%%
@article{fds360672,
Author = {Cox, D and Esnault, H and Hain, R and Harris, M and Ji, L and Saito, M-H and Saper, L},
Title = {Remembering Steve Zucker},
Journal = {Notices of the American Mathematical Society},
Volume = {68},
Number = {7},
Pages = {1156-1172},
Publisher = {American Mathematical Society},
Editor = {Cox, D and Harris, M and Ji, L},
Year = {2021},
Month = {August},
Key = {fds360672}
}
@article{fds360673,
Author = {Hain, R},
Title = {Hodge theory of the Turaev cobracket and the
Kashiwara-Vergne problem},
Journal = {Journal of the European Mathematical Society},
Volume = {23},
Number = {12},
Pages = {3889-3933},
Year = {2021},
Month = {January},
url = {http://dx.doi.org/10.4171/JEMS/1088},
Abstract = {In this paper we show that, after completing in the I -adic
topology, the Turaev cobracket on the vector space freely
generated by the closed geodesics on a smooth, complex
algebraic curve X with a quasi-algebraic framing is a
morphism of mixed Hodge structure. We combine this with
results of a previous paper on the Goldman bracket to
construct torsors of solutions to the Kashiwara-Vergne
problem in all genera. The solutions so constructed form a
torsor under a prounipotent group that depends only on the
topology of the framed surface. We give a partial
presentation of these groups. Along the way, we give a
homological description of the Turaev cobracket.},
Doi = {10.4171/JEMS/1088},
Key = {fds360673}
}
@article{fds360674,
Author = {Hain, R},
Title = {Johnson homomorphisms},
Journal = {EMS Surveys in Mathematical Sciences},
Volume = {7},
Number = {1},
Pages = {33-116},
Year = {2021},
Month = {January},
url = {http://dx.doi.org/10.4171/EMSS/36},
Abstract = {Torelli groups are subgroups of mapping class groups that
consist of those diffeomorphism classes that act trivially
on the homology of the associated closed surface. The
Johnson homomorphism, defined by Dennis Johnson, and its
generalization, defined by S. Morita, are tools for
understanding Torelli groups. This paper surveys work on
generalized Johnson homomorphisms and tools for studying
them. The goal is to unite several related threads in the
literature and to clarify existing results and relationships
among them using Hodge theory. We survey the work of
Alekseev, Kawazumi, Kuno and Naef on the Goldman-Turaev Lie
bialgebra, and the work of various authors on cohomological
methods for determining the stable image of generalized
Johnson homomorphisms. Various open problems and conjectures
are included. Even though the Johnson homomorphisms were
originally defined and studied by topologists, they are
important in understanding arithmetic properties of mapping
class groups and moduli spaces of curves. We define
arithmetic Johnson homomorphisms, which extend the
generalized Johnson homomorphisms, and explain how the
Turaev cobracket constrains their images.},
Doi = {10.4171/EMSS/36},
Key = {fds360674}
}
@article{fds353808,
Author = {Hain, R},
Title = {Hodge theory of the Goldman bracket},
Journal = {Geometry & Topology},
Volume = {24},
Number = {4},
Pages = {1841-1906},
Publisher = {Mathematical Sciences Publishers},
Year = {2020},
Month = {November},
url = {http://dx.doi.org/10.2140/gt.2020.24.1841},
Doi = {10.2140/gt.2020.24.1841},
Key = {fds353808}
}
@article{fds320426,
Author = {Hain, R and Matsumoto, M},
Title = {Universal Mixed Elliptic Motives},
Journal = {Journal of the Institute of Mathematics of
Jussieu},
Volume = {19},
Number = {3},
Pages = {663-766},
Year = {2020},
Month = {May},
url = {http://dx.doi.org/10.1017/S1474748018000130},
Abstract = {In this paper we construct a-linear tannakian category of
universal mixed elliptic motives over the moduli space of
elliptic curves. It contains , the category of mixed Tate
motives unramified over the integers. Each object of is an
object of endowed with an action of that is compatible with
its structure. Universal mixed elliptic motives can be
thought of as motivic local systems over whose fiber over
the tangential base point at the cusp is a mixed Tate
motive. The basic structure of the tannakian fundamental
group of is determined and the lowest order terms of a set
(conjecturally, a minimal generating set) of relations are
deduced from computations of Brown. This set of relations
includes the arithmetic relations, which describe the
'infinitesimal Galois action'. We use the presentation to
give a new and more conceptual proof of the Ihara-Takao
congruences.},
Doi = {10.1017/S1474748018000130},
Key = {fds320426}
}
@article{fds324840,
Author = {Hain, R},
Title = {Notes on the Universal Elliptic KZB Equation},
Journal = {Pure and Applied Mathematics Quarterly},
Volume = {12},
Number = {2},
Publisher = {International Press},
Year = {2020},
Month = {January},
url = {http://arxiv.org/abs/1309.0580v3},
Abstract = {The universal elliptic KZB equation is the integrable
connection on the pro-vector bundle over M_{1,2} whose fiber
over the point corresponding to the elliptic curve E and a
non-zero point x of E is the unipotent completion of
\pi_1(E-{0},x). This was written down independently by
Calaque, Enriquez and Etingof (arXiv:math/0702670), and by
Levin and Racinet (arXiv:math/0703237). It generalizes the
KZ-equation in genus 0. These notes are in four parts. The
first two parts provide a detailed exposition of this
connection (following Levin-Racinet); the third is a
leisurely exploration of the connection in which, for
example, we compute the limit mixed Hodge structure on the
unipotent fundamental group of the Tate curve minus its
identity. In the fourth part we elaborate on ideas of Levin
and Racinet and explicitly compute the connection over the
moduli space of elliptic curves with a non-zero abelian
differential, showing that it is defined over
Q.},
Key = {fds324840}
}
@article{fds349712,
Author = {Hain, R},
Title = {Notes on the universal elliptic KZB connection},
Journal = {Pure and Applied Mathematics Quarterly},
Volume = {16},
Number = {2},
Pages = {229-312},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.4310/PAMQ.2020.v16.n2.a2},
Abstract = {In this paper, we give an exposition of the elliptic KZB
connection over the universal elliptic curve and use it to
compute the limit mixed Hodge structure on the unipotent
fundamental group of the first order Tate curve. We also
give an explicit algebraic formula for the restriction of
the elliptic KZB connection to the moduli space of non-zero
abelian differentials on an elliptic curve.},
Doi = {10.4310/PAMQ.2020.v16.n2.a2},
Key = {fds349712}
}
@article{fds337126,
Author = {Brown, F and Hain, R},
Title = {Algebraic de Rham theory for weakly holomorphic modular
forms of level one},
Journal = {Algebra and Number Theory},
Volume = {12},
Number = {3},
Pages = {723-750},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.2140/ant.2018.12.723},
Abstract = {We establish an Eichler–Shimura isomorphism for weakly
modular forms of level one. We do this by relating weakly
modular forms with rational Fourier coefficients to the
algebraic de Rham cohomology of the modular curve with
twisted coefficients. This leads to formulae for the periods
and quasiperiods of modular forms.},
Doi = {10.2140/ant.2018.12.723},
Key = {fds337126}
}
@article{fds320425,
Author = {Hain, R},
Title = {Deligne-Beilinson Cohomology of Affine Groups},
Booktitle = {Hodge Theory and $L^2$-analysis},
Publisher = {International Press},
Editor = {Ji, L},
Year = {2017},
ISBN = {9781571463517},
url = {http://arxiv.org/abs/1507.03144},
Abstract = {The goal of this paper is to develop the theory of
Deligne-Beilinson cohomology of affine groups with a mixed
Hodge structure. The motivation comes from Hodge theory and
the study of motives, where such groups appear. Several of
Francis Brown's period computations (arXiv:1407.5167) are
interpreted as elements of the DB cohomology of the relative
unipotent completion of $SL_2(Z)$ and their cup products.
The results in this paper are used in arXiv:1403.6443 where
they are used to prove that Pollack's quadratic relations
are motivic.},
Key = {fds320425}
}
@article{fds287213,
Author = {Arapura, D and Dimca, A and Hain, R},
Title = {On the fundamental groups of normal varieties},
Journal = {Communications in Contemporary Mathematics},
Volume = {18},
Number = {4},
Pages = {1550065-1550065},
Year = {2016},
Month = {August},
ISSN = {0219-1997},
url = {http://dx.doi.org/10.1142/S0219199715500650},
Abstract = {We show that the fundamental groups of normal complex
algebraic varieties share many properties of the fundamental
groups of smooth varieties. The jump loci of rank one local
systems on a normal variety are related to the jump loci of
a resolution and of a smoothing of this variety.},
Doi = {10.1142/S0219199715500650},
Key = {fds287213}
}
@article{fds320302,
Author = {Hain, R},
Title = {The Hodge-de Rham theory of modular groups},
Volume = {427},
Pages = {422-514},
Booktitle = {Recent Advances in Hodge Theory: Period Domains, Algebraic
Cycles, and Arithmetic},
Publisher = {Cambridge University Press},
Editor = {Kerr, M and Pearlstein, G},
Year = {2016},
Month = {February},
ISBN = {9781107546295},
url = {http://dx.doi.org/10.1017/9781316387887.019},
Doi = {10.1017/9781316387887.019},
Key = {fds320302}
}
@article{fds287214,
Author = {Hain, R},
Title = {Genus 3 mapping class groups are not Kähler},
Journal = {Journal of Topology},
Volume = {8},
Number = {1},
Pages = {213-246},
Publisher = {Wiley},
Year = {2015},
Month = {March},
ISSN = {1753-8416},
url = {http://arxiv.org/abs/1305.2052},
Doi = {10.1112/jtopol/jtu020},
Key = {fds287214}
}
@article{fds287267,
Author = {Dimca, A and Hain, R and Papadima, S},
Title = {The abelianization of the Johnson kernel},
Journal = {Journal of the European Mathematical Society},
Volume = {16},
Number = {4},
Pages = {805-822},
Year = {2014},
Month = {January},
ISSN = {1435-9855},
url = {http://arxiv.org/abs/1101.1392},
Abstract = {We prove that the first complex homology of the Johnson
subgroup of the Torelli group Tg is a non-trivial, unipotent
Tg-module for all g ≥ 4 and give an explicit presentation
of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by
proving that, for a finitely generated group G satisfying an
assumption close to formality, the triviality of the
restricted characteristic variety implies that the first
homology of its Johnson kernel is a nilpotent module over
the corresponding Laurent polynomial ring, isomorphic to the
infinitesimal Alexander invariant of the associated graded
Lie algebra of G. In this setup, we also obtain a precise
nilpotence test. © European Mathematical Society
2014.},
Doi = {10.4171/JEMS/447},
Key = {fds287267}
}
@article{fds287265,
Author = {Hain, R},
Title = {Remarks on non-abelian cohomology of proalgebraic
groups},
Journal = {Journal of Algebraic Geometry},
Volume = {22},
Number = {3},
Pages = {581-598},
Publisher = {American Mathematical Society (AMS)},
Year = {2013},
Month = {June},
ISSN = {1056-3911},
url = {http://dx.doi.org/10.1090/S1056-3911-2013-00598-6},
Abstract = {In this paper we develop a theory of non-abelian cohomology
for proalgebraic groups which is used in J. Amer. Math. Soc.
24 (2011), 709-769 to study the unipotent section
conjecture. The non-abelian cohomology H 1nab(G,P) is a
scheme. The argument G is a proalgebraic group; the
coefficient group P is prounipotent with trivial center and
endowed with an outer action of G. This outer action
uniquely determines an extension Ĝ of G by P. With suitable
hypotheses, the scheme H1nab(G,P) parametrizes the P
conjugacy classes of sections of Ĝ →G. © 2013 University
Press, Inc.},
Doi = {10.1090/S1056-3911-2013-00598-6},
Key = {fds287265}
}
@article{fds287242,
Author = {Hain, R},
Title = {Normal Functions and the Geometry of Moduli Spaces of
Curves},
Volume = {1},
Pages = {527-578},
Booktitle = {Handbook of Moduli},
Publisher = {International Press},
Editor = {Farkas, G and Morrison, I},
Year = {2013},
ISBN = {9781571462572},
url = {http://arxiv.org/abs/1102.4031},
Key = {fds287242}
}
@book{fds306181,
Author = {Benson Farb and Richard Hain and Eduard Looijenga},
Title = {Moduli Spaces of Riemann Surfaces},
Volume = {20},
Series = {IAS/Park City Mathematics Series},
Pages = {x+356 pages},
Publisher = {American Mathematical Society, Providence, RI; Institute for
Advanced Study (IAS), Princeton, NJ},
Editor = {Farb, B and Hain, R and Looijenga, E},
Year = {2013},
ISBN = {978-0-8218-9887-1},
url = {http://www.ams.org/bookstore-getitem/item=PCMS-20},
Key = {fds306181}
}
@article{fds287264,
Author = {Hain, R},
Title = {Rational points of universal curves},
Journal = {Journal of the American Mathematical Society},
Volume = {24},
Number = {3},
Pages = {709-769},
Publisher = {American Mathematical Society (AMS)},
Year = {2011},
Month = {July},
ISSN = {0894-0347},
url = {http://dx.doi.org/10.1090/S0894-0347-2011-00693-0},
Doi = {10.1090/S0894-0347-2011-00693-0},
Key = {fds287264}
}
@article{fds287243,
Author = {Hain, R},
Title = {Lectures on Moduli Spaces of Elliptic Curves},
Volume = {16},
Series = {Advanced Lectures in Mathematics},
Number = {16},
Pages = {95-166},
Booktitle = {Transformation Groups and Moduli Spaces of Curves: Advanced
Lectures in Mathematics},
Publisher = {Higher Education Press},
Address = {Beijing},
Editor = {Ji, L and Yau, ST},
Year = {2010},
ISBN = {978-7-04-029842-0},
url = {http://arxiv.org/abs/0812.1803},
Key = {fds287243}
}
@article{fds287268,
Author = {Hain, R and Matsumoto, M},
Title = {Relative pro-ℓ completions of mapping class
groups},
Journal = {Journal of Algebra},
Volume = {321},
Number = {11},
Pages = {3335-3374},
Publisher = {Elsevier BV},
Year = {2009},
Month = {June},
ISSN = {0021-8693},
url = {http://dx.doi.org/10.1016/j.jalgebra.2009.02.014},
Doi = {10.1016/j.jalgebra.2009.02.014},
Key = {fds287268}
}
@article{fds287244,
Author = {Hain, R},
Title = {Relative Weight Filtrations on Completions of Mapping Class
Groups},
Volume = {52},
Series = {Advanced Studies in Pure Mathematics},
Pages = {309-368},
Booktitle = {Groups of Diffeomorphisms: Advanced Studies in Pure
Mathematics},
Publisher = {Mathematical Society of Japan},
Year = {2008},
url = {http://arxiv.org/abs/0802.0814},
Key = {fds287244}
}
@article{fds287245,
Author = {Hain, R},
Title = {Finiteness and Torelli Spaces},
Volume = {74},
Series = {Proc. Symp. Pure Math. 74},
Pages = {57-70},
Booktitle = {Problems on Mapping Class Groups and Related
Topics},
Publisher = {Amererican Mathematics Societty},
Editor = {Farb, B},
Year = {2006},
ISBN = {9780821838389},
url = {http://dx.doi.org/10.1090/pspum/074/2264131},
Doi = {10.1090/pspum/074/2264131},
Key = {fds287245}
}
@article{fds287270,
Author = {Kim, M and Hain, RM},
Title = {The Hyodo-Kato theorem for rational homotopy
types},
Journal = {Mathematical Research Letters},
Volume = {12},
Number = {2-3},
Pages = {155-169},
Year = {2005},
Month = {January},
ISSN = {1073-2780},
url = {http://hdl.handle.net/10161/8976 Duke open
access},
Abstract = {The Hyodo-Kato theorem relates the De Rham cohomology of a
variety over a local field with semi-stable reduction to the
log crystalline cohomology of the special fiber. In this
paper we prove an analogue for rational homotopy types. In
particular, this gives a comparison isomorphism for
fundamental groups.},
Doi = {10.4310/mrl.2005.v12.n2.a2},
Key = {fds287270}
}
@article{fds287271,
Author = {Hain, R and Matsumoto, M},
Title = {Galois actions on fundamental groups of curves and the
cycle},
Journal = {Journal of the Institute of Mathematics of
Jussieu},
Volume = {4},
Number = {3},
Pages = {363-403},
Publisher = {Cambridge University Press (CUP): STM Journals},
Year = {2005},
Month = {January},
ISSN = {1475-3030},
url = {http://dx.doi.org/10.1017/S1474748005000095},
Abstract = {Suppose that [formula omitted] is a subfield of [formula
omitted] for which the [formula omitted] -adic cyclotomic
character has infinite image. Suppose that [formula omitted]
is a curve of genus [formula omitted] defined over [formula
omitted], and that [formula omitted] is a [formula omitted]
-rational point of [formula omitted]. This paper considers
the relation between the actions of the mapping class group
of the pointed topological curve [formula omitted] and the
absolute Galois group [formula omitted] of [formula omitted]
on the [formula omitted] -adic prounipotent fundamental
group of [formula omitted]. A close relationship is
established between the image of the absolute Galois group
of [formula omitted] in the automorphism group of the
[formula omitted] -adic unipotent fundamental group of
[formula omitted]; andthe [formula omitted] -adic Galois
cohomology classes associated to the algebraic [formula
omitted] -cycle [formula omitted] in the Jacobian of
[formula omitted], and to the algebraic [formula omitted]
-cycle [formula omitted] in [formula omitted]. The main
result asserts that the Zariski closure of (i) in the
automorphism group contains the image of the mapping class
group of [formula omitted] if and only if the two classes in
(ii) are non-torsion and the Galois image in [formula
omitted] is Zariski dense. The result is proved by
specialization from the case of the universal curve. AMS
2000 Mathematics subject classification: Primary 11G30.
Secondary 14H30; 12G05; 14C25; 14G32. © 2005, Cambridge
University Press. All rights reserved.},
Doi = {10.1017/S1474748005000095},
Key = {fds287271}
}
@article{fds287273,
Author = {Kim, M and Hain, RM},
Title = {A De Rham–Witt approach to crystalline rational homotopy
theory},
Journal = {Compositio Mathematica},
Volume = {140},
Number = {05},
Pages = {1245-1276},
Publisher = {Wiley},
Year = {2004},
Month = {September},
ISSN = {0010-437X},
url = {http://hdl.handle.net/10161/8977 Duke open
access},
Doi = {10.1112/s0010437x04000442},
Key = {fds287273}
}
@article{fds287272,
Author = {Hain, R and Reed, D},
Title = {On the arakelov geometry of moduli spaces of
curves},
Journal = {Journal of Differential Geometry},
Volume = {67},
Number = {2},
Pages = {195-228},
Year = {2004},
Month = {Summer},
ISSN = {0022-040X},
url = {http://dx.doi.org/10.4310/jdg/1102536200},
Abstract = {In this paper we compute the asymptotics of the natural
metric on the line bundle over the moduli spaceMg associated
to the algebraic cycle C − C− in the jacobian Jac C of a
smooth projective curve C of genus g ≤ 3. The asymptotics
are related to the structure of the mapping class group of a
genus g surface. © 2004 Applied Probability
Trust.},
Doi = {10.4310/jdg/1102536200},
Key = {fds287272}
}
@article{fds287274,
Author = {Hain, R and Matsumoto, M},
Title = {Weighted completion of galois groups and galois actions on
the fundamental group of ℙ1 -{0, 1,
∞}},
Journal = {Compositio Mathematica},
Volume = {139},
Number = {2},
Pages = {119-167},
Year = {2003},
Month = {November},
ISSN = {0010-437X},
url = {http://dx.doi.org/10.1023/B:COMP.0000005077.42732.93},
Abstract = {Fix a prime number l. We prove a conjecture stated by Ihara,
which he attributes to Deligne, about the action of the
absolute Galois group on the pro-l completion of the
fundamental group of the thrice punctured projective line.
Similar techniques are also used to prove part of a
conjecture of Goneharov, also about the action of the
absolute Galois group on the fundamental group of the thrice
punctured projective line. The main technical tool is the
weighted completion of a profinite group with respect to a
reductive representation (and other appropriate data). ©
2003 Kluwer Academic Publishers.},
Doi = {10.1023/B:COMP.0000005077.42732.93},
Key = {fds287274}
}
@article{fds287246,
Author = {Hain, R},
Title = {Periods of Limit Mixed Hodge Structures},
Pages = {113-133},
Booktitle = {CDM 2002: Current Developments in Mathematics in Honor of
Wilfried Schmid & George Lusztig},
Publisher = {International Press},
Editor = {Jerison, D and Lustig, G and Mazur, B and Mrowka, T and Schmid, W and Stanley, R and Yau, ST},
Year = {2003},
url = {http://arxiv.org/abs/math/0305090},
Key = {fds287246}
}
@article{fds287275,
Author = {Hain, R and Matsumoto, M},
Title = {Tannakian Fundamental Groups Associated to Galois
Groups},
Volume = {41},
Pages = {183-216},
Booktitle = {Galois Groups and Fundamental Groups},
Publisher = {Cambridge Univ. Press},
Editor = {Schneps, L},
Year = {2003},
url = {http://arxiv.org/abs/math/0010210},
Key = {fds287275}
}
@article{fds287216,
Author = {Hain, R and Tondeur, P},
Title = {The Life and Work of Kuo-Tsai Chen [ MR1046561
(91b:01072)]},
Volume = {5},
Pages = {251-266},
Booktitle = {Contemporary trends in algebraic geometry and algebraic
topology (Tianjin, 2000)},
Publisher = {World Sci. Publ., River Edge, NJ},
Year = {2002},
ISBN = {9789810249540},
url = {http://dx.doi.org/10.1142/9789812777416_0012},
Doi = {10.1142/9789812777416_0012},
Key = {fds287216}
}
@book{fds306182,
Author = {Shiing-Shen Chern and Lei Fu and Richard M.
Hain},
Title = {Contemporary Trends in Algebraic Geometry and Algebraic
Topology},
Volume = {5},
Pages = {viii+266 pages},
Publisher = {World Scientific Publishing Co., Inc., River Edge,
NJ},
Editor = {Chern, S-S and Fu, L and Hain, R},
Year = {2002},
ISBN = {981-02-4954-3},
url = {http://www.wspc.com.sg/books/mathematics/4966.html},
Doi = {10.1142/9789812777416},
Key = {fds306182}
}
@article{fds287247,
Author = {Hain, R},
Title = {Iterated Integrals and Algebraic Cycles: Examples and
Prospects},
Volume = {5},
Pages = {55-118},
Booktitle = {Contemporary Tends in Algebraic Geometry and Algebraic
Topology},
Publisher = {World Scientific Publishing},
Year = {2002},
ISBN = {9789810249540},
url = {http://dx.doi.org/10.1142/9789812777416_0004},
Doi = {10.1142/9789812777416_0004},
Key = {fds287247}
}
@article{fds287263,
Author = {Hain, R},
Title = {The rational cohomology ring of the moduli space of abelian
3-folds},
Journal = {Mathematical Research Letters},
Volume = {9},
Number = {4},
Pages = {473-491},
Year = {2002},
url = {http://dx.doi.org/10.4310/MRL.2002.v9.n4.a7},
Doi = {10.4310/MRL.2002.v9.n4.a7},
Key = {fds287263}
}
@article{fds287262,
Author = {Hain, R and Reed, D},
Title = {Geometric proofs of some results of Morita},
Journal = {Journal of Algebraic Geometry},
Volume = {10},
Number = {2},
Pages = {199-217},
Year = {2001},
url = {http://arxiv.org/abs/math/9810054},
Key = {fds287262}
}
@article{fds287238,
Author = {Dupont, J and Hain, R and Zucker, S},
Title = {Regulators and Characteristic Classes of Flat
Bundles},
Volume = {24},
Pages = {47-92},
Booktitle = {The arithmetic and geometry of algebraic cycles (Banff, AB,
1998)},
Publisher = {American Mathematical Society},
Year = {2000},
url = {http://arxiv.org/abs/alg-geom/9202023},
Key = {fds287238}
}
@article{fds287251,
Author = {Hain, R},
Title = {Moduli of Riemann Surfaces, Transcendental Aspects, Moduli
Spaces},
Volume = {1},
Pages = {293-353},
Booktitle = {ALgebraic Geometry},
Publisher = {Abdus Salam Int. Cent. Theoret. Phys.},
Editor = {Gottsche, L},
Year = {2000},
ISBN = {92-95003-00-4},
Key = {fds287251}
}
@article{fds287248,
Author = {Hain, R},
Title = {Locally Symmetric Families of Curves and
Jacobians},
Pages = {91-108},
Booktitle = {Moduli of Curves and Abelian Varieties},
Publisher = {Friedr. Vieweg},
Editor = {Faber, C and Looijenga, E},
Year = {1999},
url = {http://arxiv.org/abs/math/9803028},
Key = {fds287248}
}
@article{fds287261,
Author = {Hain, RM},
Title = {The Hodge De Rham theory of relative Malcev
completion},
Journal = {Annales Scientifiques de l'Ecole Normale
Superieure},
Volume = {31},
Number = {1},
Pages = {47-92},
Year = {1998},
url = {http://archive.numdam.org/article/ASENS_1998_4_31_1_47_0.pdf},
Abstract = {Suppose that X is a smooth manifold and ρ : π1 (X,N) → S
is a representation of the fundamental group of X into a
real reductive group with Zariski dense image. To such data
one can associate the Malcev completion G of π1(X,x)
relative to ρ. In this paper we generalize Chen's iterated
integrals and show that the H0 of a suitable complex of
these iterated integrals is the coordinate ring of G. This
is used to show that if X is a complex algebraic manifold
and ρ is the monodromy representation of a variation of
Hodge structure over X, then the coordinate ring of G has a
canonical mixed Hodge structure. © Elsevier,
Paris.},
Doi = {10.1016/S0012-9593(98)80018-9},
Key = {fds287261}
}
@article{fds287236,
Author = {Freedman, M and Hain, R and Teichner, P},
Title = {Betti Number Estimates for Nilpotent Groups},
Volume = {5},
Pages = {413-434},
Booktitle = {Fields Medallists’ Lectures},
Publisher = {World Science},
Editor = {Atiyah, and Iagolnitzer},
Year = {1997},
ISBN = {9789810231026},
url = {http://dx.doi.org/10.1142/9789812385215_0045},
Doi = {10.1142/9789812385215_0045},
Key = {fds287236}
}
@article{fds287239,
Author = {Hain, R and Looijenga, E},
Title = {Mapping Class Groups and Moduli Spaces of
Curves},
Volume = {62},
Pages = {97-142},
Booktitle = {Algebraic geometry—Santa Cruz 1995},
Publisher = {American Mathematical Society},
Year = {1997},
url = {http://arxiv.org/abs/alg-geom/9607004},
Key = {fds287239}
}
@article{fds287260,
Author = {Hain, R},
Title = {Infinitesimal presentations of the Torelli
groups},
Journal = {Journal of the American Mathematical Society},
Volume = {10},
Number = {3},
Pages = {597-651},
Year = {1997},
url = {http://www.ams.org/jams/1997-10-03/},
Doi = {10.1090/S0894-0347-97-00235-X},
Key = {fds287260}
}
@article{fds287257,
Author = {Hain, RM},
Title = {The existence of higher logarithms},
Journal = {Compositio Mathematica},
Volume = {100},
Number = {3},
Pages = {247-276},
Year = {1996},
ISSN = {0010-437X},
url = {http://arxiv.org/abs/alg-geom/9308005},
Abstract = {In this paper we establish the existence of all higher
logarithms as Deligne cohomology classes in a sense slightly
weaker than that of [13, Sect. 12], but in a sense that
should be strong enough for defining Chem classes on the
algebraic K-theory of complex algebraic varieties. In
particular, for each integer p ≥ 1, we construct a
multivalued holomorphic function on a Zariski open subset of
the self dual grassmannian of p-planes in ℂ2p which
satisfies a canonical 2p + 1 term functional equation. The
key new technical ingredient is the construction of a
topology on the generic part of each Grassmannian which is
coarser than the Zariski topology and where each open
contains another which is both a K (π, 1) and a rational K
(π, 1). © 1996 Kluwer Academic Publishers.},
Key = {fds287257}
}
@article{fds287258,
Author = {Hain, RM and Yang, J},
Title = {Real Grassmann polylogarithms and Chern classes},
Journal = {Mathematische Annalen},
Volume = {304},
Number = {1},
Pages = {157-201},
Year = {1996},
url = {http://dx.doi.org/10.1007/BF01446290},
Doi = {10.1007/BF01446290},
Key = {fds287258}
}
@article{fds287259,
Author = {Elizondo, EJ and Hain, RM},
Title = {Chow varieties of abelian varieties},
Journal = {Sociedad Matemática Mexicana. Boletí n. Tercera
Serie},
Volume = {2},
Number = {2},
Pages = {95-99},
Year = {1996},
Abstract = {We prove that if A is an abelian variety over ℂ acting
algebraically on a complex projective variety X, then the
Euler characteristic of X equals the Euler characteristic of
the fixed point set XA. We obtain that if A is an abelian
variety and X is a principal A-bundle over a projective
variety Y, then the Euler characteristic of a Chow variety
in X equals either zero or the Euler characteristic of a
Chow variety of Y.},
Key = {fds287259}
}
@article{fds287240,
Author = {Hain, RM},
Title = {Torelli Groups and Geometry of Moduli Spaces of
Curves},
Volume = {28},
Pages = {97-143},
Booktitle = {Current Topics in Complex Algebraic Geometry},
Publisher = {Cambridge Univ. Press},
Editor = {Clements, CH and Kollar, J},
Year = {1995},
url = {http://www.msri.org/publications/books/Book28/},
Key = {fds287240}
}
@article{fds287249,
Author = {Hain, RM},
Title = {Classical Polylogarithms, Motives},
Volume = {55},
Pages = {3-42},
Booktitle = {Motives (Seattle, WA, 1991)},
Publisher = {American Mathematical Society},
Year = {1994},
Key = {fds287249}
}
@article{fds287241,
Author = {Hain, RM},
Title = {Completions of Mapping Class Groups and the Cycle
C-C},
Volume = {150},
Pages = {75-105},
Booktitle = {Mapping class groups and moduli spaces of Riemann surfaces
(Göttingen, 1991/Seattle, WA, 1991)},
Publisher = {American Mathematical Society},
Year = {1993},
ISSN = {0271-4132},
url = {http://dx.doi.org/10.1090/conm/150/01287},
Doi = {10.1090/conm/150/01287},
Key = {fds287241}
}
@book{fds306184,
Author = {Carl-Friedrich Bodigheimer and Richard M. Hain},
Title = {Mapping Class Groups and Moduli Spaces of Riemann
Surfaces},
Volume = {150},
Pages = {xx+372-xx+372},
Publisher = {American Mathematical Society, Providence,
RI},
Editor = {Bödigheimer, C-F and Hain, R},
Year = {1993},
ISBN = {0-8218-5167-5},
url = {http://dx.doi.org/10.1090/conm/150},
Doi = {10.1090/conm/150},
Key = {fds306184}
}
@article{fds287250,
Author = {Hain, RM},
Title = {Nil-manifolds as links of isolated singularities},
Journal = {Compositio Mathematica},
Volume = {84},
Number = {1},
Pages = {91-99},
Publisher = {KLUWER ACADEMIC PUBL},
Year = {1992},
ISSN = {0010-437X},
url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992JR84500008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
Key = {fds287250}
}
@article{fds287234,
Author = {Hain, RM},
Title = {Algebraic Cycles and Variations of Mixed Hodge Structure,
Complex Geometry and Lie Theory},
Volume = {53},
Pages = {175-221},
Booktitle = {Complex geometry and Lie theory (Sundance, UT,
1989)},
Publisher = {American Mathematical Society},
Year = {1991},
ISBN = {9780821814925},
url = {http://dx.doi.org/10.1090/pspum/053/1141202},
Doi = {10.1090/pspum/053/1141202},
Key = {fds287234}
}
@article{fds287235,
Author = {Hain, RM and MacPherson, R},
Title = {Introduction to Higher Logarithms},
Volume = {37},
Pages = {337-353},
Booktitle = {Properties of Polylogarithms},
Publisher = {American Mathematical Societ},
Editor = {Lewin, L},
Year = {1991},
ISBN = {9780821816349},
url = {http://dx.doi.org/10.1090/surv/037/15},
Doi = {10.1090/surv/037/15},
Key = {fds287235}
}
@article{fds287231,
Author = {Hain, RM and MacPherson, R},
Title = {Higher Logarithms},
Journal = {Illinois Journal of Mathematics},
Volume = {34},
Number = {2},
Pages = {392-475},
Year = {1990},
ISSN = {0019-2082},
url = {http://projecteuclid.org/euclid.ijm/1255988272},
Doi = {10.1215/ijm/1255988272},
Key = {fds287231}
}
@article{fds287232,
Author = {Hain, R and Tondeur, P},
Title = {The Life and Work of Kuo Tsai Chen},
Journal = {Illinois Journal of Mathematics},
Volume = {34},
Number = {2},
Pages = {175-190},
Publisher = {Duke University Press},
Year = {1990},
ISSN = {0019-2082},
url = {http://projecteuclid.org/euclid.ijm/1255988263},
Doi = {10.1215/ijm/1255988263},
Key = {fds287232}
}
@article{fds287233,
Author = {Hain, R},
Title = {Biextensions and heights associated to curves of odd
genus},
Journal = {Duke Mathematical Journal},
Volume = {61},
Number = {3},
Pages = {859-898},
Year = {1990},
ISSN = {0012-7094},
url = {http://dx.doi.org/10.1215/S0012-7094-90-06133-2},
Doi = {10.1215/S0012-7094-90-06133-2},
Key = {fds287233}
}
@article{fds287255,
Author = {Durfee, AH and Hain, RM},
Title = {Mixed Hodge Structures on the Homotopy of
Links},
Journal = {Mathematische Annalen},
Volume = {280},
Pages = {69-83},
Year = {1988},
ISSN = {0025-5831},
url = {http://dx.doi.org/10.1007/BF01474182},
Doi = {10.1007/BF01474182},
Key = {fds287255}
}
@article{fds287225,
Author = {Hain, RM and Zucker, S},
Title = {A Guide to Unipotent Variations of Mixed Hodge
Structure},
Journal = {Proceedings of the U.S. Spain Workshop},
Volume = {1246},
Pages = {92-106},
Publisher = {Springer-Verlag},
Year = {1987},
url = {http://dx.doi.org/10.1007/BFb0077532},
Doi = {10.1007/BFb0077532},
Key = {fds287225}
}
@article{fds287226,
Author = {Hain, RM},
Title = {Higher Albanese Manifolds},
Journal = {Proceedings of the U.S. Spain Workshop},
Volume = {1246},
Pages = {84-91},
Publisher = {Springer-Verlag},
Year = {1987},
url = {http://dx.doi.org/10.1007/BFb0077531},
Doi = {10.1007/BFb0077531},
Key = {fds287226}
}
@article{fds287227,
Author = {Hain, RM},
Title = {Iterated Integrals and Mixed Hodge Structures on Homotopy
Groups},
Journal = {Proceedings of the U.S. Spain Workshop},
Volume = {1246},
Pages = {75-83},
Publisher = {Springer-Verlag},
Year = {1987},
url = {http://dx.doi.org/10.1007/BFb0077530},
Doi = {10.1007/BFb0077530},
Key = {fds287227}
}
@article{fds287228,
Author = {Hain, RM},
Title = {The Geometry of the Mixed Hodge Structure on the Fundamental
Group},
Volume = {46},
Pages = {247-282},
Booktitle = {Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine,
1985)},
Publisher = {American Mathematical Society},
Year = {1987},
Key = {fds287228}
}
@article{fds287229,
Author = {Hain, RM and Zucker, S},
Title = {Truncations of Mixed Hodge Complexes},
Journal = {Proceedings of the U.S. Spain Workshop},
Volume = {1246},
Pages = {107-114},
Publisher = {Spring-Verlag},
Year = {1987},
url = {http://dx.doi.org/10.1007/BFb0077533},
Doi = {10.1007/BFb0077533},
Key = {fds287229}
}
@article{fds287230,
Author = {Carlson, JA and Hain, RM},
Title = {Extensions of Variations of Mixed Hodge Structure},
Pages = {39-65},
Publisher = {Theorie de Hodge},
Year = {1987},
Key = {fds287230}
}
@article{fds287252,
Author = {Hain, RM and Zucker, S},
Title = {Unipotent variations of mixed Hodge structure},
Journal = {Inventiones Mathematicae},
Volume = {88},
Number = {1},
Pages = {83-124},
Year = {1987},
ISSN = {0020-9910},
url = {http://dx.doi.org/10.1007/BF01405093},
Doi = {10.1007/BF01405093},
Key = {fds287252}
}
@article{fds287254,
Author = {Hain, RM},
Title = {The de rham homotopy theory of complex algebraic varieties
I},
Journal = {K-Theory},
Volume = {1},
Number = {3},
Pages = {271-324},
Year = {1987},
ISSN = {0920-3036},
url = {http://dx.doi.org/10.1007/BF00533825},
Abstract = {In this paper we use Chen's iterated integrals to put a
mixed Hodge structure on the homotopy Lie algebra of an
arbitrary complex algebraic variety, generalizing work of
Deligne and Morgan. Similar techniques are used to put a
mixed Hodge structure on other topological invariants
associated with varieties that are accessible to rational
homotopy theory such as the cohomology of the free loopspace
of a simply connected variety. © 1987 D. Reidel Publishing
Company.},
Doi = {10.1007/BF00533825},
Key = {fds287254}
}
@article{fds287256,
Author = {Hain, RM},
Title = {The de Rham homotopy theory of complex algebraic varieties.
II},
Journal = {$K$-Theory. An Interdisciplinary Journal for the
Development, Application, and Influence of $K$-Theory in the
Mathematical Sciences},
Volume = {1},
Number = {5},
Pages = {481-497},
Year = {1987},
ISSN = {0920-3036},
url = {http://dx.doi.org/10.1007/BF00536980},
Abstract = {We show that the local system of homotopy groups, associated
with a topologically locally trivial family of smooth
pointed varieties, underlies a good variation of mixed Hodge
structure. In particular we show that there is a limit mixed
Hodge structure on homotopy associated with a degeneration
of such varieties. © 1987 Kluwer Academic
Publishers.},
Doi = {10.1007/BF00536980},
Key = {fds287256}
}
@article{fds287223,
Author = {Hain, RM},
Title = {On the indecomposable elements of the bar
construction},
Journal = {Proceedings of the American Mathematical
Society},
Volume = {98},
Number = {2},
Pages = {312-316},
Publisher = {JSTOR},
Year = {1986},
Month = {January},
ISSN = {0002-9939},
url = {http://dx.doi.org/10.2307/2045704},
Abstract = {An explicit formula for a canonical splitting s:
Qℬ(ℰ.)⟶ℬ(ℰ.) of the projection
ℬ(ℰ.)⟶Qℬ(ℰ.) of the bar construction on a
commutative d.g. algebraℰ.onto its indecomposables is
given. We prove that s induces a d.g. algebra isomorphism
Λ(Qℬ(ℰ.))⟶ℬ(ℰ.) and that H(Qℬ(ℰ.)) is
isomorphic with QH(ℬ(ℰ.)). © 1986 American Mathematical
Society.},
Doi = {10.1090/S0002-9939-1986-0854039-5},
Key = {fds287223}
}
@article{fds287215,
Author = {HAIN, RM},
Title = {CORRECTION},
Journal = {TOPOLOGY},
Volume = {25},
Number = {4},
Pages = {585-586},
Year = {1986},
ISSN = {0040-9383},
url = {http://dx.doi.org/10.1016/0040-9383(86)90034-0},
Doi = {10.1016/0040-9383(86)90034-0},
Key = {fds287215}
}
@article{fds287222,
Author = {Hain, RM},
Title = {Mixed Hodge structures on homotopy groups},
Journal = {American Mathematical Society. Bulletin. New
Series},
Volume = {14},
Number = {1},
Pages = {111-114},
Publisher = {American Mathematical Society (AMS)},
Year = {1986},
ISSN = {0273-0979},
url = {http://dx.doi.org/10.1090/S0273-0979-1986-15410-8},
Doi = {10.1090/S0273-0979-1986-15410-8},
Key = {fds287222}
}
@article{fds287224,
Author = {Hain, RM},
Title = {On a Generalization of Hilbert’s 21st Problem},
Journal = {Annales Scientifiques de l’École Normale Supérieure.
Quatrième Série},
Volume = {19},
Number = {4},
Pages = {609-627},
Publisher = {Societe Mathematique de France},
Year = {1986},
ISSN = {0012-9593},
url = {http://www.numdam.org/item?id=ASENS_1986_4_19_4_609_0},
Doi = {10.24033/asens.1520},
Key = {fds287224}
}
@article{fds287253,
Author = {Hain, RM},
Title = {Iterated integrals, intersection theory and link
groups},
Journal = {Topology. An International Journal of Mathematics},
Volume = {24},
Number = {1},
Pages = {45-66},
Year = {1985},
ISSN = {0040-9383},
url = {http://dx.doi.org/10.1016/0040-9383(85)90044-8},
Doi = {10.1016/0040-9383(85)90044-8},
Key = {fds287253}
}
@article{fds320236,
Author = {HAIN, RM},
Title = {ITERATED INTEGRALS AND HOMOTOPY PERIODS},
Journal = {MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY},
Volume = {47},
Number = {291},
Pages = {1-98},
Publisher = {AMER MATHEMATICAL SOC},
Year = {1984},
Month = {January},
Key = {fds320236}
}
@misc{fds218732,
Author = {R.M. Hain},
Title = {The de Rham homotopy theory of complex algebraic varieties
(unpublished version)},
Year = {1984},
url = {http://www.math.duke.edu/faculty/hain/papers/big_red.pdf},
Key = {fds218732}
}
@book{fds287237,
Author = {Hain, RM},
Title = {Iterated Integrals and Homotopy Periods},
Volume = {47},
Pages = {iv-98},
Publisher = {American Mathematical Society},
Year = {1984},
url = {http://dx.doi.org/10.1090/memo/0291},
Doi = {10.1090/memo/0291},
Key = {fds287237}
}
@article{fds287269,
Author = {Duchamp, T and Hain, RM},
Title = {Primitive Elements in Rings of Holomorphic
Functions},
Journal = {Journal für die Reine und Angewandte Mathematik.
[Crelle’s Journal]},
Volume = {346},
Number = {346},
Pages = {199-220},
Publisher = {WALTER DE GRUYTER GMBH},
Year = {1984},
ISSN = {0075-4102},
url = {http://dx.doi.org/10.1515/crll.1984.346.199},
Doi = {10.1515/crll.1984.346.199},
Key = {fds287269}
}
@article{fds287221,
Author = {Hain, RM},
Title = {Twisting Cochains and Duality Between Minimal Algebras and
Minimal Lie Algebras},
Journal = {Transactions of the American Mathematical
Society},
Volume = {277},
Number = {1},
Pages = {397-411},
Publisher = {JSTOR},
Year = {1983},
ISSN = {0002-9947},
url = {http://dx.doi.org/10.2307/1999363},
Doi = {10.2307/1999363},
Key = {fds287221}
}
@article{fds287220,
Author = {Hain, RM},
Title = {Iterated Integrals, Minimal Models and Rational Homotopy
Theory},
Year = {1980},
Key = {fds287220}
}
@article{fds287219,
Author = {Hain, RM},
Title = {A characterization of smooth functions defined on a Banach
space},
Journal = {Proceedings of the American Mathematical
Society},
Volume = {77},
Number = {1},
Pages = {63-67},
Publisher = {American Mathematical Society (AMS)},
Year = {1979},
ISSN = {0002-9939},
url = {http://dx.doi.org/10.2307/2042717},
Abstract = {<p>A sufficient condition for a function defined on a Banach
space to be <inline-formula content-type="math/mathml"> ??
<mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD">
<mml:msup> <mml:mi>C</mml:mi> <mml:mi>k</mml:mi> </mml:msup>
</mml:mrow> <mml:annotation encoding="application/x-tex">{C^k}</mml:annotation>
</mml:semantics> </mml:math> </inline-formula> is given.
This enables us to characterize the <inline-formula
content-type="math/mathml"> ?? <mml:semantics> <mml:mrow
class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi>
<mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi>
</mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^\infty
}</mml:annotation> </mml:semantics> </mml:math>
</inline-formula> functions from one Banach space into
another Banach space as those functions that, for each
positive integer <italic>m</italic>, have the property that
the composition of the function with each <inline-formula
content-type="math/mathml"> ?? <mml:semantics> <mml:mrow
class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi>
<mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi>
</mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^\infty
}</mml:annotation> </mml:semantics> </mml:math>
</inline-formula> function from <inline-formula
content-type="math/mathml"> ?? <mml:semantics> <mml:mrow
class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow
class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD">
<mml:mi mathvariant="bold">R</mml:mi> </mml:mrow>
</mml:mrow> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow>
<mml:annotation encoding="application/x-tex">{{\mathbf
{R}}^m}</mml:annotation> </mml:semantics> </mml:math>
</inline-formula> into the domain of the function is
<inline-formula content-type="math/mathml"> ??
<mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD">
<mml:msup> <mml:mi>C</mml:mi> <mml:mi mathvariant="normal">∞<!--
∞ --></mml:mi> </mml:msup> </mml:mrow> <mml:annotation
encoding="application/x-tex">{C^\infty }</mml:annotation>
</mml:semantics> </mml:math> </inline-formula>.</p>},
Doi = {10.1090/s0002-9939-1979-0539632-8},
Key = {fds287219}
}
@article{fds287218,
Author = {Eades, P and Hain, RM},
Title = {On Circulant Weighing Matrices},
Journal = {Ars Combinatoria},
Volume = {2},
Pages = {265-284},
Year = {1976},
ISSN = {0381-7032},
Key = {fds287218}
}
@article{fds9675,
Author = {Richard M. Hain},
Title = {Moduli of Riemann Surfaces, Transcendental
Aspects},
Journal = {Moduli Spaces in Algebraic Geometry, ICTP Lecture Notes 1,
L. Gottsche editor, 2000, 293--353},
url = {http://arxiv.org/abs/math/0003144},
Key = {fds9675}
}
@article{fds8872,
Author = {Richard M. Hain},
Title = {Classical Polylogarithms},
Journal = {Motives, Proc. Symp. Pure Math. 55 part 2 (1994),
3--42},
Key = {fds8872}
}
@article{fds8846,
Author = {Richard M. Hain},
Title = {Algebraic cycles and variations of mixed Hodge
structure},
Journal = {Complex Geometry and Lie Theory, Proc. Symp. Pure Math, 53,
(1991), 175--221},
Key = {fds8846}
}
@article{fds8855,
Author = {Richard M. Hain},
Title = {The de Rham homotopy theory of complex algebraic varieties
I},
Journal = {Journal of K-Theory 1 (1987), 271--324},
url = {http://www.math.duke.edu/faculty/hain/papers/dht1.pdf},
Key = {fds8855}
}
@article{fds8856,
Author = {Richard M. Hain},
Title = {The de Rham homotopy theory of complex algebraic varieties
II},
Journal = {Journal of K-Theory 1 (1987), 481--497},
url = {http://www.math.duke.edu/faculty/hain/papers/dht2.pdf},
Key = {fds8856}
}
@article{fds8870,
Author = {Peter Eades and Richard M. Hain},
Title = {On circulant weighting matrices},
Journal = {Ars Combinatoria, 2 (1976), 265--284},
Key = {fds8870}
}
|
| 
Mathematics Department