Curriculum vitæ. Tomoyuki Arakawa. Representation theory, vertex operator algebras and mathematical physics.

Transcription

1 Curriculum Citæ Tomoyuki Arakawa July 4, 2018 Research areas: Representation theory, vertex operator algebras and mathematical physics. Curriculum vitæ First name and family name: Tomoyuki Arakawa. Nationality: Japanese. Professional address: Research Institute for Mathematical Sciences, Kyoto University, Kyoto Japan Position: Professor. Personal address: 27-4 Yamada-cho Kitashirakawa Sakyo-ku Kyoto Japan Webpage: Academic positions RIMS, Kyoto University, Japan, Professor, April, 2018-present. RIMS, Kyoto University, Japan, Associate Professor, October March, 2018, Nara Women s University, Japan, Associate Professor, April 2005-October Nagoya University, postdoctoral position, April 1999-March 2005.

2 Tomoyuki Arakawa 2 Visiting positions MIT, USA, Visiting Associate Professor, February 2016-January, Instituto de Mathématica e Estatística/IME/USP, Visiting Professor, São Paulo, Brazil, November 15, 2015-December 14, University of Poitiers, France, Visiting Professor, September 29, October 31, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, Visiting Professor, October 31, 2013-January 28, London Mathematical Society Scheme 2, October 9-29, The University of Sydney, Visiting Professor, April 15, 2013-May 15, Nagoya University, Visiting Associate Professor, April 1, 2013-March 31, Education Ph.D. Mathematics, Nagoya University, March Dissertation: Drinfeld functor and finite-dimensional representations of Yangian. Advisor: Tsuchiya Akihiro. M.A. Mathematics, Nagoya University, March B.S. Mathematics, Kyoto University, March Awards 2018 ICM Invited Talk Autumn Prize, Mathematical Society of Japan Algebra Prize, Mathematical Society of Japan The Young Scientist Prize, the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology of Japan Takebe Katahiro Prise, Mathematical Society of Japan.

3 Tomoyuki Arakawa 3 Grants JSPS Grant-in-Aid for Scientific Research (A) No. 17H01086, W-algebras and applications, (43,680,000JPY). JSPS Grant-in-Aid for challenging Exploratory Research No , Geometric methods in vertex algebras, (4,030,000JPY). JSPS Grant-in-Aid for Scientific Research (B) No , New developments in representation theory of W-algebras, (14,820,000JPY). JSPS Grant-in-Aid for challenging Exploratory Research No , New developments of vertex algebra theory, (3,640,000JPY). JSPS Grant-in-Aid for Scientific Research (B) No , A comprehensive research of vertex algebras, especially the W-algebras, (17,030,000JPY). JSPS Grant-in-Aid for Young Scientists (B) No , Field theory and representation theory, (3,500,000JPY). Administrative responsibilities Member of RIMS Research Project 2018 VOAs and Symmetries. Member of the committee of library experts at RIMS. April Co-organiser with Syu Kato and Hiraku Nakajima of RIMS representation theory seminar, October 2011-present. Co-organiser with Karin Baur, Victor Kac and Anne Moeau of a two-weeks program Geometry and Representation Theory at the Erwin Schrödinger institute of Vienna, Austria, January 16-27, Organizer of the conference Perspectives from vertex algebras, Kyoto, July 21-24, Co-organizer with Syu Kato and Hiraku Nakajiama of the conference Representation Theory and Related Topics, Irako, Japan, February 16-20, Co-organizer with Syu Kato and Hiraku Nakajiama of Winter School on Representation Theory, RIMS Kyoto, January 19-23, Co-organizer of the weekly joint colloquium of RIMS and the mathematical department of Kyoto University, April 2012-March Member of the public relations committee at Kyoto University, April March The responsible of the academic affairs staff (responsible for scheduling the lectures, welcoming students, etc) in Mathematics Department, Nara Women s University, April, 2009-March, 2011.

4 Tomoyuki Arakawa 4 Member of the public relations committee at Nara Women s University, April, 2006-March, Panelist of JSPS grant, Panelist of NSF grant, Washington DC, January, Organizer of many local conferences in Japan. Teaching experience 2016 Spring: 18.S998 Introduction to vertex algebras, graduate course, MIT, USA Spring and Autumn:, Seminar on Representation Theory and Vertex Algebras A,B,C,D, Master level, Kyoto University Spring: Mathematical Theory of Symmetries II (lectures on representation theory), undergraduate class (year not specified), Kyoto University Spring: Invitation to Modern Mathematics and Mathematical Sciences, undergraduate class (year not specified), Kyoto University Spring and Autumn: Seminar on Infinite-dimensional Algebras A,B,C,D, Master level, Kyoto University Spring and Autumn: Seminar on Mathematics, undergraduate class, 4th year, Kyoto University Autumn: Mathematical Theory of Symmetries II (lectures on representation theory), undergraduate class (year not specified), Kyoto University Spring: Invitation to Modern Mathematics and Mathematical Sciences, undergraduate class (year not specified), Kyoto University Spring: Invitation to Modern Mathematics and Mathematical Sciences, undergraduate class (year not specified), Kyoto University Spring and Autumn: Seminar on Mathematics, undergraduate class, 4th year, Kyoto University Autumn: Mathematical Theory of Symmetries B (lectures on representation theory), undergraduate class (year not specified), Kyoto University Autumn: Mathematical Theory of Symmetries B (lectures on representation theory), undergraduate class (year not specified), Kyoto University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University.

5 Tomoyuki Arakawa Autumn: Representation theory, undergraduate class, 3rd year, Nara Women s University Autumn: Linear Algebra II, undergraduate class, 1st year, Nara Women s University Autumn: Mathematics à la carte, undergraduate class for general students (year not specified), Nara Women s University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University Spring: Calculus I, undergraduate class, 1st year, Nara Women s University Autumn: Calculus II, undergraduate class, 1st year, Nara Women s University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University Spring: Complex Analysis I, undergraduate class, 3rd year, Nara Women s University Autumn: Complex Analysis II, undergraduate class, 3rd year, Nara Women s University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University Spring: Algebra I, undergraduate class, 3rd year, Nara Women s University Autumn: Algebra II, undergraduate class, 3rd year, Nara Women s University Spring: Representation theory and Mathematical Physics, Master level, Nara Women s University Spring: Algebra I, undergraduate class, 3rd year, Nara Women s University Autumn: Algebra II, undergraduate class, 3rd year, Nara Women s University. Research supervisions (Master and Ph.D students) Since April 2018: Master Supervisor of Soma Sugimoto (RIMS, Kyoto University) Since April 2016: Doctoral Supervisor of Naoki Genra (RIMS, Kyoto University).

6 Tomoyuki Arakawa 6 April March 2016: Master Supervisor of Naoki Genra (RIMS, Kyoto University). Naoki is now a student of doctoral courses at RIMS. Title: Screening operators for W-algebras. Papers from the Master Thesis: Screening operators for W-algebras, Sel. Math. New Ser., published online. April March 2012: Master Supervisor of Ai Matsuda, Nara Women s University. Title: Free field realization of affine Kac-Moody algebra of type A at level 1. April March 2012: Master Supervisor of Mari Nishitani, Nara Women s University. Title: On Weyl s character formula and dimensional formula. April March 2011: Master Supervisor of Yuki Yamamoto, Nara Women s University. Title: On hook length formula of skew Young tableau. April March 2010: Master Supervisor of Miki Sakashita, Nara Women s University. Title: Denominator formula for W -algebras. Publications (articles, lecture notes, preprints) Refereed papers 1. Associated Varieties and Higgs Branches (A Survey), to appear in Contemp. Math. 2. (with A. Premet) Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras, Trans. Moscow Math. Soc. 2017, (with C. Jiang) Coset Vertex Operator Algebras and W-Algebras, C. Sci. China Math. (2017) (with K. Kawasetsu) Quasi-lisse vertex algebras and modular linear differential equations, to appear in Kostant Memorial Volume, Birkhauser. 5. (with A. Moreau) On the irreducibility of associated varieties of W-algebras, J. Alg. 500, 15 April 2018, Pages (with A. Moreau) Sheets and associated varieties of affine vertex algebras, to appear in Adv. Math., Volume 320, 7 November 2017, Pages (with T. Creutzig and A. Linshaw) Cosets of Bershadsky-Polyakov algebras and rational W-algebras of type A, Sel. Math. New Ser., October 2017, Volume 23, Issue 4, pp

7 Tomoyuki Arakawa 7 8. (with K. Kawasetsu, T. Creutzig and A. Linshaw) Orbifolds and cosets of minimal W-algebras, Comm. Math. Phys.. October 2017, Volume 355, Issue 1, pp (with V. Futorny and L.-E. Ramirez) Weight representations of admissible affine vertex algebras, Comm. Math. Phys., 353 (2017), no.3, (with A. Molev) Explicit generators in rectangular affine W-algebras of type A, Lett. Math. Phys. 107(1), 47-59, (with A. Moreau) Joseph ideals and lisse minimal W-algebras, J. Inst. Math. Jussieu, J. Inst. Math. Jussieu, 17 (2018), no. 2, (with W. Wang) Modular affine vertex algebras and baby Wakimoto modules, Proceedings of Symposia in Pure Mathematics, Volume 92 (2016), (with H. Yamada and H. Yamauchi) Vertex operator algebras associated with Z/kZ-codes, to appear in Springer Proceedings in Mathematics & Statistics, Vol Rationality of admissible affine vertex algebras in the category O, Duke Math. J., Volume 165, Number 1 (2016), Rationality of W-algebras: principal nilpotent cases, Ann. Math. 182 (2015), (with T. Kuwabara and F. Malikov) Localization of affine W-algebras, Comm. Math. Phys., April 2015, Volume 335, Issue 1, Associated varieties of modules over Kac-Moody algebras and C 2 -cofiniteness of W-algebras, Int. Math. Res. Notices (2015) Vol Two-sided BGG resolutions of admissible representations, Represent. Theory 18 (2014), (with C.-H. Lam and H. Yamada) Zhu s algebra, C 2 -algebra and C 2 - cofiniteness of parafermion vertex operator algebras, Adv. Math., vol.264 (2014), Rationality of Bershadsky-Polyakov vertex algebras, Comm. Math. Phys., October 2013, Volume 323, Issue 2, W-algebras at the critical level, Contemp. Math., 565, 1-14, A remark on the C 2 -cofiniteness condition on vertex algebras, Math. Z. vol. 270, no. 1-2, , (with P. Fiebig) The linkage principle for restricted critical level representations of affine Kac-Moody algebras, Compos. Math., 148, , 2012.

8 Tomoyuki Arakawa (with F. Malikov) A chiral Borel-Weil-Bott theorem, Adv. Math., 229 (2012) (with P. Fiebig) On the restricted Verma modules at the critical level, Trans. Amer. Math. Soc. 364 (2012), (with D. Chebotarov and F. Malikov) Algebras of twisted chiral differential operators and affine localization of g-modules, Sel. Math. New Ser., vol.17, no. 1, 1-46, Representation theory of W-algebras, II, Adv. Stud. Pure Math. 61(2011), Representation Theory of W-Algebras, Invent. Math., Vol. 169 (2007), no. 2, A New Proof of the Kac-Kazhdan Conjecture, Int. Math. Res. Not Art. ID 27091, 5 pages. 30. Representation Theory of Superconformal Algebras and the Kac-Roan- Wakimoto Conjecture, Duke Math. J., Vol. 130 (2005), No. 3, Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction, Int. Math. Res. Not. 2004, no.15, Drinfeld functor and finite-dimensional representations of Yangian, Comm. Math. Phys. 205 (1999), no. 1, (with T. Suzuki) Duality between sl n (C) and the degenerate affine Hecke algebra, J. Algebra 209 (1998), no. 1, (wih T. Suzuki and A. Tsuchiya) Degenerate double affine Hecke algebra and conformal field theory. Topological field theory, primitive forms and related topics (Kyoto, 1996), 1-34, Progr. Math., 160, Birkhauser, (with T. Nakanishi, K. Oshima and A. Tsuchiya) Spectral decomposition of path space in solvable lattice model. Comm. Math. Phys. 181 (1996), no. 1, Lecture Notes 1. Introduction to W-algebras and their representation theory, In: Callegaro F., Carnovale G., Caselli F., De Concini C., De Sole A. (eds) Perspectives in Lie Theory. Springer INdAM Series, vol 19. Springer. Preprints 1. (with A. Linshaw) Singular support of a vertex algebra and the arc space of its associated scheme, arxiv: [math.rt].

9 Tomoyuki Arakawa 9 2. (with A. Moreau) Arc spaces and chiral symplectic cores, arxiv: [math.rt]. 3. (with T. Creutzig and A. Linshaw) W-algebras as coset vertex algebras, arxiv: [math.qa]. 4. Representation theory of W-algebras and Higgs branch conjecture, submitted to the Proceedings of the ICM (with C.-H. Lam and H. Yamada) Parafermion vertex operator algebras and W-algebras, arxiv: [math.rt]. 6. (with J. van Ekeren) Modularity of relatively rational vertex algebras and fusion rules of regular affine W-algebras, arxiv: [math.rt]. Advanced lectures and mini-courses (outside Japan) November 28 - December 2, 2016: invited as a mentor for the Workshop on W-algebras, University of Melbourne. December 2014-January 2015: Introduction to W-algebras and their representation theory (12 hours lectures), Vertex algebras, W-algebras, and applications, The Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy. April 2013: Introduction to representation theory of W-algebras, a mini-course lecture, the University of Sydney. December 2012: Affine category O and representation theory of W-algebras (3 lectures), Category O : geometry and categorification, Centre International de Rencontres Mathématiques, Luminy. December 2012: Recent development in representation theory of W-algebras, Algebraic Structures in Integrable Systems (3 lectures), Moscow University. June 2005: Representation theory of W-algebras, mini-course lecture, Schroedinger Institute, Vienna, June International Conference talks 1. Coset construction and quantum geometric Langlands program, Vertex Operator Algebras, Number Theory, And Related Topics A Conference In Honor Of Geoffrey Mason, June, 2018, Sacramento California, USA. 2. On recent development of representation theory of W-algebras and related topics. Gauge Theory, Geometric Langlands And Vertex Operator Algebras, March 24, 2018, Perimeter Institute for Theoretical Physics, Canada.

10 Tomoyuki Arakawa Chiralization of Moore-Tachikawa 2d TQFTs, The 3rd KTGU Mathematics Workshop for Young Researchers, February 17, 2018, Kyoto University. 4. Higgs branch conjecture for Class S theories, Affine, Vertex and W- algebras, December 14, 2017, Rome, Italy. 5. W-algebras, Autumn Prize Winner talk, MSJ meeting, Yamagata University, September 12, Higgs branch conjecture for Class S theories Affine, Vertex and W- algebras, Roma, Istituto Nazionale di Alta Matematica, December 11-15, Joseph ideals and Higgs branches, Algebraic Modes of Representations The Canicular Days in honor of Anthony Joseph s 75th birthday, The Weizmann Institute of Science, Israel, July 16-18, Moore-Tachikawa conjecture and vertex algebras, Representation Theory XV IUC, Dubrovnik, Croatia, June 18 25, Moore-Tachikawa conjecture and chiral algebras of class S, 7th Seminar on Conformal Field Theory, Technische Universität Darmstadt, Germany, February 3, Associated varieties of vertex algebras, Construction of genus zero chiral algebras of class S (two talks), Exact operator algebras in superconformal field theories, Perimeter Institute for Theoretical Physics, Canada, December 14-16, Moore-Tachikawa conjecture and chiral algebras of class S, plenary talk, 60th Annual Meeting of the Australian Mathematical Society, Australian National University, Canberra, December 5 8, On the 2d TQFT associated with vertex algebras, Conference in Finite Groups and Vertex Algebras dedicated to Robert L. Griess on the occasion of his 71st birthday, August 26, 2016, Academia Sinica, Taipei, Taiwan. 13. Equivariant affine W-algebras, Nilpotent Orbits and Representation Theory, June 16, 2016, Centro di Ricerca Matematica Ennio De Giorgi (CRM), Pisa, Italy. 14. Deligne exceptional series, Feigin-Frenkel conjecture, and W-algebras, Representation theory and symplectic singularities in honour of Sasha Premet s 60th birthday, April 4, 2016, ICMS, Edinburgh, UK. 15. Modular invariance of trace functions of Kac-Wakimoto admissible representations Lie and Jordan algebras, Their representations and Applications VI, dedicated to Efin Zelmanov s 60th birthday, December 13-19, 2015, Bento Goncalves, Brazil.

11 Tomoyuki Arakawa Sheets and affine vertex algebras, Vertex operator algebra and Related Topics, September 10, 2015, Sichuan University, Chengdu, China. 17. Joseph ideals and lisse minimal W-algebras, Summer School and Workshop on Lie Theory and Representation Theory IV, July 2, 2015, East China Normal University, Shanghai, China. 18. Admissible representations and minimal models of W-algebras I, II, Representation Theory XIV, July 23 and 25, 2015, Dubrovnik, Croatia. 19. Trace functions of Kac-Wakimoto admissible representations, Taitung Workshop on finite groups, VOA and algebraic combinatorics, March 8, Minimal models of W-algebras, Algebraic Lie theory and representation theory, International Centre for Mathematical Sciences (ICMS), Edinburgh, UK, September 1, Feigin-Frenkel, Adamovic-Milas, and Frenkel-Kac-Wakimoto, Workshop Lie theory and mathematical physics, Centre de recherches mathématiques, Université de Montréal, Canada, May 22, The Frenkel-Kac-Raul-Wang conjecture and quantized Drinfeld-Sokolov reduction, Hualien Workshop on Finite Groups, VOA, Algebra Combinatorics and Related Topics, National Dong Hua University, Taiwan, March 22, W-algebras and Vinberg s problem for centralizers, Symmetries in Mathematics and Physics II in honor of Prof. Victor Kac s 70th birthday, IMPA, Rio de Janeiro, Brazil, June 28, An application of affine W-algebras, Taitung Workshop on group theory, VOA and algebraic combinatorics, Taitung University, Taiwan, March 27, Nilpotent orbits and the Kac-Wakimoto conjecture, Conference on Groups, VOAs and Related Structures in Honor of Masahiko Miyamoto, University of Tsukuba, Japan, September 11, Rationality of W -algebras, The XXIX International Colloquium on Group-Theoretical Methods in Physics, Chern Institute of Mathematics Tianjin, China, August 20, Rationality of admissible affine vertex algebras in the category O, Conference on Vertex Operator Algebras, Finite Groups and Related Topics, Academia Sinica, Taiwan December 18, Localization of affine W-algebras at the critical level, Perspectives in Algebraic Lie Theory, Isaac Newton Institute for Mathematical Sciences, September 15, 2011.

12 Tomoyuki Arakawa Rationality and smoothness of W-algebras, Representation Theory of Algebraic Groups and Quantum Groups, Nagoya, Japan, August 2, Varieties of nilpotent orbits, Kac-Moody algebras, and W-algebras, Workshop and Summer School on Lie Theory and Representation Theory II, East China Normal University, Shanghai, China, July 20, Representation Theory of W-algebras, joint AMS-TMS meeting, Tunghai University, Taichung, Taiwan, December 15, Representation theory of W-algebras, International Conference on Algebra in Memory of Kostia Beidar, National Cheng Kung University, Tainan, Taiwan, March Representation theory of -algebras and superconformal algebras, International conference on infinite-dimensional Lie theory, Morningside center of Mathematics Chinese academy of Science, Beijing, China, July Colloquium talks 1. Coset construction and quantum geometric Langlands program, RIMS, Kyoto University, April 18, Vertex algebras and symplectic varieties University of Alberta, March 29, Vertex Algebras and Symplectic Varieties, William J. Spencer Lectures, Kansas State University November 28, 2017, 4. Vertex operator algebras and symplectic varieties, UCSC, USA, March 7, Moore-Tachikawa conjecture and chiral algebras of class S, Sydney UNSW Joint Colloquium, Australia, November 25, Vertex algebras and symplectic varieties, the University of Poitiers, France, November 2, Vertex algebras and symplectic varieties, University of Texas at Arlington, USA, September 30, The Adamović-Milas conjecture and application, University of Zagreb, Croatia, June 1, Pentagonal number theorem and representation theory, University of Virginia, USA, April 21, W-algebras and Frenkel- Kac-Wakimoto conjecture, Academia Sinica, Taiwan, March 12, 2015.

13 Tomoyuki Arakawa W-Algebras as Generalization of Infinite-Dimensional Lie Algebras, Friedrich- Alexander-Universität Erlangen-Nürnberg, Germany, December 3, Chiral Hamiltonian reduction and representation theory, Nagoya, Japan, May 11, BRST reduction and representation theory of W-algebras, RIMS, Kyoto University, Japan, October 13, Character formulae of W-algebras, Osaka University, Osaka, Japan, December 3, Quantum BRST reduction and representation theory, University of Virginia, USA, April 5, Vertex algebras associated with Slodowy slices, RIMS, Kyoto University, Japan, November 27, W-Algebras and their representations, Tohoku University, Sendai, Japan, October 23, Overseas Seminar talks 1. Vertex algebras and symplectic varieties, Algebra and Combinatorics Seminar, North Carolina State University, January 12, Representation theory of W-algebras and Higgs branch conjecture, Algebra Seminar, Kansas State University, November 27, Chiralization of Moore-Tachikawa conjecture, Representation Theory, UMassAmherst, September Vertex algebras and Higgs branche conjecture, MIT Infinite Dimensional Algebra Seminar, September 22, Affine W-algebras, School Seminar, the University of Melbourne, April 27, Coset Construction of W-algebras, Algebra and Number Theory Seminar, UCSC, March 10, GKO construction of minimal series W-algebras, MIT Infinite Dimensional Algebra Seminar, February 17, 3, 201y, MIT, USA. 8. Moore-Tachikawa conjecture and chiral algebras of class S, Séminaire Géométrie Algébrique, Laboratoire Paul Painlevé, Université de Lille, France, January 31, On the 2dTQFT associated with vertex algebras, MIT Infinite Dimensional Algebra Seminar, September 9, 2016, MIT, USA.

14 Tomoyuki Arakawa Beyond C 2 -cofinitenss, Algebra Seminar, June 7, 2016, University of Zagreb, Croatia. 11. Vertex algebras and symplectic varieties, Alegebra Seminar, May 18, 2016, University of Southern California, USA. 12. Vertex algebras and symplectic varieties, CMSA Special Mathematical Physics Seminar, May 13, 2016, Harvard University, USA. 13. Vertex algebras and symplectic varieties, Algebra Seminar, April 22, 2016, University of Virginia, USA. 14. Deligne exceptional series, Feigin-Frenkel conjecture, and W-algebras, Boston University Geometry and Physics Seminar, March 16, 2016, Boston University, USA. 15. Associated varieties of vertex algebras, MIT Infinite Dimensional Algebra Seminar, February 5, 2016, MIT, USA. 16. Associated varieties and chiral algebras of class S, JC String Seminar, Theoretical Physics Tnstitute ICTP-SAIFR, December 11, 2015, Sao Paulo, Brazil. 17. Joseph ideals and lisse minimal W-algebras, Algebra Seminar, Universidade Federal Fluminense, December 4, 2015, Rio de Janeiro, Brazil. 18. Associated varieties of vertex algebras, Algebra Seminar, Universidade de São Paulo, São Paulo, Brazil, November 19, Localization of affine W-algebras at the critical level, Algebra Seminar, Technische Universität Darmstadt, Darmstadt, Germany, October 21, Nilpotent orbits, affine Kac-Moody algebras, and affine W-algebra, Séminaire Caen Cergy Clermont Paris - Théorie des Représentations, Université Diderot-Paris 7, Paris, France, October 17, Orbites nilpotentes et W-algébres affines, Séminaire d algébre de Lyon, Lyon, France, October 9, Nilpotent orbits and affine W-algebras, Séminaire Groupes de Lie et espaces des modules, Université de Genève, Switzerland, October 7, Localization of affine W-algebras at the critical level, Algebra Seminar, Université de Poitiers, France, October 2, Affine W-algebras and their representations, Algebra Seminar, Université de Poitiers, France, December 9, Affine W-algebras and Vinberg s problem for centralizers, Emmy-Noether- Seminar, Erlangen, Germany, December 6, 2013.

15 Tomoyuki Arakawa Feigin-Frenkel center and W-algebras II, Emmy-Noether-Seminar, Erlangen, Germany, November 29, Feigin-Frenkel center and W-algebras I, Emmy-Noether-Seminar, Erlangen, Germany, November 22, Affine W-algebras and Vinberg s problem for centralizers, Algebra Seminar, Sydney University, Australia, April 19, Semi-infinite restriction functors and applications, Emmy-Noether-Seminar, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, December 21, Affine W-algebras, Algebra Seminar, University of York, UK, October 24, Affine W-algebras, Algebra Seminar, the University of Edinburgh, UK, October 18, Affine W-algebras, Algebra Seminar, Birmingham University, UK, October 13, Affine W-algebras, Manchester Algebra Seminar, Manchester University, October 11, Localization of affine W-algebras at the critical level, Algebraic geometry and representation theory seminar, Weizmann institute, Israel, May 30, Admissible affine vertex algebra of type A, Algebraic geometry and representation theory seminar, Weizmann institute, Israel, May 19, Associated varieties of Kac-Wakimoto admissible representations, USC Algebra Seminar, University of Southern California, USA, April 19, Representation theory of W-algebras and superconformal algebras, Infinite- Dimensional Algebra Seminar, MIT, USA, October Representation theory of W-algebras and superconformal algebras, Geometry, Symmetry and Physics Seminar, Yale University, USA, October Quantized reduction and representations of W-algebras, Infinite-Dimensional algebras seminar, UCBerkeley, USA, September 2003.