Updated on 2024/11/22

Information

 

写真a

 
WENG LIN
 
Organization
Faculty of Mathematics Division of Algebra and Geometry Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Joint Graduate School of Mathematics for Innovation （Concurrent）
Title
Professor
Profile
1) Between 1989-98, we developed a theory of relative Bott-Chern secondary characteristic classes, based on which we established an arithmetic Grothendieck-Riemann-Roch theorem for l.c.i. morphisms. 2) We also develop an Arakelov theory for surfaces with respect to singular metrics by establishing an arithmetic Deligne-Riemann-Roch isometry for them. Consequently, we study arithmetic aspect of the moduli spaces of punctured Riemann surfaces by introducing certain natural metrized line bundles related with Weil-Petersson metrics, Takhtajan-Zograf metrics. Intrinsic relations among them, some of which are open problems, are exposed as well. The difficulty here is that classical approach on determinant metric does not work. 3) We introduce genuine non-abelain L functions for global fields, based on a new cohomology, stability and Langlands' theory of Eisenstein series, and expose the relation between these non-abelian Ls and what we call the Arthur periods. Basic properties such as meromorphic continuation and functional equation(s) are established as well. In particular we show that the rank two non-abelian zetas for number fields satisfy the Riemann Hypothesis. 4) We develop a Program on what we call Geometric Arithmetic, in which an approach to non-abelian Class Field Theory using stability and an approach to the Riemann Hypothesis using intersection, together with a study on non-abelian L functions, are included. 5) We initiated an Arakelov approach to the study of what we call Kobayashi-Hitchin correspondence for manifolds aiming at establishing the equivalence between intersection stability and existence of KE metrics. I spent several years in discussion with Mabuchi. These almost weekly discussions prove to be quite crucial to problems involved. I have no formal publication in it. But one can trace them from some papers of Mabuchi. 6) Other works such as metrized version of projective flatness of certain bundles and degenerations of Riemann surfaces are of some importance to the related fields. 7) We are studying zeta functions and general class field theory using stability and Galois representations. In particular, together with Zagier, we establish the Riemann hypothesis for non-abelian zeta functions of elliptic curves on finite fields. 8) We have just published a book on "Zeta Functions for Reductive Groups and Their Zeros" with World Scientific in February 2018. In this book, we develop a basic theory for these functions, establish the spacial uniformity of zeta functions on the equivalence of rank n non-abelian zeta functions and SL(n)-zeta functions, based on Siegel-Langland' theory of Eisenstein series. In particular, we confirm a central conjecture on "Parabolic Reduction, Stability and the Volumes". The key to this is an analytic version of the Mumford'S GIT correspondence between un-stable principle bundles and the parabolic subgroups of the associated reductive groups. This itself is based on an equivalence between Arthur's analytic truncation on the adelic spaces and the geo-arithmetic truncation of stability on principal bundles. Finally, we prove the Riemann hypothesis for our zeta functions. The book consists of 7 parts: Part 1 Non-Abelian Zeta Function Part 2 Rank 2 Zeta Functions Part 3 Eisensetin Periods and Multiple Zeta Functions Part 4 Zeta Functions for Reductive Groups Part 5 Algebraic and Analytic Structures and Riemann Hypothesis Part 6 Geometric Structures and Riemann Hypothesis Appendices (with K. Sugahara) Five Essays On Arithmetic Cohomology Recently, I develop a theory of high rank algebraic codes and construct arithmetic characteristic curves. Most of the works listed above can be found either at xxx.lanl.gov or at MathSciNet.
Homepage
External link

Research Interests・Research Keywords

  • Research theme： non-abelian zeta function for curves

    Keyword： Riemann Hypothesis, zeta fucntions

    Research period： 2021.10 - 2022.3

  • Research theme： p-adic Quantum Gates

    Keyword： p-adic numbers, p-adic quantum bits, p-adic quantum gates, universality of p-adic quantum gates

    Research period： 2020.4 - 2023.4

  • Research theme： arithmetic characteristic curves, arithmetic Higgs bundles

    Keyword： arithmetic characteristic curves, arithmetic Higgs bundles

    Research period： 2019.1 - 2020.3

  • Research theme： Uniformity of zeta functions

    Keyword： zeta function, uniformity

    Research period： 2015.4 - 2020.3

  • Research theme： Stability and Arithmetic Geometry

    Keyword： stability, zeta function

    Research period： 2010.4 - 2015.3

  • Research theme： Zeta Functions for Reductive Groups and Their Zeros

    Keyword： Zeta Functions, Reductive Groups, Riemann Hypothesis

    Research period： 2000.12 - 2020.4

  • Research theme： Arithmetic Aspects of Moduli Spaces of Punctured Riemann Surfaces

    Keyword： Weil-Petersson, Takhtajan-Zograf

    Research period： 2000.3

  • Research theme： Geometric Arithmetic

    Keyword： Non-abelian Class Field Theory, Abelian and Non-Abelian Zeta Functions

    Research period： 1999.6

  • Research theme： Relative Bott-Chern Secondary Characteristic Classes and Arithmetic Grothendieck-Riemann-Roch Theorem for L.C.I. Morphisms

    Keyword： Relative Bott-Chern Secondary Class, Grothendieck-Riemann-Roch Theorem

    Research period： 1990.6

Papers

  • Higher-rank zeta functions and $SL_n$-zeta functions for curves Reviewed International journal

    Lin WENG, Don Zagier

    米国科学アカデミー紀要(PNAS)   PNAS March 24, 2020 117 (12) ( PNAS March 24, 2020 117 (12) )   6398 - 6408   2020.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    Higher-rank zeta functions and $SL_n$-zeta functions for curves, Lin WENG and Don Zagier

    Other Link： https://www.pnas.org/content/117/12/6398

  • Higher rank zeta functions for elliptic curves Reviewed International journal

    L. Weng, D. Zagier

    米国科学アカデミー紀要(PNAS)   PNAS March 3, 2020 117 (9) ( PNAS March 3, 2020 117 (9) )   4546 - 4558   2020.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    Higher rank zeta functions for elliptic curves, L. Weng and D. Zagier

    Other Link： https://www.pnas.org/content/117/9/4546

  • Parabolic reduction, stability and the mass I: Special Linear Groups

    LIN WENG

    RIMS Kôkyûroku 1826   168 - 179   2013.3

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    Language：English   Publishing type：Research paper (other academic)  

  • Deligne pairing and determinant bundle Reviewed

    Indranil Biswas, Georg Schumacher, Lin Weng

    Electronic Research Announcements in Mathematical Sciences   18   91 - 96   2011.12

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    Language：English   Publishing type：Research paper (scientific journal)  

    Let X → S be a smooth projective surjective morphism, where X and S are integral schemes over ℂ. Let L0,L1, · · ·,Ln-1,Ln be line bun- dles over X. There is a natural isomorphism of the Deligne pairing 〈L0, · · ·,Ln〉 with the determinant line bundle Det(⊕ n/i=0(Li - OX)).

    DOI： 10.3934/era.2011.18.91

  • Stability and arithmetic: an extract of essence Invited Reviewed

    Lin WENG

    Algebraic number theory and related topics 2008, 187–220, RIMS Kôkyûroku Bessatsu, B19, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010   2011.10

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    Stability and arithmetic: an extract of essence, Algebraic number theory and related topics 2008, 187–220, RIMS Kôkyûroku Bessatsu, B19, Res. Inst. Math. Sci. (RIMS), Kyoto, 2010

  • Symmetries and the Riemann Hypothesis Invited Reviewed

    Lin WENG

    Advanced Studies in Pure Mathematics   58   2010.6

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    Language：English   Publishing type：Research paper (other academic)  

    Symmetries and the Riemann Hypothesis

  • Stability and Arithmetic Reviewed

    Lin WENG

    Advanced Studies in Pure Mathematics   58   2010.6

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    Language：English   Publishing type：Research paper (other academic)  

    Stability and Arithmetic

  • Zeta Functions for Sp(2n), appendix to The Riemann hypothesis for Weng's zeta function of Sp(4) over Q by M. Suzuki Reviewed International journal

    Lin WENG

    Journal of Number Theory   2009.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    Zeta Functions for Sp(2n)

  • Zeta Functions for G_2 and Their Zeros Reviewed International journal

    M. Suzuki and L. Weng

    International Mathematics Research Notice (IMRN)   2009.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    Zeta Functions for G_2 and Their Zeros

  • The asymptotic behavior of the Takhtajan-Zograf metric Reviewed International journal

    K. Obitsu, W.-K. To and L. Weng

    Communications in Mathematical Physics   2008.11

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    Language：English   Publishing type：Research paper (scientific journal)  

    The asymptotic behavior of the Takhtajan-Zograf metric

  • Deligne products of line bundles over moduli spaces of curves Reviewed

    L. Weng, D. Zagier

    Communications in Mathematical Physics   281 ( 3 )   793 - 803   2008.8

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    Language：English   Publishing type：Research paper (scientific journal)  

    We study Deligne products for forgetful maps between moduli spaces of marked curves by offering a closed formula for tautological line bundles associated to marked points. In particular, we show that the Deligne products for line bundles on the total spaces corresponding to "forgotten" marked points are positive integral multiples of the Weil-Petersson bundles on the base moduli spaces.

    DOI： 10.1007/s00220-008-0494-5

  • Volume of truncated fundamental domains Reviewed

    Henry H. Kim, Lin Weng

    Proceedings of the American Mathematical Society   135 ( 6 )   1681 - 1688   2007.6

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1090/S0002-9939-07-08784-9

  • A Geometric Approach to L-Functions

    Weng, Lin

    The Conference on L-Functions   2007.2

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    Language：English   Publishing type：Research paper (other academic)  

    Other Link： http://www.worldscibooks.com/mathematics/6363.html

  • A Rank Two Zeta and Its Zeros International journal

    Weng, Lin

    J. Ramanujan Math. Soc.   2006.10

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    Language：English   Publishing type：Research paper (scientific journal)  

    Other Link： http://www.ramanujanmathsociety.org/jrmsAbst/paper1-Sept06.pdf

  • Geometric Arithmetic: A Program

    Weng, Lin

    Arithmetic Geometry and Number Theory   2006.8

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    Language：English   Publishing type：Research paper (other academic)  

    Other Link： http://www.worldscibooks.com/mathematics/6115.html

  • Non-abelian zeta functions for function fields Reviewed

    Lin Weng

    American Journal of Mathematics   127 ( 5 )   973 - 1017   2005.10

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    Language：English   Publishing type：Research paper (scientific journal)  

    In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields. More precisely, We first introduce new yet genuine non-abelian zeta functions for curves defined over finite fields, by a "weighted count" on rational points over the corresponding moduli spaces of semi-stable vector bundles using moduli interpretation of these points. Then we define non-abelian L-functions for curves over finite fields using integrations of Eisenstein series associated to L2-automorphic forms over certain generalized moduli spaces.

    DOI： 10.1353/ajm.2005.0035

  • L2-Metrics, Projective Flatness and Families of Polarized Abelian Varieties

    To, Wing-Keung; Weng, Lin

    Transactions of American Mathematical Society   356 ( 7 )   2685 - 2707   2004.3

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    Language：English  

    L^2-metrics, projective flatness and
    families of polarized abelian varieties.

    DOI： 10.1090/S0002-9947-03-03488-3

    Other Link： http://www.ams.org/tran/2004-356-07/S0002-9947-03-03488-3/S0002-9947-03-03488-3.pdf

  • Refined Brill-Noether Locus Non-Abelian Zeta Functions for Elliptic Curves

    Weng, Lin

    Algebraic geometry in East Asia   2002.10

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    Language：English  

    Refined Brill-Noether locus non-abelian zeta functions
    for elliptic curves.

  • Zeta Functions defined by Two Polynomials

    Matsumoto, K.; Weng, Lin

    Number Theoretic Methods   2002.10

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    Language：English   Publishing type：Research paper (other academic)  

  • Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces Reviewed

    Wing Keung To, Lin Weng

    Pacific Journal of Mathematics   197 ( 2 )   441 - 489   2001.2

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    We show that a family of line bundles of degree zero over a plumbing family of Riemann surfaces with a separating (resp. non-separating) node p admits a nice (resp. almost nice) family of flat p-singular Hermitian metrics. As a consequence, we give necessary and sufficient conditions for a family of line bundles over such families of Riemann surfaces to admit an (almost) nice family of p-singular Hermitian metrics which are admissible with respect to the canonical/hyperbolic (1,1)-forms on the Riemann surfaces.

    DOI： 10.2140/pjm.2001.197.441

  • Ω-admissible theory II. Deligne pairings over moduli spaces of punctured Riemann surfaces Reviewed

    Lin Weng

    Mathematische Annalen   320 ( 2 )   239 - 283   2001.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    In Part I, Deligne-Riemann-Roch isometry is generalized for punctured Riemann surfaces equipped with quasi-hyperbolic metrics. This is achieved by proving the Mean Value Lemmas, which explicitly explain how metrized Deligne pairings for ω-admissible metrized line bundles depend on ω. In Part II, we first introduce several line bundles over Knudsen-Deligne-Mumford compactification of the moduli space (or rather the algebraic stack) of stable N-pointed algebraic curves of genus g, which are rather natural and include Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles. Then we use Deligne-Riemann-Roch isomorphism and its metrized version (proved in Part I) to establish some fundamental relations among these line bundles. Finally, we compute first Chern forms of the metrized Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles by using results of Wolpert and Takhtajan-Zograf, and show that the so-called Takhtajan-Zograf metric on the moduli space is algebraic.

    DOI： 10.1007/PL00004473

  • Green's Functions for Quasi-Hyperbolic Metrics on Degenerating Riemann Surfaces with a Separating Node International journal

    To, Wing-Keung; Weng, Lin

    Annals of Global Analysis and Geometry   1999.12

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  • Green's Functions for Quasi-Hyperbolic Metrics on Degenerating Riemann Surfaces with a Separating Node Reviewed

    Wing Keung To, Lin Weng

    Annals of Global Analysis and Geometry   17 ( 3 )   239 - 265   1999.1

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    In this article, we consider a family of compact Riemann surfaces of genus q ≥ 2 degenerating to a Riemann surface with a separating node and many non-separating nodes. We obtain the asymptotic behavior of Green's functions associated to a continuous family of quasi-hyperbolic metrics on such degenerating Riemann surfaces.

    DOI： 10.1023/A:1006506623667

  • Ω-Admissible theory Reviewed

    Lin Weng

    Proceedings of the London Mathematical Society   79 ( 3 )   481 - 510   1999.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1112/S0024611599011995

  • Curvature of the L2-metric on the direct image of a family of Hermitian-Einstein vector bundles Reviewed

    Wing Keung To, Lin Weng

    American Journal of Mathematics   120 ( 3 )   649 - 661   1998.6

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    For a holomorphic family of simple Hermitian-Einstein holomorphic vector bundles over a compact Kähler manifold, the locally free part of the associated direct image sheaf over the parameter space forms a holomorphic vector bundle, and it is endowed with a Hermitian metric given by the L2 pairing using the Hermitian-Einstein metrics. Our main result in this paper is to compute the curvature of the L2-metric. In the case of a family of Hermitian holomorphic line bundles with fixed positive first Chern form and under certain curvature conditions, we show that the L2-metric is conformally equivalent to a Hermitian-Einstein metric. As applications, this proves the semi-stability of certain Picard bundles, and it leads to an alternative proof of a theorem of Kempf.

  • Standard modules of level 1 for sl̂2 in terms of virasoro algebra representations Reviewed

    Lin Weng

    Communications in Algebra   26 ( 2 )   613 - 625   1998.1

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    DOI： 10.1080/00927879808826151

  • The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces Reviewed

    Wing Keung To, Lin Weng

    Manuscripta Mathematica   93 ( 4 )   465 - 480   1997.8

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    In this article, we consider a family of compact Riemann surfaces of genus q ≥ 2 degenerating to a Riemann surface of genus q-1 with a non-separating node. We show that the Green's functions associated to a continuous family of quasi-hyperbolic metrics on such degenerating Riemann surfaces simply degenerate to that on the smooth part of the noded Riemann surface.

  • Analytic torsions of spheres Reviewed

    Lin Weng, Yuching You

    International Journal of Mathematics   7 ( 1 )   109 - 125   1996.2

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    DOI： 10.1142/S0129167X96000074

  • A result on bicanonical maps of surfaces of general type Reviewed

    Lin Weng

    Osaka Journal of Mathematics   32 ( 2 )   467 - 473   1995.6

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  • Singular moduli and the arakelov intersection Reviewed

    Lin Weng

    tohoku mathematical journal, second series   47 ( 3 )   345 - 356   1995.1

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    The values of the modular j-function at imaginary quadratic arguments in the upper half plane are usually called singular moduli. In this paper, we use the Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as a degenerate one of Gross and Zagier on Heegner points and derivatives of L-series, and is parellel to the result of Gross and Zagier on singular moduli.

    DOI： 10.2748/tmj/1178225521

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Books

  • Zeta Functions for Reductive Groups and Their Zeros

    Lin WENG（Role：Sole author）

    World Scientific  2018.2 

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    Responsible for pages：pp 528+xxvii   Language：English   Book type：Scholarly book

    Zeta Functions for Reductive Groups and Their Zeros

    Other Link： https://www.worldscientific.com/worldscibooks/10.1142/10723

  • Zeta functions of reductive groups and their zeros

    Lin Weng

    World Scientific Publishing Co. Pte Ltd  2018.2 

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    Language：English  

    This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields. Namely, the geometric one, built up from stability of principal lattices and an arithmetic cohomology theory, and the analytic one, from Langlands' theory of Eisenstein systems and some techniques used in trace formula, respectively. Apparently different, they are unified via a Lafforgue type relation between Arthur's analytic truncations and parabolic reductions of Harder-Narasimhan and Atiyah-Bott. Dominated by the stability condition and/or the Lie structures embedded in, these zeta functions have a standard form of the functional equation, admit much more refined symmetric structures, and most surprisingly, satisfy a weak Riemann hypothesis. In addition, two levels of the distributions for their zeros are exposed, i.e. a classical one giving the Dirac symbol, and a secondary one conjecturally related to GUE. This book is written not only for experts, but for graduate students as well. For example, it offers a summary of basic theories on Eisenstein series and stability of lattices and arithmetic principal torsors. The second part on rank two zeta functions can be used as an introduction course, containing a Siegel type treatment of cusps and fundamental domains, and an elementary approach to the trace formula involved. Being in the junctions of several branches and advanced topics of mathematics, these works are very complicated, the results are fundamental, and the theory exposes a fertile area for further research.

    DOI： 10.1142/9789813230651

  • Algebraic and Arithmetic Structures of Moduli Spaces

    Iku Nakamura and Lin WENG (eds)

    Japan Math Soc  2010.6 

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    Responsible for pages：58, 479   Language：English   Book type：Scholarly book

    Algebraic and Arithmetic Structures of Moduli Spaces

  • Conference on L-Functions

    Weng, Lin; Kaneko, Masanobu (eds)（Role：Edit）

    World Scientific  2007.1 

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    Language：English   Book type：Scholarly book

    Other Link： http://www.worldscibooks.com/mathematics/6363.html

  • Arithmetic Geometry and Number Theory

    Weng, Lin; Nakamura, Iku (eds)（Role：Edit）

    World Scientific  2006.8 

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    Language：English   Book type：Scholarly book

    Other Link： http://www.worldscibooks.com/mathematics/6115.html

  • Hyperbolic Metrics, Selberg Zeta Functions and Arakelov Theory for Punctured Riemann Surfaces

    Weng, Lin（Role：Sole author）

    Math Dept, Osaka University  1998.5 

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    Responsible for pages：Lecture Note Series in Math. Vol.6   Language：English   Book type：Scholarly book

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Presentations

  • Zeta Functions and Their Zeros Invited

    翁 林

    2014.7 

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    Event date： 2014.7

    Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Venue：北海道大学   Country：Japan  

    Zeta Functions and Their Zeros

  • Eisenstein periods I,II International conference

    翁 林

    Bundles over Surfaces and Eisenstein Periods for Loop Groups  2014.7 

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    Event date： 2014.6 - 2014.7

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Kyushu University   Country：Japan  

    Bundles over Surfaces and Eisenstein Periods for Loop Groups

  • Cohen-Lenstra Heuristics for Relative Shafarevich-Tate Groups Invited International conference

    翁 林

    7th China-Japan Seminar on Number Theory  2013.10 

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    Event date： 2013.10 - 2013.11

    Language：English   Presentation type：Oral presentation (general)  

    Venue：九州大学   Country：Japan  

    Lin WENG, Cohen-Lenstra Heuristics for Relative Shafarevich-Tate Groups, 7th China-Japan Seminar on Number Theory

  • Global adelic cohomology groups for arithmetic varieties Invited International conference

    LIN WENG

    Pan Asia Number Theory 2013  2013.7 

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    Event date： 2013.7

    Language：English   Presentation type：Oral presentation (general)  

    Venue：VIASM, Hanoi   Country：Viet Nam  

    Global adelic cohomology groups for arithmetic varieties, Pan Asia Number Theory 2013

  • General Uniformity of Zeta Functions Invited International conference

    翁 林

    Global invariants and moduli spaces  2013.5 

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    Event date： 2013.5

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Korea Institute for Advanced Studies   Country：Korea, Republic of  

    General Uniformity of Zeta Functions, Global invariants and moduli spaces, KIAS

    Other Link： http://home.kias.re.kr/MKG/h/WGIMS2013/?pageNo=182

  • Higher rank zeta functions and Riemann Hypothesis for elliptic curves Invited International conference

    LIN WENG

    Arithmetic and Algebraic Geometry 2013  2013.1 

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    Event date： 2013.1

    Language：English  

    Venue：Univ of Tokyo   Country：Japan  

    Higher rank zeta functions and Riemann Hypothesis for elliptic curves, Arithmetic and Algebraic Geometry 2013

  • Higher rank zeta functions and Riemann Hypothesis for elliptic curves Invited International conference

    LIN WENG

    Arithmetic and Algebraic Geometry 2013  2013.1 

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    Event date： 2013.1

    Language：English  

    Venue：Univ of Tokyo   Country：Japan  

    researchmap

  • Non-abelian Zeta Functions for Elliptic Curves and Their Zeros Invited International conference

    LIN WENG

    2012 Conference on L Functions  2012.8 

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    Event date： 2012.8

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Jeju   Country：Korea, Republic of  

    Non-abelian Zeta Functions for Elliptic Curves and Their Zeros, 2012 Conference on L Functions, Jeju, S. Korea

    Other Link： http://workshop.kias.re.kr/CLF2012/

  • Non-Abelian Zeta Functions Invited International conference

    LIN WENG

    p-adic Modular Forms and Arithmetic  2012.6 

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    Event date： 2012.6

    Language：English   Presentation type：Oral presentation (general)  

    Venue：UCLA   Country：United States  

    Non-Abelian Zeta Functions, p-adic Modular Forms and Arithmetic, June 18-23, 2012, UCLA

    Other Link： http://www.math.ucla.edu/~galois07/Conference_12/

  • Tamagawa number conjecture and new zeta functions for Riemann surfaces Invited International conference

    LIN WENG

    Symposium on Arithmetic & Geometry  2012.6 

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    Event date： 2012.6

    Language：English   Presentation type：Oral presentation (general)  

    Venue：Kyushu Univ   Country：Japan  

    Tamagawa number conjecture and new zeta functions for Riemann surfaces, Symposium on Arithmetic & Geometry, Kyushu Univ, Japan

    Other Link： http://www2.math.kyushu-u.ac.jp/~weng/conf2012.html

  • Parabolic reduction, stability and volumes of fundamental domains International conference

    翁林

    Automorphic forms and automorphic functions  2012.1 

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    Event date： 2012.1

    Presentation type：Oral presentation (general)  

    Venue：RIMS, 京都大学・京都   Country：Japan  

    Parabolic reduction, stability and volumes of fundamental domains, Automorphic forms and automorphic functions, RIMS, Kyoto Univ (2012.1.19)

  • A local family index theorem in log geometry Invited International conference

    翁林

    Tokyo-Seoul conference in mathematics  2011.12 

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    Event date： 2011.12

    Presentation type：Oral presentation (general)  

    Venue：東京大学・東京   Country：Japan  

    A local family index theorem in log geometry, Tokyo-Seoul conference in mathematics, Tokyo Univ (2011.12.3)

  • A construction of zeta functions Invited

    翁林

    2011.11 

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    Event date： 2011.11 - 2011.12

    Presentation type：Public lecture, seminar, tutorial, course, or other speech  

    Venue：京都大学   Country：Japan  

    A construction of zeta functions, Intensive Lectures at Kyoto Univ (2012.11. 28 -12. 2)

  • Relative Bott-Chern secondary characteristic classes and arithmetic Riemann-Roch theorem Invited International conference

    翁林

    Number Theory and related topics  2011.6 

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    Event date： 2011.6 - 2012.6

    Presentation type：Oral presentation (general)  

    Venue：中国科学技術大学・中国   Country：China  

    Relative Bott-Chern secondary characteristic classes and arithmetic Riemann-Roch theorem, Number Theory and related topics, USTC (2011.6.7)

  • A Construction of Non-Abelian L-Functions Invited International conference

    Lin WENG

    Workshop on L-Functions  2011.4 

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    Event date： 2011.4

    Presentation type：Oral presentation (general)  

    Venue：FUKUOKA   Country：Japan  

    A Construction on Non-Abelian L-Functions, Workshop on L-Functions, Fukuoka, Japan (2011.4.23)

    Other Link： http://www2.math.kyushu-u.ac.jp/~weng/conf.html

  • Relative Bott-Chern Secondary Characteristic Classes Invited International conference

    Lin WENG

    Symposium on Complex Geometry  2010.7 

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    Event date： 2010.7

    Presentation type：Oral presentation (general)  

    Venue：Institute of Mathematics Research, The University of Hong Kong  

    Relative Bott-Chern Secondary Characteristic Classes, Symposium on Complex Geometry, Univ. Hong Kong, Hong Kong (2010.7.23)

  • Arithmetic Riemann-Roch and Geometry of Riemann Surfaces Invited International conference

    Lin WENG

    Lectures on Spectral Invariants and Moduli Spaces  2010.6 

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    Event date： 2010.6

    Presentation type：Oral presentation (general)  

    Venue：Korea Institute for Advanced Studies   Country：Korea, Republic of  

    Arithmetic Riemann-Roch and Geometry of Riemann Surfaces, KIAS, S. Korea (2010.6.22)

  • Zeta Functions for (G,P)/Q Invited International conference

    Lin WENG

    Zeta Function Days in Seoul  2009.9 

    　More details

    Event date： 2009.8 - 2009.9

    Presentation type：Oral presentation (general)  

    Venue：Seoul   Country：Korea, Republic of  

    Zeta Functions for (G,P)/Q

    Other Link： http://math.yonsei.ac.kr/haseo/ZFD2009/

  • Stability and Arithmetic Invited International conference

    Lin WENG

    Algebraic Number Theory and Related Topics  2008.12 

    　More details

    Event date： 2008.12

    Presentation type：Oral presentation (general)  

    Venue：RIMS, Kyoto University   Country：Japan  

    Lin WENG, Stability and Arithmetic, Algebraic Number Theory and Related Topics, RIMS, Kyoto University, Dec 11, 2008

  • Symmetries and the Riemann Hypothesis Invited

    Lin WENG

    Algebraic Geometry and its new developments  2008.11 

    　More details

    Event date： 2008.11

    Presentation type：Oral presentation (general)  

    Venue：Kyoto University   Country：Japan  

    Lin WENG, Symmetries and the Riemann Hypothesis, Algebraic Geometry and its new developments, Algebraic Geometry and its recent developments, Kyoto University, Nov 21, 2008

  • Symmetries and the Riemann Hypothesis Invited International conference

    Lin WENG

    L functions in Arithmetic and Geometry  2008.6 

    　More details

    Event date： 2008.6 - 2008.8

    Presentation type：Oral presentation (general)  

    Venue：Muenster Universty   Country：Germany  

    Lin Weng, Symmetries and the Riemann Hypothesis, L-Functions in Arithmetic and Geometry, Muenster, Germany, 06,26, 2008

  • ARAKELOV GEOMETRY AND COMPLEX GEOMETRY(?) Invited

    翁林（LIN WENG）

    日本数学会１９９８年春季総合分科会  1998.3 

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    Presentation type：Oral presentation (invited, special)  

    Country：Japan  

    ARAKELOV GEOMETRY AND COMPLEX GEOMETRY(?), Japan Math. Soc Annual Meeting (Spring) 1998

  • Deligne Pairings over Moduli Spaces of Marked Stable Curves Invited

    Lin WENG

    Symposium of Algebra (1999)  1999.8 

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    Venue：Tokyo Univ   Country：Japan  

    Deligne Pairings over Moduli Spaces of Marked Stable Curves, at 44th Symposium of Algebra, Tokyo Univ, Tokyo(1999)

  • New Local and Global Non-Abelian Zeta Functions for Elliptic Curves Invited International conference

    Lin WENG

    China-Japan Seminar (2nd)  2001.3 

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    Venue：Izuka   Country：Japan  

    New Local and Global Non-Abelian Zeta Functions for Elliptic Curves, at China-Japan Seminar (2nd), Izuka, Japan (2001)

  • Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves Invited International conference

    Lin WENG

    Algebraic Geometry in East Asia  2001.8 

    　More details

    Country：Japan  

    Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves, at Algebraic Geometry in East Asia, Kyoto, Japan (2001)

  • New Non-Abelian Zeta Functions Invited International conference

    Lin WENG

    Riemann Hypothesis Conference (2ed)  2002.5 

    　More details

    Venue：Courant Institute of Math. Sciences, NYU   Country：United States  

    New Non-Abelian Zeta Functions, at Riemann Hypothesis Conference (2ed), Courant Institute, USA, 2002

  • New Non-Abelian Zeta Functions Invited International conference

    Lin WENG

    L-Functions in Arithmetic  2002.9 

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    Venue：Muenster Universty   Country：Germany  

    New Non-Abelian Zeta Functions, at L Function in Arithmetic, Muenster, Germany, (2002)

  • New Non-Abelian Zeta Functions Invited

    Lin WENG

    Algebraic Number Theory and Related Topics  2002.12 

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    Venue：RIMS, Kyoto Univ   Country：Japan  

    New Non-Abelian Zeta Functions, at Algebraic Number Theory and Related Topics, RIMS, Kyoto, Japan (2002)

  • Weil-Petersson Metrics, Takhtajan-Zograf Metrics and Their Degenerations Invited International conference

    Lin WENG

    Complex Geometry in Tokyo  2002.12 

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    Venue：TIT   Country：Japan  

    Weil-Petersson Metrics, Takhtajan-Zograf Metrics and Their Degenerations, at Complex Geometry in Tokyo, TIT, Tokyo, Japan (2002)

  • NON-ABELIAN ZETA FUNCTIONS Invited

    翁林(Lin WENG)

    日本数学会2003年秋季総合分科会  2003.9 

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    Presentation type：Oral presentation (invited, special)  

    Venue：千葉大学   Country：Japan  

    Non-abelian zeta functions, , Japan Math. Soc Annual Meeting (Autumn) 2003

  • Micro Reciprocity Law, Tannakian Category and Non-abelian Class Field Theory Invited International conference

    Lin WENG

    Conference on Non-Commutative Number Theory  2003.9 

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    Venue：Durham   Country：United Kingdom  

    Micro Reciprocity Law, Tannakian Category and Non-abelian Class Field Theory, at Conference on Non-Commutative Number Theory, Durham, UK(2003)

  • Stability in Arithmetic and Geometry Invited International conference

    Lin WENG

    Differential Geometry in Tokyo  2004.12 

    　More details

    Venue：TIT   Country：Japan  

    Stability in Arithmetic and Geometry, at Differential Geometry in Tokyo, TIT, Tokyo, Japan (2004)

  • Non-Abelian L Functions for Number Fields Invited International conference

    Lin WENG

    Algebraic Geometry and Number Theory  2005.6 

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    Venue：Euler Institute, St Petersberg, Russia   Country：Russian Federation  

    Non-Abelian L Functions for Number Fields, at Algebraic Geometry and Number Theory, Euler Institure, St Petersberg, Russia (2005)

  • Non-Abelian L-Functions Invited International conference

    Lin WENG

    Conference on L-Functions  2006.2 

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    Venue：Fukuoka   Country：Japan  

    Non-Abelian L-Functions, at Conference on L-Functions, Fukuoka, Japan(2006)

  • General Class Field Theory Invited International conference

    Lin WENG

    Euler 300: Arithmetic Geometry  2007.6 

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    Presentation type：Oral presentation (general)  

    Venue：Euler Institute, St Petersberg   Country：Russian Federation  

    Lin WENG, General Class Field Theory, Euler 300: Arithmetic Geometry, 06, 2007

  • General Class Field Theory Invited International conference

    Lin WENG

    Algebraic and Arithmetic Structures of Moduli Spaces  2007.9 

    　More details

    Presentation type：Oral presentation (general)  

    Venue：Sapporo   Country：Japan  

    Lin WENG, General Class Field Theory, Algebraic and Arithmetic Structures of Moduli Spaces, Sapporo, Japan, 09,2007

    Other Link： http://coe.math.sci.hokudai.ac.jp/sympo/moduli2007/

  • Stability in Arithmetic Invited International conference

    L. Weng

    Complex Geometry in Osaka  2007.11 

    　More details

    Presentation type：Oral presentation (general)  

    Venue：Osaka   Country：Japan  

    Lin WENG, Stability in Arithmetic, Complex geometry in Osaka, Japan, 11, 2007

  • Motivic Euler Product and Its Applications Invited International conference

    翁 林

    Arithmetic and Algebraic Geometry 2014  2014.1 

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    Language：English   Presentation type：Oral presentation (general)  

    Venue：東京大学   Country：Japan  

    Lin WENG, Motivic Euler Product and Its Applications, Arithmetic and Algebraic Geometry 2014, Tokyo Univ

▼display all

MISC

Academic Activities

  • 座長（Chairmanship） International contribution

    Bundles over Surfaces and Eisenstein Periods for Loop Groups  （ Kyushu University Japan ） 2014.6 - 2014.7

    　More details

    Type：Competition, symposium, etc. 

  • 主催 International contribution

    Bundles over Surfaces and Eisenstein Periods for Loop Groups  （ Kyushu University Japan ） 2014.6 - 2014.7

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    First Kyushu Joint Seminar  （ Kyushu University, Fukuoka Japan ） 2013.5

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Symposium on Automorphic Functions and Arithmetic Geometry: One for Prof. L. Lafforgue's visit  （ Kyushu University, Fukuoka Japan ） 2013.4

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    Type：Competition, symposium, etc. 

  • 主催 International contribution

    Symposium on Automorphic Functions and Arithmetic Geometry: One for Prof. L. Lafforgue's visit  （ Kyushu University, Fukuoka Japan ） 2013.4

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    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Symposium on Arithmetic Geometry  （ Kyushu Univ Japan ） 2012.10

    　More details

    Type：Competition, symposium, etc. 

  • 主催 International contribution

    Symposium on Arithmetic Geometry  （ Kyushu University, Fukuoka Japan ） 2012.10

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Symposium on Arithmetic & Geometry  （ Kyushu Univ Japan ） 2012.6

    　More details

    Type：Competition, symposium, etc. 

  • 主催 International contribution

    Symposium on Arithmetic & Geometry  （ Kyushu University, Fukuoka Japan ） 2012.6

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Workshop on L-Functions  （ FUKUOKA Japan ） 2011.4

    　More details

    Type：Competition, symposium, etc. 

  • Organizer International contribution

    Workshop on L-Functions  （ FUKUOKA Japan ） 2011.4

    　More details

    Type：Competition, symposium, etc. 

  • Organizer International contribution

    Algebraic and Arithmetic Aspects of Moduli Spaces  （ Sapporo Japan ） 2007.9 - Present

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Algebraic and Arithmetic Structures of Moduli Spaces  （ Sapporo Japan ） 2007.9 - 2019.6

    　More details

    Type：Competition, symposium, etc. 

  • Organizer International contribution

    Conference on L-Functions  （ FUKUOKA Japan ） 2006.2 - Present

    　More details

    Type：Competition, symposium, etc. 

    Number of participants：130

  • 不明

    Conference on L-Functions  （ Fukuoka Japan ） 2006.2

    　More details

    Type：Competition, symposium, etc. 

  • 不明 International contribution

    Arithmetic Geometry and Number Theory  （ Karatsu Japan ） 2005.3 - Present

    　More details

    Type：Competition, symposium, etc. 

  • Organizer International contribution

    Arithmetic Geometry and Number Theory  （ KARATSU Japan ） 2005.3 - 2022.3

    　More details

    Type：Competition, symposium, etc. 

  • 不明

    Towards IC Stability  （ Japan ） 2004.5 - Present

    　More details

    Type：Competition, symposium, etc. 

  • Organizer

    Towards IC Stability  （ Japan ） 2004.1 - Present

    　More details

    Type：Competition, symposium, etc. 

▼display all

Educational Activities

  • For the undergraduate study,
    we currently follow the tradition of this institute in choosing textbooks and
    in evaluating studends. Particularly, we assign many tutorial problems for our
    students in helping them to understand what has been taught in the class.
    Normally, we spend lots of time to explain many of these problems as well.
    The results are quite encouraging. The first half of 2014 was a tough one.
    Simply too heavy.

    For graduate study, we bring the students to the up-most frontier of the
    current research while explaining the basic materials, and encourage the students
    to have their independent thinking towards mathematics.

Class subject

  • 線形代数学Ⅱ

    2023.10 - 2024.3   Second semester

  • 線形代数学II

    2023.10 - 2024.3   Second semester

  • 代数学III

    2023.10 - 2024.3   Second semester

  • 代数幾何学大意

    2023.10 - 2024.3   Second semester

  • 数学特論１

    2023.10 - 2024.3   Second semester

  • 数学特論１

    2023.10 - 2024.3   Second semester

  • 代数学Ⅲ

    2023.10 - 2024.3   Second semester

  • 代数幾何学大意

    2023.10 - 2024.3   Second semester

  • 入門線形代数II

    2023.6 - 2023.8   Summer quarter

  • 線形代数学Ⅰ

    2023.4 - 2023.9   First semester

  • 線形代数学I

    2023.4 - 2023.9   First semester

  • 数学特論2

    2023.4 - 2023.9   First semester

  • 数論大意

    2023.4 - 2023.9   First semester

  • 数論大意

    2023.4 - 2023.9   First semester

  • 数学特論２

    2023.4 - 2023.9   First semester

  • 入門線形代数I

    2023.4 - 2023.6   Spring quarter

  • 代数学Ⅲ

    2022.10 - 2023.3   Second semester

  • 代数学III

    2022.10 - 2023.3   Second semester

  • 線形代数学Ⅱ

    2022.10 - 2023.3   Second semester

  • 入門線形代数学II

    2022.6 - 2022.8   Summer quarter

  • 数理科学特論１４

    2022.4 - 2022.9   First semester

  • 線形代数学I

    2022.4 - 2022.9   First semester

  • 数理科学特別講義XⅣ

    2022.4 - 2022.9   First semester

  • 線形代数学Ⅰ

    2022.4 - 2022.9   First semester

  • 入門線形代数学I

    2022.4 - 2022.6   Spring quarter

  • 線形代数学Ⅱ

    2021.10 - 2022.3   Second semester

  • 線形代数学・同演習I,II

    2021.4 - 2022.3   Full year

  • 線形代数学Ⅰ

    2021.4 - 2021.9   First semester

  • 線形代数学

    2021.4 - 2021.9   First semester

  • 線形代数学・演習I

    2021.4 - 2021.9   First semester

  • 線形代数学Ⅰ

    2021.4 - 2021.9   First semester

  • 微分積分学・同演習II

    2020.10 - 2021.3   Second semester

  • 微分積分学・同演習B

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習B

    2020.10 - 2021.3   Second semester

  • 微分積分学・同演習I

    2020.4 - 2020.9   First semester

  • 微分積分学・同演習A

    2020.4 - 2020.9   First semester

  • 線形代数学・同演習A

    2020.4 - 2020.9   First semester

  • 微分積分学

    2019.10 - 2020.3   Second semester

  • 線形代数学・同演習Ｂ

    2019.10 - 2020.3   Second semester

  • 数学展望

    2019.4 - 2019.9   First semester

  • 線形代数学・同演習Ａ

    2019.4 - 2019.9   First semester

  • 微分積分学・同演習Ⅲ

    2019.4 - 2019.9   First semester

  • 微分積分学・同演習Ⅲ

    2019.4 - 2019.9   First semester

  • 微分積分学・同演習Ⅲ

    2019.4 - 2019.9   First semester

  • 数理科学特論９

    2018.10 - 2019.3   Second semester

  • 微分積分学・同演習Ｂ

    2018.10 - 2019.3   Second semester

  • 線形代数学・同演習Ｂ

    2018.10 - 2019.3   Second semester

  • 数理科学特別講義Ⅸ

    2018.10 - 2019.3   Second semester

  • 線形代数同演習

    2018.4 - 2019.3   Full year

  • 微分積分同演習

    2018.4 - 2019.3   Full year

  • 数学展望

    2018.4 - 2018.9   First semester

  • 微分積分学・同演習Ａ

    2018.4 - 2018.9   First semester

  • 線形代数学・同演習Ａ

    2018.4 - 2018.9   First semester

  • 数学展望

    2018.4 - 2018.9   First semester

  • 微分積分学･同演習Ⅱ

    2017.10 - 2018.3   Second semester

  • 微分積分学･同演習Ⅱ

    2017.10 - 2018.3   Second semester

  • 微分積分同演習

    2017.4 - 2018.3   Full year

  • 線形代数

    2017.4 - 2017.9   First semester

  • 線形代数

    2017.4 - 2017.9   First semester

  • 微分積分学･同演習Ⅰ

    2017.4 - 2017.9   First semester

  • 微分積分学･同演習Ⅰ

    2017.4 - 2017.9   First semester

  • 数学展望

    2017.4 - 2017.9   First semester

  • 数学展望

    2017.4 - 2017.9   First semester

  • 線形代数

    2016.4 - 2016.9   First semester

  • 線形代数

    2016.4 - 2016.9   First semester

  • 微積A/B・演習

    2015.4 - 2016.3   Full year

  • 代数学I・演習

    2015.4 - 2015.9   First semester

  • 微積分

    2014.4 - 2015.3   Full year

  • 数学IIB

    2014.4 - 2014.9   First semester

  • 代数学I

    2014.4 - 2014.9   First semester

  • 代数学II

    2013.10 - 2014.3   Second semester

  • 数学IIB

    2013.4 - 2013.9   First semester

  • 代数学・演習 II

    2012.10 - 2013.3   Second semester

  • 数学IIB

    2012.4 - 2012.9   First semester

  • 微分積分学(医）

    2011.10 - 2012.3   Second semester

  • 数学 IIB

    2011.4 - 2011.9   First semester

  • 微分積分学(医）

    2011.4 - 2011.9   First semester

  • 数学ⅡＢ

    2010.4 - 2010.9   First semester

  • 線形代数同演習A

    2010.4 - 2010.9   First semester

  • 微分積分学同演習A

    2010.4 - 2010.9   First semester

  • 代数幾何学基礎・演習

    2010.4 - 2010.9   First semester

  • 微分積分学同演習B

    2009.10 - 2010.3   Second semester

  • 数論基礎と演習

    2009.10 - 2010.3   Second semester

  • 数学特論C1

    2008.10 - 2009.3   Second semester

  • 微分積分

    2008.10 - 2009.3   Second semester

  • 微分積分学　同演習

    2008.4 - 2009.3   Full year

  • 線形

    2008.4 - 2008.9   First semester

  • 代数幾何大意

    2007.10 - 2008.3   Second semester

  • 代数幾何大意

    2007.10 - 2008.3   Second semester

  • ４年講究

    2007.4 - 2008.3   Full year

  • 線形代数

    2007.4 - 2007.9   First semester

  • 表現論大意

    2007.4 - 2007.9   First semester

  • 表現論大意

    2007.4 - 2007.9   First semester

  • 微分積分続論

    2007.4 - 2007.9   First semester

  • 基礎数学演習

    2006.4 - 2007.3   Full year

  • 微分積分学　同演習

    2006.4 - 2007.3   Full year

  • 微分積分続論

    2006.4 - 2006.9   First semester

  • 複素解析学

    2006.4 - 2006.9   First semester

▼display all

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2013  国際数学中心、清華大学  Domestic/International Classification:Overseas 

    Semester, Day Time or Duration：Nov-Dec, 2013

  • 2011  京都大学・理学部・数学科  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration：28, 11 -- 2, 12, 2011

Outline of Social Contribution and International Cooperation activities

  • Japan in Today's World

    未来の科学者委員会委員

    留学⽣センター委員会委員

    研究活動基礎支援専門委員会委員

Social Activities

  • 未来の科学者委員会委員

    2023.4

    　More details

    Audience：Infants,　Schoolchildren,　Junior students,　High school students

    Type：Other

  • 未来の科学者委員会委員

    2022.4

    　More details

    Audience：Infants,　Schoolchildren,　Junior students,　High school students

    Type：Other

  • 未来の科学者委員会委員

    2021.4

    　More details

    Audience：Infants,　Schoolchildren,　Junior students,　High school students

    Type：Other

  • 未来の科学者委員会委員

    2020.4

    　More details

    Audience：Infants,　Schoolchildren,　Junior students,　High school students

    Type：Other

  • 未来の科学者委員会委員

    2019.10

    　More details

    Audience：Infants,　Schoolchildren,　Junior students,　High school students

    Type：Other