WENG LIN
Organization
Faculty of Mathematics Division of Algebra and Geometry Professor
School of Sciences Department of Mathematics（Joint Appointment）
Graduate School of Mathematics Department of Mathematics（Joint Appointment）
Joint Graduate School of Mathematics for Innovation
（Joint Appointment）
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.
External link
Research Interests・Research Keywords
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Research theme：non-abelian zeta function for curves
Keyword：Riemann Hypothesis, zeta fucntions
Research period： 2021.10 - 2022.3
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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
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Research theme：arithmetic characteristic curves, arithmetic Higgs bundles
Keyword：arithmetic characteristic curves, arithmetic Higgs bundles
Research period： 2019.1 - 2020.3
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Research theme：Uniformity of zeta functions
Keyword：zeta function, uniformity
Research period： 2015.4 - 2020.3
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Research theme：Stability and Arithmetic Geometry
Keyword：stability, zeta function
Research period： 2010.4 - 2015.3
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Research theme：Zeta Functions for Reductive Groups and Their Zeros
Keyword：Zeta Functions, Reductive Groups, Riemann Hypothesis
Research period： 2000.12 - 2020.4
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Research theme：Arithmetic Aspects of Moduli Spaces of Punctured Riemann Surfaces
Keyword：Weil-Petersson, Takhtajan-Zograf
Research period： 2000.3
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Research theme：Geometric Arithmetic
Keyword：Non-abelian Class Field Theory, Abelian and Non-Abelian Zeta Functions
Research period： 1999.6
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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
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Higher-rank zeta functions and $SL_n$-zeta functions for curves Reviewed International journal
Lin WENG, Don Zagier
PNAS March 24, 2020 117 (12) ( PNAS March 24, 2020 117 (12) ) 6398 - 6408 2020.3
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Higher rank zeta functions for elliptic curves Reviewed International journal
L. Weng, D. Zagier
PNAS March 3, 2020 117 (9) ( PNAS March 3, 2020 117 (9) ) 4546 - 4558 2020.2
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Parabolic reduction, stability and the mass I: Special Linear Groups
LIN WENG
168 - 179 2013.3
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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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Stability and arithmetic: an extract of essence Invited Reviewed
Lin WENG
2011.10
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Symmetries and the Riemann Hypothesis Invited Reviewed
Lin WENG
Advanced Studies in Pure Mathematics 58 2010.6
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Stability and Arithmetic Reviewed
Lin WENG
Advanced Studies in Pure Mathematics 58 2010.6
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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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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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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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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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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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A Geometric Approach to L-Functions
Weng, Lin
The Conference on L-Functions 2007.2
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A Rank Two Zeta and Its Zeros International journal
Weng, Lin
J. Ramanujan Math. Soc. 2006.10
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Geometric Arithmetic: A Program
Weng, Lin
Arithmetic Geometry and Number Theory 2006.8
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Non-abelian zeta functions for function fields Reviewed
Lin Weng
American Journal of Mathematics 127 ( 5 ) 973 - 1017 2005.10
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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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Refined Brill-Noether Locus Non-Abelian Zeta Functions for Elliptic Curves
Weng, Lin
Algebraic geometry in East Asia 2002.10
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Zeta Functions defined by Two Polynomials
Matsumoto, K.; Weng, Lin
Number Theoretic Methods 2002.10
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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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Ω-admissible theory II. Deligne pairings over moduli spaces of punctured Riemann surfaces Reviewed
320 ( 2 ) 239 - 283 2001.1
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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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Wing Keung To, Lin Weng
Annals of Global Analysis and Geometry 17 ( 3 ) 239 - 265 1999.1
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Ω-Admissible theory Reviewed
79 ( 3 ) 481 - 510 1999.1
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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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Standard modules of level 1 for sl̂2 in terms of virasoro algebra representations Reviewed
26 ( 2 ) 613 - 625 1998.1
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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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Analytic torsions of spheres Reviewed
Lin Weng, Yuching You
International Journal of Mathematics 7 ( 1 ) 109 - 125 1996.2
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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
Books
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Zeta Functions for Reductive Groups and Their Zeros
Lin WENG（ Role： Sole author）
World Scientific 2018.2
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Zeta functions of reductive groups and their zeros
Lin Weng
World Scientific Publishing Co. Pte Ltd 2018.2
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Algebraic and Arithmetic Structures of Moduli Spaces
Iku Nakamura and Lin WENG (eds)
Japan Math Soc 2010.6
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Weng, Lin; Kaneko, Masanobu (eds)（ Role： Edit）
World Scientific 2007.1
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Arithmetic Geometry and Number Theory
Weng, Lin; Nakamura, Iku (eds)（ Role： Edit）
World Scientific 2006.8
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Hyperbolic Metrics, Selberg Zeta Functions and Arakelov Theory for Punctured Riemann Surfaces
Weng, Lin（ Role： Sole author）
Math Dept, Osaka University 1998.5
Presentations
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Zeta Functions and Their Zeros Invited
2014.7
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Eisenstein periods I,II International conference
Bundles over Surfaces and Eisenstein Periods for Loop Groups 2014.7
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Cohen-Lenstra Heuristics for Relative Shafarevich-Tate Groups Invited International conference
7th China-Japan Seminar on Number Theory 2013.10
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Global adelic cohomology groups for arithmetic varieties Invited International conference
LIN WENG
Pan Asia Number Theory 2013 2013.7
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General Uniformity of Zeta Functions Invited International conference
Global invariants and moduli spaces 2013.5
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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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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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Non-Abelian Zeta Functions Invited International conference
LIN WENG
p-adic Modular Forms and Arithmetic 2012.6
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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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Parabolic reduction, stability and volumes of fundamental domains International conference
Automorphic forms and automorphic functions 2012.1
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A local family index theorem in log geometry Invited International conference
Tokyo-Seoul conference in mathematics 2011.12
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A construction of zeta functions Invited
2011.11
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Relative Bott-Chern secondary characteristic classes and arithmetic Riemann-Roch theorem Invited International conference
Number Theory and related topics 2011.6
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A Construction of Non-Abelian L-Functions Invited International conference
Lin WENG
Workshop on L-Functions 2011.4
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Relative Bott-Chern Secondary Characteristic Classes Invited International conference
Lin WENG
Symposium on Complex Geometry 2010.7
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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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Zeta Functions for (G,P)/Q Invited International conference
Lin WENG
Zeta Function Days in Seoul 2009.9
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Stability and Arithmetic Invited International conference
Lin WENG
Algebraic Number Theory and Related Topics 2008.12
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Symmetries and the Riemann Hypothesis Invited
Lin WENG
Algebraic Geometry and its new developments 2008.11
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Symmetries and the Riemann Hypothesis Invited International conference
Lin WENG
L functions in Arithmetic and Geometry 2008.6
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ARAKELOV GEOMETRY AND COMPLEX GEOMETRY(?) Invited
1998.3
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Deligne Pairings over Moduli Spaces of Marked Stable Curves Invited
Lin WENG
Symposium of Algebra (1999) 1999.8
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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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Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves Invited International conference
Lin WENG
Algebraic Geometry in East Asia 2001.8
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New Non-Abelian Zeta Functions Invited International conference
Lin WENG
Riemann Hypothesis Conference (2ed) 2002.5
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New Non-Abelian Zeta Functions Invited International conference
Lin WENG
L-Functions in Arithmetic 2002.9
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New Non-Abelian Zeta Functions Invited
Lin WENG
Algebraic Number Theory and Related Topics 2002.12
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Weil-Petersson Metrics, Takhtajan-Zograf Metrics and Their Degenerations Invited International conference
Lin WENG
Complex Geometry in Tokyo 2002.12
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NON-ABELIAN ZETA FUNCTIONS Invited
2003.9
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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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Stability in Arithmetic and Geometry Invited International conference
Lin WENG
Differential Geometry in Tokyo 2004.12
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Non-Abelian L Functions for Number Fields Invited International conference
Lin WENG
Algebraic Geometry and Number Theory 2005.6
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Non-Abelian L-Functions Invited International conference
Lin WENG
Conference on L-Functions 2006.2
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General Class Field Theory Invited International conference
Lin WENG
Euler 300: Arithmetic Geometry 2007.6
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General Class Field Theory Invited International conference
Lin WENG
Algebraic and Arithmetic Structures of Moduli Spaces 2007.9
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Stability in Arithmetic Invited International conference
L. Weng
Complex Geometry in Osaka 2007.11
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Motivic Euler Product and Its Applications Invited International conference
Arithmetic and Algebraic Geometry 2014 2014.1
MISC
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Automorphic Forms, Eisenstein Series and Spectral Decompositions
Weng, Lin
Arithmetic Geometry and Number Theory, World Scientific 2006.8
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Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces
Obitsu, Kunio; To, Wing-Keung; Weng, Lin
Arithmetic Geometry and Number Theory, World Scientific 2006.8
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Stability and New Non-Abelian Zeta Functions
Weng, Lin
Number Theoretic Methods, Kluwer Acad. Publ. 2002.6
Academic Activities
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座長（Chairmanship） International contribution
2014.6 - 2014.7
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主催 International contribution
2014.6 - 2014.7
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不明 International contribution
2013.5
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不明 International contribution
2013.4
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主催 International contribution
2013.4
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不明 International contribution
2012.10
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主催 International contribution
2012.10
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不明 International contribution
2012.6
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主催 International contribution
2012.6
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不明 International contribution
2011.4
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Organizer International contribution
Workshop on L-Functions （ FUKUOKA Japan ） 2011.4
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Organizer International contribution
Algebraic and Arithmetic Aspects of Moduli Spaces （ Sapporo Japan ） 2007.9 - Present
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不明 International contribution
2007.9 - 2019.6
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Organizer International contribution
Conference on L-Functions （ FUKUOKA Japan ） 2006.2 - Present
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不明
2006.2
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不明 International contribution
2005.3 - Present
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Organizer International contribution
Arithmetic Geometry and Number Theory （ KARATSU Japan ） 2005.3 - 2022.3
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不明
（ 唐津 ） 2004.5 - Present
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Organizer
Towards IC Stability （ Japan ） 2004.1 - Present
Educational Activities
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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
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線形代数学II
2023.10 - 2024.3 Second semester
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代数学III
2023.10 - 2024.3 Second semester
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代数幾何学大意
2023.10 - 2024.3 Second semester
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数学特論１
2023.10 - 2024.3 Second semester
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数学特論１
2023.10 - 2024.3 Second semester
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代数学Ⅲ
2023.10 - 2024.3 Second semester
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代数幾何学大意
2023.10 - 2024.3 Second semester
-
線形代数学Ⅱ
2023.10 - 2024.3 Second semester
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入門線形代数II
2023.6 - 2023.8 Summer quarter
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線形代数学I
2023.4 - 2023.9 First semester
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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
-
線形代数学Ⅰ
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
-
線形代数学Ⅱ
2022.10 - 2023.3 Second semester
-
代数学Ⅲ
2022.10 - 2023.3 Second semester
-
入門線形代数学II
2022.6 - 2022.8 Summer quarter
-
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
-
数理科学特論１４
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
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
-
線形代数学Ⅰ
2021.4 - 2021.9 First semester
-
微分積分学・同演習B
2020.10 - 2021.3 Second semester
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線形代数学・同演習B
2020.10 - 2021.3 Second semester
-
微分積分学・同演習II
2020.10 - 2021.3 Second 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・同演習I
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
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微分積分学･同演習Ⅱ
2017.10 - 2018.3 Second semester
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微分積分同演習
2017.4 - 2018.3 Full year
-
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
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
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微積分
2014.4 - 2015.3 Full year
-
代数学I
2014.4 - 2014.9 First semester
-
数学IIB
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
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微分積分学同演習B
2009.10 - 2010.3 Second semester
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数論基礎と演習
2009.10 - 2010.3 Second semester
-
数学特論C1
2008.10 - 2009.3 Second semester
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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
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代数幾何大意
2007.10 - 2008.3 Second semester
-
代数幾何大意
2007.10 - 2008.3 Second semester
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４年講究
2007.4 - 2008.3 Full year
-
線形代数
2007.4 - 2007.9 First semester
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表現論大意
2007.4 - 2007.9 First semester
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表現論大意
2007.4 - 2007.9 First semester
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微分積分続論
2007.4 - 2007.9 First semester
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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
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複素解析学
2006.4 - 2006.9 First semester
Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.
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2013 国際数学中心、清華大学 Domestic/International Classification:Overseas
Semester, Day Time or Duration：Nov-Dec, 2013
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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
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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
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未来の科学者委員会委員
2023.4
-
未来の科学者委員会委員
2022.4
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未来の科学者委員会委員
2021.4
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未来の科学者委員会委員
2020.4
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未来の科学者委員会委員
2019.10