Haruzo HIDA

Distinguished Research Professor of Mathematics

Department of Mathematics, University of California, Los Angeles, California 90095-1555

Office Phone: (310) 206-3382

For e-mail address, see html

- Research visit again to TIFR, Mumbai, India from November 14 to December 15, 2024, attending a conference: [html]. Alongside, after TIFR, there will be a short research visit to HRI (Prayagraj, India) and IISc (Bangalore, India).
- An organizer of the ICTS conference: "Automorphic Forms and the Bloch–Kato Conjecture" from May 19 to May 30, 2025, Bengaluru, India.

- Fujiwara anniversary conference at University of Tokyo.
**Arithmetic Geometry, Algebraic Geometry and Analytic Geometry**[html], Tokyo Japan, from July 1st to July 5th, 2024.

Lecture at the conference: [Adjoint L-values and the Tate conjecture]. - A visit to Hokkaido University (Sapporo, Japan) in late June, and a number theory seminar talk: [Iwasawa's dream]
- A lecture series on Tate conjecture for quaternionic Shimura varieties at National Taiwan University
from March 19 to Mid June 2024 (Tuesdays),

**Lecture notes:**

Lecture 1: [pdf], Lecture 2: [pdf], Lecture 3: [pdf], Lecture 4: [pdf], Lecture 5: [pdf], Lecture 6: [pdf], Lecture 7: [pdf], Lecture 8: [pdf], Lecture 9: [pdf], Lecture 10: [pdf], Lecture 11: [pdf], Lecture 12: [pdf], Lecture 13: [pdf] (Last lecture),

and a visit to Academia Sinica (Taipei, Taiwan) in late June. - AIM workshop at CalTech:

from January 29 to February 2 (2024) at Caltech, Pasadena [html].**Analytic, arithmetic, and geometric aspects of automorphic forms**

mid-October 2023.**A research visit to Peking university, Beijing, China**

Lectures at Peking University [pdf], Morningside Center of Mathematics [pdf] and a colloquium talk at Renmin University.### International conference:

August 20-26, 2023 in Bedlewo, Poland [html].**Galois Representations and Automorphic Forms**

for May-June, 2023.**A research visit to Tata Institute of Fundamental Research (TIFR), Mumbai, India**A talk is given on May 31 at TIFR.

Alongside, research visits to Harish-Chandra Research Institute, Prayagraj, India and Indian Institute of Technology Kanpur, India are planned after the TIFR visit.

for April 10-15, 2023.**A research visit to Columbia University**

[html] for March 13-17 2023. Paderborn University, Paderborn, Germany.**A conference in memory of Claus-Günther Schmidt: "Special values of L-functions"**

Organising Committee: Haruzo Hida (UCLA), Fabian Januszewski (Paderborn University), Tadashi Ochiai (Osaka University), A. Raghuram (Fordham University).

from March 18 to 31 in 2023 (a seminar talk note [pdf]).**A research visit to Universite de Paris XIII**

[html] for 1/15-20/2023 Invited and attended online.**A BIRS conference: "Arithmetic Aspects of Deformation Theory (23w5134)"**

for November-December, 2022. A series of lectures: 1st talk notes [pdf] on adjoint L-value formula (which is also the notes for Pune talk), 2nd lecture notes [pdf] on local indecomposability of modular Galois representation.**A research visit to Tata Institute of Fundamental Research (TIFR), Mumbai, India****A colloquium talk on November 7 (2022) at Ashoka University, Delhi, India.****A colloquium talk on November 11 (2022) at Indian Institute of Technology Bombay, Mumbai, India.**

The pdf file [pdf] of the notes of the talk (the content of the talk at Ashoka U. and IIT is based on this note also).**A colloquium talk on November 17 (2022) at Tata Institute of Fundamental Research (TIFR), Mumbai, India**

The pdf file [pdf] of the notes of the talk (the content of the talk at IISER Pune is based on this note).**A colloquium talk on December 2 (2022) at IISER Pune, India**

9/27/2022.**A UCLA student seminar talk**- ICTS hybrid conference organized by Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS).

International Center for Theoretical Sciences, Bangalore, India.**Elliptic curves and the special values of L-functions, 08 August 2022 to 19 August 2022****A link to the notes of Hida's lecture:**[1st lecture], [2nd lecture], [3rd lecture], [last lecture].

- CEFIPRA online conference Organized by Baskar Balasubramanyam (IISER Pune, India), Vincent Pilloni (LMO, Paris Sacley),
Jacques Tilouine (Universite Paris 13) and Haruzo Hida (UCLA).
**L-functions and Iwasawa theory, November 15-19, 2021**The slide file of Hida's lecture at this conference: [pdf].

- Paris XIII SGAM seminar "Adjoint L-value as period integral" on May 28, 2021, slide file: [pdf], another talk [pdf].
- ICTS online conference
Organized by Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China)
from August 2 to August 7 in 2021 (Indian time).
**Elliptic Curves and the Special Values of L-Functions**

- Math 207c Spring 2020
- Math 205a Fall 2019
- Math 207a Winter 2019
- Math 207b Spring 2018
- Math 207a Winter 2018
- Math 205c Spring 2017
- Math 205b Winter 2017
- Math 205a Fall 2016
- Math 207b Winter 2016
- Math 205a Fall 2015
- Math 207b Winter 2014
- Math 207b Winter 2013
- Math 207b Winter 2012

- Koji Kitagawa, 1991 (1963-2007)
- Brad Wilson, 1993
- Chandrashekhar Khare, 1995 Khare's homepage
- Eknath Ghate, 1996 Ghate's homepage
- Sheena Cho, 1999, the thesis of Sheena Cho is a part of her joint work with V. Vatsal. Here is Vatsal's web site which contains the preprint: [Vatsal's home page]
- Ami Fischman, 2001, his paper (which is a part of his thesis) [Fischman's home page]
- Hsin-Tai Wu, 2001,
- Cristian Virdol, 2005, his papers (including his thesis) [Virdol's homepage]
- Hae-Sang Sun, 2007, his papers (including his thesis) [Sun's home page]
- Craig Citro, 2009, his papers [Citro's home page]
- Lin Chen, 2009, (passed away untimely in 2009 after graduation)
- Miljan Brakočević, 2011
- Bin Zhao, 2014, his papers [Research Gate]
- Ashay Burungale, 2015, his papers [Ashay's homepage]
- Jaclyn Lang, 2016, her papers [Jackie's homepage]
- Geunho Gim, 2018
- Jaehoon Lee, 2019
- John Yu, 2019

A brief [CV] and Mazur's account on Hida's work with Koji Doi [pdf] (see also the first page of [pdf]). Doi was an important figure in Hida's life as a mentor and also the one who introduced Hida Number Theory (as Hida did not have any under-graduate level knowledge of Mathematics until towards the end of his junior year of the undergraduate study when he somehow met Professor Doi in Kyoto). Doi passed away in summer 2016. Shimura momorial article [Notice AMS] (pdf file) and Taiwan Academia Sinica interview in Chinese [pdf].

Full List of Publication by H. Hida [pdf] and List of publications with review (subscription to MathSciNet necessary to view) [html]

H. Hida, *Elementary Modular Iwasawa Theory*, published in January 2022 in ``Series on Number Theory and its Application **16**", World Scientific:

[World Scientific web site on this book] (preface and Chapter 1 available free posted on this page),
a slide file for the summary of Chapter 4 [pdf]

H. Hida, *Elliptic Curves and Arithmetic Invariants*, Springer Monographs in Mathematics, 2013,

[Springer link] and
[Springer web site of this book]

H. Hida, *Geometric Modular Forms and Elliptic Curves*, Second Expanded Edition,
World Scientific Publishing Co., Singapore, 2011,

[World Scientific web site on this book]
(Chapter 1 is free to download from this site)

H. Hida, *Hilbert Modular Forms and Iwasawa Theory,*
Oxford Mathematical Monographs, Oxford University Press, 2006

[
Oxford web site on this book].
A list of misprints (as of 10/16/22):
[pdf]

H. Hida, *p-Adic Automorphic Forms on Shimura Varieties*,
Springer Monographs in Mathematics, 2004,

[Springer link],
A list of misprints (as of 6/26/07):
[pdf]

H. Hida, *Modular Forms and Galois Cohomology*,
Cambridge Studies in advanced mathematics **69**, 2000,

[
Cambridge University Press web site on this book
],
A list of misprints (as of March 1, 2021):
[pdf]

H. Hida, *Geometric Modular Forms and Elliptic Curves*,
World Scientific Publishing Co., Singapore, 2000,

A list of misprints (as of September 16, 2011):
[pdf]

H. Hida, *Elementary Theory of
L-functions and Eisenstein series*,
1993, Cambridge University Press, Book
[Cambridge web page]

*p-Adic Aspects of Modular Forms*, edited by Baskar Balasubramanyam, Haruzo Hida, A Raghuram, Jacques Tilouine, World Scientific Publishing Co., Singapore, 2016,

[World Scientific web site on this book]
(Chapter 1 is free to download from this site)

These works are supported partially by various NSF grants if acknowledged.

H. Hida, *The universal ordinary deformation ring associated to a real quadratic field,*
preprint [Version of 3/10/21] (e=2 is stil an open question), published online in 2022, Math. Sciences, Proc. Indian Academy of Sci.,
reprint from Springer [pdf], reprint from Indian Academy [pdf],
a Youtube link to a lecture at Columbia U.
[11/19/20], a slide for a graduate student seminar lecture [pdf].

H. Hida, *Local indecomposability via a presentation of the Hecke algebra,* appendix to "Class groups and local indecomposability for non-CM forms"
by F. Castella and C. Wang-Erickson, Journal of the European Mathematical Society, EMS site: [EMS] (entire paper),
a preprint version: [ArXiv].

H. Hida, *Cyclicity of adjoint Selmer groups and fundamental units,* posted on Project Euclid: [pdf],
preprint version of 12/28/20 [pdf],
"Development of Iwasawa theory - The Centennial of K. Iwasawa's Birth" from Advanced Studies in Pure Mathematics **86** (2020), 351-411 (MSJ), a slide
at Iwasawa 2017 [pdf].

H. Hida and J. Tilouine, *Symmetric Power Congruence Ideals and Selmer Groups,* preprint version of 10/12/18 [pdf],
Journal of the Inst. of Math. Jussieu. **19** (2020), 1521-1572 ,
[html].

A. Burungale and H. Hida, *p-rigidity and Iwasawa mu-invariants*, Algebra & Number Theory **11** (2017), 1921-1951,
a link to a reprint [html],
a preprint version,
[pdf].

H. Hida, *Control of Lambda-adic Mordell-Weil groups*,
in "Elliptic Curves, Modular Forms and Iwasawa Theory" pp.253-294
(Coates 70th anniversary proceedings volume in "Proceedings in Mathematical Sciences **188**, 2016" from Springer), a preprint version
[pdf], Springer web page
[htm] (ISBN 978-3-319-45032-2).

H. Hida, *Arithmetic of adjoint L-values*, Chapter 6 of *p-Adic Aspects of Modular Forms,* pp.185-236, World Scientific, 2016,
Beijing lecture series web page,
Lecture notes: No.1 [pdf], No.2 [pdf].

H. Hida, *Growth of Hecke fields along a p-adic analytic family of modular forms*,
"Families of Automorphic Forms and the Trace Formula", pp.129-173,
Simons Symposia, Springer, 2016, DOI 10.1007/978-3-319-41424-9-4, a reprint [pdf],
Springer web site for the book [html].

A. Burungale and H. Hida, *Andre-Oort conjecture and non-vanishing of central L-values over Hilbert class fields,*
Forum of Mathematics, Sigma 4 (2016), e20, 26 pp, DOI: [htm].

H. Hida, *Limit Mordell-Weil groups and their p-adic closure,*
Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015) 221-264, Reprint file from Documenta Math: [pdf].

H. Hida and J. Tilouine, *Big image of Galois representations and the congruence ideal,*
in the proceedings of the 2013 Bonn conference, Hausdorff
trimester, LMS Lecture notes **420** (2015), 217-254, preprint, a version of 8/16/14 [pdf].

H. Hida, *Big Galois representations and p-adic L-functions*, Compositio Math. **151** (2015), 603-664,
doi:10.1112/S0010437X14007684, link to the journal repreint file
[pdf],
a preprint version of 7/6/2014:[pdf],
a slide for Paris talk [pdf].

A. Burungale, H. Hida and Shilin Lai, *On the Frobenius fields of abelian varieties over number fields,* preprint: [ArXiv] a version of 6/23/2024,

H. Hida, *Non-vanishing of integrals of a mod p modular form, a preliminary version,* preprint: [Version of 1/24/24],
ICTS hybrid conference lectures: [1st lecture], [2nd lecture], [3rd lecture], [last lecture],

H. Hida, *Adjoint L-value as a period integral and the mass formula of Siegel-Shimura,* to appear in Kyoto Journal of Mathematics, preprint: [Version of 4/18/23] (a preliminary version),
slide files [pdf] (11/15/21), [pdf] (4/14/23).

A. Burungale, H. Hida and Y. Tian, *Horizontal variation of Tate--Shafarevich groups,* a version of 12/31/17 [ArXiv],

H. Hida, *Anticyclotomic cyclicity conjecture,* preprint (a version of 6/23/17) [pdf], Rubinfest slide [pdf],
a BIRS talk slide [pdf].

H. Hida, *A series of lectures at Tata institute of fundamental research (Mumbai, India)* 6/25/15-7/23/15,
1. Graduate students seminar [pdf],
2. Two lectures for limit Tate-Shafarevich groyps [pdf], [pdf],
3. Colloquium talk [pdf],
4. A lecture on limit Mordell-Weil groups [pdf].

H. Hida, *Analytic variation of Tate-Shafarevich groups*,
preprint, a version of 11/2/17 [pdf].

H. Hida, *On the rank of Mordell-Weil groups of abelian varieties of GL(2)-type*, preprint, a version of 11/20/14 [pdf].

These works are supported partially by various NSF grants as acknowledged in each article.

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