### Special Issue on Modular Forms and String Theory in honor of Noriko Yui

The Guest Editors for this special issue are

Charles Doran (University of Alberta, Canada)
Yasuhiro Goto (Hokkaido University of Education at Hakodate, Japan)
Ling Long (Louisiana State University, USA)

This special issue of SIGMA is related to the Banff International Research Station workshop entitled “Modular Forms in String Theory”, which was held from September 25th to September 30th, 2016. During this workshop we celebrated the work of Professor Noriko Yui and recognized her outstanding contributions to number theory/arithmetic geometry in relation to physics (string theory).

Number theorists/arithmetic geometers and string theorists have traditionally had very few interactions, living as it were in parallel universes. This trend changed when the workshop series on “Number Theory and Physics at the Crossroads” got started in early 2000, with Noriko Yui being one of the principal architects. Among her other contributions to the field, Noriko Yui has been the managing editor for the journal “Communications in Number Theory and Physics” since 2006.

Noriko Yui started her career at Tsuda University in Japan, and obtained her Ph.D. from Rutgers University in 1974. Her Ph.D. Thesis was on “Elliptic Curves and Formal Groups”. Her formal thesis advisor was Richard T. Bumby (Rutgers University), though her Ph.D. Thesis was strongly influenced by Frans Oort (Utrecht University). Noriko Yui held academic positions in Germany, the United States, and Canada before she started her current position at Queen's University in 1987. She has had many visiting positions and has given many invited talks all over the world. In particular, Noriko Yui regularly visits Tsuda University to give graduate courses and/or organize workshops on Calabi–Yau varieties, mirror symmetry and related topics. Thanks to such activities, a lot of young mathematicians have been encouraged to pursue their career in mathematics and interactions of researchers from many branches of mathematics have been greatly promoted.

In her long academic career, Noriko Yui has done distinguished work on elliptic and hyper-elliptic curves, formal groups, Fermat/diagonal varieties, and more recently, on the arithmetic properties of Calabi–Yau varieties and their $L$-functions in connection with the mirror symmetry (conjecture) in string theory.

Noriko Yui has supervised or co-supervised many Ph.D. students all over the world, which include: Chiao-Hun Chen, Swantje Gährs, Alice Garbarnati, Yasuhiro Goto, Ira Helsloot, Kristin Lauter, Ling Long, Alex Molnar, Ronald van Luijk, Walter Tautz, Thomas Valente. Also she has supervised more than twenty postdoctoral fellows. This long list of postdoctoral fellows includes, Simon Rose, Ian Kiming, Remke Kloosterman, Robert Osburn, Jaap Top, and Yifan Yang, who attended the Banff workshop.

Noriko Yui was elected a Fellow of the Fields Institute in 2006. She has been extremely active in organizing conferences and workshops. This proceedings is in line with the following list of previous ones co-edited by Noriko Yui:

1. Yui N., Lewis J.D. (Editors), Calabi–Yau varieties and mirror symmetry, Proceedings of the Workshop on Arithmetic, Geometry and Physics around Calabi–Yau Varieties and Mirror Symmetry (Toronto, ON, July 23–29, 2001), Fields Institute Communications, Vol. 38, Amer. Math. Soc., Providence, RI, 2003, xvi+367 pp.
2. Lewis J.D., Yui N., Yau S.-T. (Editors), Mirror symmetry. V, Proceedings of the Workshop on Calabi–Yau Varieties and Mirror Symmetry (Banff, AB, December 6–11, 2003), AMS/IP Studies in Advanced Mathematics, Vol. 38, Amer. Math. Soc., Providence, RI, International Press, Somerville, MA, 2006, x+576 pp.
3. Yui N., Verrill H., Doran C.F. (Editors), Modular forms and string duality, Proceedings of the BIRS Workshop on Modular Forms and String Duality (Banff, AB, June 3–8, 2006), Fields Institute Communications, Vol. 54, Amer. Math. Soc., Providence, RI, Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2008, xviii+297 pp.
4. Laza R., Schütt M., Yui N. (Editors), Arithmetic and geometry of K3 surfaces and Calabi–Yau threefolds, Proceedings of the workshop held at the Fields Institute and University of Toronto (Toronto, ON, August 16–25, 2011), Fields Institute Communications, Vol. 67, Springer, New York, Fields Institute for Research in Mathematical Sciences, Toronto, ON, 2013, xxvi+602 pp.
5. Laza R., Schütt M., Yui N. (Editors), Calabi–Yau varieties: arithmetic, geometry and physics. Lecture notes on concentrated graduate courses. Lectures from the workshops held at the Fields Institute for Mathematical Sciences (July 1 – December 31, 2013), Fields Institute Monographs, Vol. 34, Fields Institute for Research in Mathematical Sciences, Toronto, ON; Springer, New York, 2015, x+547 pp.

This issue includes 21 papers covering various topics related to Noriko Yui's work.

We wish to thank also all the workshop participants, all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reports.

The Guest Editors

Papers in this Issue:

Integral Regulators for Higher Chow Complexes
Muxi Li
SIGMA 14 (2018), 118, 12 pages   [ abs   pdf ]
Normal Functions over Locally Symmetric Varieties
Ryan Keast and Matt Kerr
SIGMA 14 (2018), 116, 18 pages   [ abs   pdf ]
Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
Scott Carnahan, Takahiro Komuro and Satoru Urano
SIGMA 14 (2018), 114,   8 pages   [ abs   pdf ]
Zhegalkin Zebra Motives Digital Recordings of Mirror Symmetry
Jan Stienstra
SIGMA 14 (2018), 110, 29 pages   [ abs   pdf ]
Hyper-Algebras of Vector-Valued Modular Forms
Martin Raum
SIGMA 14 (2018), 108, 17 pages   [ abs   pdf ]
Hesse Pencils and 3-Torsion Structures
Ane S.I. Anema, Jaap Top and Anne Tuijp
SIGMA 14 (2018), 102, 13 pages   [ abs   pdf ]
A Note on the Formal Groups of Weighted Delsarte Threefolds
Yasuhiro Goto
SIGMA 14 (2018), 097, 12 pages   [ abs   pdf ]
Computing Special $L$-Values of Certain Modular Forms with Complex Multiplication
Wen-Ching Winnie Li, Ling Long and Fang-Ting Tu
SIGMA 14 (2018), 090, 32 pages   [ abs   pdf ]
A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
SIGMA 14 (2018), 086, 16 pages   [ abs   pdf ]
The Chevalley-Weil Formula for Orbifold Curves
Luca Candelori
SIGMA 14 (2018), 071, 17 pages   [ abs   pdf ]
Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
SIGMA 14 (2018), 057, 13 pages   [ abs   pdf ]
The Künneth Formula for the Twisted de Rham and Higgs Cohomologies
Kai-Chieh Chen and Jeng-Daw Yu
SIGMA 14 (2018), 055, 14 pages   [ abs   pdf ]
Evaluation of Certain Hypergeometric Functions over Finite Fields
Fang-Ting Tu and Yifan Yang
SIGMA 14 (2018), 050, 18 pages   [ abs   pdf ]
Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds
Shinobu Hosono and Hiromichi Takagi
SIGMA 14 (2018), 039, 37 pages   [ abs   pdf ]
Manifold Ways to Darboux-Halphen System
John Alexander Cruz Morales, Hossein Movasati, Younes Nikdelan, Raju Roychowdhury and Marcus A.C Torres
SIGMA 14 (2018), 003, 14 pages   [ abs   pdf ]
A Universal Genus-Two Curve from Siegel Modular Forms
SIGMA 13 (2017), 089, 17 pages   [ abs   pdf ]
Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces
Remke Kloosterman
SIGMA 13 (2017), 087, 22 pages   [ abs   pdf ]
Twists of Elliptic Curves
Max Kronberg, Muhammad Afzal Soomro and Jaap Top
SIGMA 13 (2017), 083, 13 pages   [ abs   pdf ]
Hodge Numbers from Picard-Fuchs Equations
Charles F. Doran, Andrew Harder and Alan Thompson
SIGMA 13 (2017), 045, 23 pages   [ abs   pdf ]
GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
Jie Zhou
SIGMA 13 (2017), 030, 32 pages   [ abs   pdf ]
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
Atsushi Kanazawa
SIGMA 13 (2017), 024, 13 pages   [ abs   pdf ]