The Hausdorff Research Institute for Mathematics, Bonn. April 2012.

The Fourier Institute Conference on Gromov-Witten Theory (Video) "Counting the lattice points on the moduli space of curves." The Fourier Institute, Grenoble. July 2011.

The Fourier Institute Summer School on Moduli of Curves and Gromov-Witten Theory "Hurwitz numbers and new recursion formulae in GW theory." A series of lectures delivered at the Fourier Institute, Grenoble. June 2011.

BIRS Workshop on Number Theory and Physics at the Crossroads "A topological recursion in B-model as the Laplace transform of a combinatorial equation." Banff International Research Station. May 2011.

Fifth Ibero-American Congress on Geometry: "Topological Recursion in Gromov-Witten Theory." Pucon, Chile. December 2010. (Talk Slides)

Complex Algebraic Geometry: A workshop on the occasion of Herbert Kurke's 70th birthday: "The Laplace transform of Hurwitz numbers." Humboldt University of Berlin, Germany. October 2009.

AIM Workshop on Recursion structures in topological string theory and enumerative geometry: "Laplace Transform, Cut-And-Join Equation, and the Bouchard-Marino Conjecture." AIM, Palo Alto. June 2009.

The 16th Osaka City University International Academic Symposium, Riemann Surfaces, Harmonic Maps and Visualization: "An integrable system approach to the newly discovered topological recursion." Osaka, Japan, December 2008.

IPMU Mini Workshop, A New Recursion from Random Matrices and Topological String Theory: "Deformation of tau functions and the Eynard-Orantin topological recursion." IPMU, Japan, December 2008.

KIAS Workshop on Gromov-Witten Theory and Related Topics: "Where do the Virasoro constraints and the KdV/KP equations come from?" KIAS, Korea. June 2008.

Moduli 2008--Bundles, Gerbes, and Derived Categories in String Theory: "New developments in topological string theory and intersection theory on the moduli spaces of Riemann surfaces." Salamanca, Spain. May 2008.

RIMS International Project Research Conference, Moduli Space and Enumerative Geometry: Lecture Series "Intersection theory of the moduli space of Riemann surface and integrable system. I. Mumford class and Weil-Petersson volume; II. Hodge class and Hurwitz number; III. New point of view to Witten-Kontsevitch theory." Kyoto University. April 2008.

RIMS International Project Research Conference, New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry: "Hitchin integrable systems and KP-type equations." RIMS, Kyoto. January 2008.

RIMS International Conference on Geometry Related to Integrable Systems: "Integrable systems associated with character varieties." RIMS, Kyoto. September 2007.

London Mathematical Society Durham Symposium, Methods of Integrable Systems in Geometry: "Integrable Systems in Gromov-Witten Theory." Durham, England. August 2006.

2005 AMS Summer Institute on Algebraic Geometry. "Witten-Kontsevich theory revisited." AMS Summer Research Institute at University of Washington. July 2005.

The 34th ENCOUNTER with MATHEMATICS-- Theory of Nonlinear Special Functions and Applications of Painleve Equations: Lecture Series "1. From Gauss to Painleve: A story of new probability distributions; 2. Generating functions as special functions: Adding geometries." Chuo University, Tokyo. July 2005.

International Research Group Intensive Course--Local fields, algebraic geometry, generalized KP-hierarchy: Lecture Series "Symplectic geometry of the moduli spaces of pointed Riemann surfaces and the Virasoro constraints, I, II, III, IV." Humboldt University, Berlin. June 2005.

Winter School, Miami 2004: "Symplectic volume of the moduli of bordered Riemann surfaces and Witten-Kontsevich theory---a survey." University of Miami. December 2004.

2004 Workshop on Algebraic Geometry and Physics--Matrix Models and Algebraic Geometry: "Symplectic geometry of the moduli space of pointed algebraic curves." IST, Lisbon, Portugal. September 2004.

International Conference in Honor of Pierre van Moerbeke on the Occasion of his 60th Anniversary, Integrable Systems: "Matrix-type integrals over non-commutative algebras and volume of representation spaces." Poitiers, France. June 2004.

2003 Mathematical Society of Japan Fall General Meeting Invited Address, Infinite Analysis Session: "Geometry of Matrix Integrals." Mathematical Society of Japan Fall General Meeting, Chiba University, Japan. September 2003.

Probabilistic Operator Algebra Workshop and Seminar: "Geometry of Matrix Integrals Over Operator Algebras." UC Berkeley. August 2003.

YITP International Conference on Random Matrix Theory and Related Topics: "Duality of Orthogonal and Symplectic Matrix Integrals and Quaternionic Feynman Graphs." Yukawa Institute of Theoretical Physics, Kyoto. December 2002.

CIMAT International Workshop on Integrable Systems, Algebraic, Analytic and Geometric Aspects: "Duality in matrix integrals." CIMAT, Mexico. September 2002.

MSRI Workshop on Recent Progress in Random Matrix Theory and Its Applications: "Graphical Expansion of Non-Commutative Matrix Integrals." MSRI, Berkeley. September 2002.

The 38th Mathematical Society of Japan Summer Research Seminars on Several Complex Variables: Lecture Series "Grothendieck's Dessins d'Enfants and Moduli Theory of Riemann Surfaces, From a function theoretic point of view." Toyama, Japan. July 1999.

Mathematical Association of America Invited Address: "Collision of Infinitely Many Solitons and Tiling of a Surface." MAA Meeting at Stanford University. February 1998.

Workshop on Supersymmetry and Integrable Models: "Asymptotic Expansion of a Hermitian Matrix Integral." Chicago, Illinois. June 1997.

Special Session, The 921st AMS Western Section Meeting at Corvallis: "Continuum Solitons and Matrix Integrals." Oregon State University, Corvallis. April 1997.

Special Session, The 920th AMS Eastern Section Meeting at College Park: "Geometry of Commuting Differential Operators." University of Maryland, College Park. April 1997.

Annual Autumn School Lecture Series, Graduate College of Nonlinear Analysis and Geometry: "Topology of the moduli space of Riemann surfaces." Humboldt University of Berlin, Germany. September 1996.

Mathematisches Forschungsinstitut Oberwolfach Workshop, Complex Varieties and Vector Bundles: "Coverings of Riemann surfaces, vector bundles on them, and integrable systems." Oberwolfach, Germany. August 1995.

Mathematical Society of Japan Summer Institute for Youth: Lecture Series "Topology of moduli spaces and integrable systems." Mathematical Society of Japan. July 1995.

ICTP International Conference on Topological and Geometrical Problems Related to Quantum Field Theory: "Moduli of vector bundles on curves and integrable systems." ICTP, Trieste. March 1995.

Mathematisches Forschungsinstitut Oberwolfach Workshop, Integrable Systems from a Quantum Point of View: Invited Address. Oberwolfach, Germany. June 1994.

The Second Mathematical Society of Japan International Research Institute, Topology of Moduli Space of Curves: "The Kontsevich conjectures on matrix tau-functions." Kyoto, Japan. September 1993.

The 31st Taniguchi International Symposium, Field theory and low-dimensional topology: "Matrix Integrals and Integrable Systems." Kansei Gakuin Sengari Seminar House, Sanda, Japan. January 1993.

RIMS International Conference, 3-4 dimensional topology and field theory: Invited Address. RIMS, Kyoto. January 1993.

Special Session, The 877th AMS Western Section Meeting at Los Angeles: "Commuting ordinary versus partial differential operators." University of Southern California, Los Angeles. November 1992.

MPI-Bonn Workshop Complex Geometry: "A characterization of Prym varieties." Max-Planck-Institut fuer Mathematik, Bonn. April 1992.

MPI-Bonn Oberseminar: "Prym varieties and commuting flows on the infinite-dimensional Grassmannians." Max-Planck-Institut fuer Mathematik, Bonn. January 1992.

MPI-Bonn Workshop Complex Geometry: "Vector bundles on curves and commuting differential operators." Max-Planck-Institut fuer Mathematik, Bonn. October 1991.

The 27th Taniguchi International Symposium, Einstein metrics and Yang-Mills connections: "Vector bundles on curves and Grassmannians." Kansei Gakuin Sengari Seminar House, Sanda, Japan. December 1990.

Osaka International Conference on Complex Geometry and Related Topics held in commemoration of 50th anniversary of Osaka University: "Categorical equivalence between vector bundles on algebraic curves and points on Grassmannians." Osaka University, Japan. December 1990.

Special Session, The 862nd AMS Western Section Meeting at Irvine: "A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves." University of California, Irvine. November 1990.

ICM90 Satellite--International Conference on Algebraic Geometry and Analytic Geometry: "Super Grassmannians and Jacobians of super curves." Tokyo, Japan. August 1990.

1990 AMS Summer Research Institute on Dfferential Geometry: "Vector bundles on curves, Grassmannians, and the super-Schottky problem." AMS Summer Research Institute at UCLA. July 1990.

Joint AMS-IMS-SIAM Conference on the Schottky Problem: "A characterization of Jacobians of super curves." University of Massachusetts, Amherst. June 1990.

The 9th Annual Western States Mathematical Physics Meeting: "Super Grassmannians and algebraic super curves." California Institute of Technology, Pasadena. February 1990.

Berkeley-Santa Cruz-Stanford Geometry Conference: "Super Grassmannians and super Riemann surfaces." UC Berkeley. December 1989.

Mathematisches Forschungsinstitut Oberwolfach Workshop, Special Complex Varieties: "Infinite-dimensional Grassmannians, vector bundles on curves and commuting differential operators." Oberwolfach, Germany. August 1989.

The 18th International Conference on Dfferential Geometrical Methods in Theoretical Physics: "Infinite-dimensional orbits of the KP system and vector bundles on Riemann surfaces." Lake Tahoe, California. July 1989.

NATO Advanced Study Institute--Summer School on Physics and Geometry: Lecture Series "Riemann surfaces and the KP system." Lake Tahoe, California. June 1989.

Special Session, The 848th AMS Eastern Section Meeting at Worcester: "A correspondence between an infinite Grassmannian and vector bundles on algebraic curves." College of the Holy Cross, Worcester, Massachusetts. April 1989.

IAS Members Seminar: "Jacobi, Virasoro and Kac-Moody actions on an infinite Grassmannian." The Institute for Advanced Study, Princeton. November 1988.

1987 AMS Summer Research Institute on Theta Functions: "Super KP equation." AMS Summer Research Institute at Bowdoin College. July 1987.

MSRI Conference on Infinite Dimensional Lie Groups: "Schottky problem and infinite dimensional Lie groups." MSRI, Berkeley. May 1984.

MSRI Workshop on Vertex Operators: "Infinite-dimensional formal Lie group--a bridge connecting the linear world and the non-linear world." MSRI, Berkeley. November 1983.

1983 AMS Summer Research Institute on Partial Dfferential Equations: "Linear structure in soliton equations." AMS Summer Research Institute at UC Berkeley. July 1983.

MSRI Workshop on Dfferential Systems: "Linear structure in soliton equations." MSRI, Berkeley. May 1983.

M and Phi--International Conference on Mathematical Physics, Gauge Theory Session: "Instantons and line geometry." Lausanne, Switzerland. August 1979.

"Integrable Systems, Ribbon Graphs, and Eynard-Orantin Formalism." An 8-hour Mini Course, Tsinghua University, Beijing, China. September 2010.

"Mirror Symmetry, Intersection Theory on Moduli Spaces, and Random Matrix Theory." University of Salamanca, Spain. May 2008.

"New Developments in Topological String Theory." Tohoku University, Japan. April 2008.

"A New Point of View in Witten-Kontsevich Theory." Nagoya University, Japan. July 2005.

"Geometry and Matrix Integrals." Nagoya University, Japan. September 2003.

"Algebraic Geometry, Topology, and Analysis of Matrix Integrals." Humboldt University of Berlin, Germany. April-May 2002.

"Algebraic Geometry of Integrable Systems." Humboldt University of Berlin, Germany. November 1995.

"Moduli of Vector Bundles and Hitchin's Hamiltonian Systems." Kyoto University, Japan. July 1995.

"Matrix Integrals, Topology of Moduli Spaces, and Integrable Systems." Kyoto University, Japan. November-December 1994.