eBook ISBN:  9781470414702 
Product Code:  CONM/608.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470414702 
Product Code:  CONM/608.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 608; 2014; 318 ppMSC: Primary 14; 20; 22; 32
This volume contains the proceedings of an NSF/Conference Board of the Mathematical Sciences (CBMS) regional conference on Hodge theory, complex geometry, and representation theory, held on June 18, 2012, at the Texas Christian University in Fort Worth, TX. Phillip Griffiths, of the Institute for Advanced Study, gave 10 lectures describing nowclassical work concerning how the structure of Shimura varieties as quotients of MumfordTate domains by arithmetic groups had been used to understand the relationship between Galois representations and automorphic forms. He then discussed recent breakthroughs of Carayol that provide the possibility of extending these results beyond the classical case. His lectures will appear as an independent volume in the CBMS series published by the AMS.
This volume, which is dedicated to Phillip Griffiths, contains carefully written expository and research articles. Expository papers include discussions of NoetherLefschetz theory, algebraicity of Hodge loci, and the representation theory of \(SL_{2}(\mathbb{R})\). Research articles concern the Hodge conjecture, HarishChandra modules, mirror symmetry, Hodge representations of \(Q\)algebraic groups, and compactifications, distributions, and quotients of period domains. It is expected that the book will be of interest primarily to research mathematicians, physicists, and upperlevel graduate students.
ReadershipGraduate students and research mathematicians interested in Hodge theory, algebraic/complex geometry, representation theory, mirror symmetry and related topics.

Table of Contents

Articles

Donu Arapura, Xi Chen and SuJeong Kang — The smooth center of the cohomology of a singular variety

John Brevik and Scott Nollet — Developments in NoetherLefschetz theory

James A. Carlson and Domingo Toledo — Compact quotients of nonclassical domains are not Kähler

Eduardo Cattani and Aroldo Kaplan — Algebraicity of Hodge loci for variations of Hodge structure

Mark Green and Phillip Griffiths — On the differential equations satisfied by certain HarishChandra modules

Tatsuki Hayama — KatoUsui partial compactifications over the toroidal compactifications of Siegel spaces

Aroldo Kaplan and Mauro Subils — On the equivalence problem for bracketgenerating distributions

Matt Kerr — Notes on the representation theory of $SL_{2}(\mathbb {R})$

Matt Kerr — Cup products in automorphic cohomology: The case of $Sp_{4}$

James D. Lewis — Hodge type conjectures and the BlochKato theorem

C. Robles — Principal Hodge representations

Sampei Usui — A study of mirror symmetry through log mixed Hodge theory


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This volume contains the proceedings of an NSF/Conference Board of the Mathematical Sciences (CBMS) regional conference on Hodge theory, complex geometry, and representation theory, held on June 18, 2012, at the Texas Christian University in Fort Worth, TX. Phillip Griffiths, of the Institute for Advanced Study, gave 10 lectures describing nowclassical work concerning how the structure of Shimura varieties as quotients of MumfordTate domains by arithmetic groups had been used to understand the relationship between Galois representations and automorphic forms. He then discussed recent breakthroughs of Carayol that provide the possibility of extending these results beyond the classical case. His lectures will appear as an independent volume in the CBMS series published by the AMS.
This volume, which is dedicated to Phillip Griffiths, contains carefully written expository and research articles. Expository papers include discussions of NoetherLefschetz theory, algebraicity of Hodge loci, and the representation theory of \(SL_{2}(\mathbb{R})\). Research articles concern the Hodge conjecture, HarishChandra modules, mirror symmetry, Hodge representations of \(Q\)algebraic groups, and compactifications, distributions, and quotients of period domains. It is expected that the book will be of interest primarily to research mathematicians, physicists, and upperlevel graduate students.
Graduate students and research mathematicians interested in Hodge theory, algebraic/complex geometry, representation theory, mirror symmetry and related topics.

Articles

Donu Arapura, Xi Chen and SuJeong Kang — The smooth center of the cohomology of a singular variety

John Brevik and Scott Nollet — Developments in NoetherLefschetz theory

James A. Carlson and Domingo Toledo — Compact quotients of nonclassical domains are not Kähler

Eduardo Cattani and Aroldo Kaplan — Algebraicity of Hodge loci for variations of Hodge structure

Mark Green and Phillip Griffiths — On the differential equations satisfied by certain HarishChandra modules

Tatsuki Hayama — KatoUsui partial compactifications over the toroidal compactifications of Siegel spaces

Aroldo Kaplan and Mauro Subils — On the equivalence problem for bracketgenerating distributions

Matt Kerr — Notes on the representation theory of $SL_{2}(\mathbb {R})$

Matt Kerr — Cup products in automorphic cohomology: The case of $Sp_{4}$

James D. Lewis — Hodge type conjectures and the BlochKato theorem

C. Robles — Principal Hodge representations

Sampei Usui — A study of mirror symmetry through log mixed Hodge theory