Wataru KAI's web page
甲斐 亘のホームページ
Aza-Aoba 6-3, Sendai 980-8578, Japan.
I'm not an Associate Professor so I can't supervise a graduate student!
e-mail: kaiw(a)tohoku.ac.jp
News
March 2024: new preprint
"Equi-dimensionalization via subdivision of simplices"
https://arxiv.org/abs/2403.03062
June 2023: New preprint
"Linear patterns of prime elements in number fields"
https://arxiv.org/abs/2306.16983
3/4/2023: Video recording of my latest 20 minutes talk
"The Green-Tao theorem for number fields (and beyond)"
in Edinburgh is available at:
https://www.youtube.com/playlist?list=PLUbgZHsSoMEWd-QIL5igkHaAEw-k0FQxY
27/09/2022: New preprint
"Notes on Mitsui's Prime Number Theorem with Siegel zeros"
https://arxiv.org/abs/2209.11816
29/03/2022: From now on, I will be staying at University of Milan until March 2024 by JSPS funding.
Photo: April 2022,
Lake Maggiore, Italy
Publications
[Preprints]
Equi-dimensionalization via subdivision of simplices
https://arxiv.org/abs/2403.03062Linear patterns in prime elements in number fields.
https://arxiv.org/abs/2306.16983Notes on Mitsui's Prime Number Theorem with Siegel zeros. https://arxiv.org/abs/2209.11816
The Green-Tao theorem for affine curves over F_q. https://arxiv.org/abs/2101.00839
Constellations in prime elements of number fields. Joint with Masato Mimura, Akihiro Munemasa, Shin-ichiro Seki and Kiyoto Yoshino. https://arxiv.org/abs/2012.15669
[Published Articles]
Unramified logarithmic Hodge--Witt cohomology and P^1-invariance. Joint with Shusuke Otabe and Takao Yamazaki. Forum of Mathematics, Sigma, Volume 10, 2022, e19.
https://www.doi.org/10.1017/fms.2022.6 [open access!]
https://arxiv.org/abs/2105.07433Isomorphism up to bounded torsion between relative K_0-groups and Chow groups with modulus. with Ryomei Iwasa, Journal of the Institute of Mathematics of Jussieu, Volume 20, Issue 6, November 2021, 1947--1968.
https://doi.org/10.1017/S1474748020000055 [open access!]
arxiv:1811.04675 [math.KT]A moving lemma for algebraic cycles with modulus and contravariance. [Based on my doctoral thesis.]
International Mathematics Research Notices IMRN, Volume 2021, Issue 1, January 2021, Pages 475–522.
https://doi.org/10.1093/imrn/rnz018 [open access!]
arXiv:1507.07619 [math.AG]Chern classes with modulus. with Ryomei Iwasa, Nagoya Math. J., 236 (2019) Shuji Saito 60 volume, 84-133
https://doi.org/10.1017/nmj.2018.52
arXiv:1611.07882 [math.KT]
An online talk by my co-author.
[Warning] There has been found a gap in the proof of the Whitney sum formula. Specifically, Proposition 3.4 doesn't follow so easily from the commutative diagram (11). Please wait for an update, although I haven't been able to have enough time for this. (08 May 2021)
Notes on a p-adic exponential map for the Picard group. TOKYO J. MATH. VOL. 42, NO. 1, 2019, 35--49.
DOI: 10.3836/tjm/1502179262
arXiv:1309.6186 [Based on my master's thesis.]Suslin’s moving lemma with modulus. with H. Miyazaki. Ann. K-theory 3 (1) 2018, 55-70. https://doi.org/10.2140/akt.2018.3.55
arXiv:1604.04356Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus. with F. Binda, J. Cao, R. SugiyamaJ. Algebra 469 (2017) 437–463.
https://dx.doi.org/10.1016/j.jalgebra.2016.07.036
arXiv:1503.02161 [Based on our collaboration during my visit to Essen in summer 2014.]A higher-dimensional generalization of Lichtenbaum duality in terms of the Albanese map. Compos. Math. 152 (2016) 1915–1934.
https://doi.org/10.1112/S0010437X16007600
arXiv:1512.02026
[Survey]
数体におけるGreen-Taoの定理. (In Japanese. "The Green-Tao theorem for number fields") in RIMS Kôkyûroku No.2225 代数的整数論とその周辺 Algebraic Number Theory and Related Topics. Not peer-reviewed. 4 figures.
https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2225.htmlChow's moving lemma with modulus.in K-Theory (the Proceedings of International Colloquium 2016 on K-theory TIFR), 127--142, Hindustan Book Agency, New Delhi, India, 2018.
Some recent
conference and seminar talks
See here for an almost comprehensive list of talks
Techniques to move algebraic cycles, old and new
Seminar on periods and motives, 清華大学丘成桐数学科学中心 (Yau Mathematical Sciences Center, Tsinghua University), China (online), 25 April 2024.
https://ymsc.tsinghua.edu.cn/info/1053/3465.htm
Video recording:
http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Techniques_to_move_algebraic_cycles_old_and_new.html
Linear patterns of prime elements in number fields
- 2024 Feb: Séminaire de théorie des nombres de l'IMJ-PRG
https://www.imj-prg.fr/tn/STN/stnj.html - 2024 Jan: New Directions in Rational Points (50 minutes)
https://www.birs.ca/events/2024/5-day-workshops/24w4002 - 2023 Nov 8: London Number Theory Seminar
https://researchseminars.org/seminar/LNTS
- 2024 Feb: Séminaire de théorie des nombres de l'IMJ-PRG
The Green-Tao Theorem for number fields and beyond
- 2023 Jun 15: Gruppen und topologische Gruppen, University of Milan (35 minutes)
https://www.gtgconference.eu/Next.html
- 2023 Jun 15: Gruppen und topologische Gruppen, University of Milan (35 minutes)
The Green-Tao theorem for number fields (and beyond).
- 2023 Mar 9: Gauge Fields in Arithmetic, Topology & Physics (20 minutes)
video https://www.youtube.com/playlist?list=PLUbgZHsSoMEWd-QIL5igkHaAEw-k0FQxY
- 2022 Dec 16: Arithmetic Geometry Seminar, University of Milan
The Green-Tao theorem for number fields
- 2021 Dec 16: Algebraic Number Theory and Related Topics, Kyoto University RIMS. Notes
- 2021 Nov 22: Number Theory Seminar, Tohoku University. Notes
- 2021 May 05: Oberseminar Topologie, Universität Osnabrück. Whiteboards
- 2021 Mar 22: Math Seminar at RIKEN, Japan.
- 2021 Feb 09: Algebraic Geometry Seminar at KAIST.
Events (co)organized
Singularities and Arithmetic, 2020 (as one of the local organizers)
Yatsugatake workshop 2019 (along with many co-organizers)
Yatsugatake workshop 2016 (along with co-organizers)
Other services
(Co)organizer for Number Theory Seminar of Tohoku University, 2018-2023
Events and institutions visited since 2018
2024:
New Directions in Rational Points (7-12 Jan.)
https://www.birs.ca/events/2024/5-day-workshops/24w4002
2023:
Algebraic Number Theory and Related Topics 2023 (11-15 Dec.) https://sites.google.com/view/rims-ant2023/
Haramura 2023 (6-10 Sep.)
http://www.lcv.ne.jp/~smaki/en/yatsugatakeWS/index.html
A Festival Remembering Victor Snaith: Topology, Number Theory and Interaction (July)
https://heilbronn.ac.uk/2022/07/25/remembering-vic-snaith/Random Matrices from Quantum Chaos to the Riemann Zeta Function
- A Celebration in Honour of Jon Keating’s 60th Birthday
Gruppen und topologische Gruppen
https://www.gtgconference.eu/Next.html
A Panorama of Homotopy Theory --- A Conference in Honour of Mike Hopkins (June)
https://www.maths.ox.ac.uk/groups/topology/panorama-homotopy-theoryGauge Fields in Arithmetic, Topology & Physics. (Mar)
https://www.icms.org.uk/GaugeFieldsMotives in Tokyo (Feb)
2022: Harnessing motivic invariants (Essen)
The University of Milan (03.2022--03.2024)
2021: Algebraic Number Theory and Related Topics, Kyoto University RIMS (12.2021)
2020: The University of Milan (03.2020)
2019: NCMW - The Bloch-Kato conjecture (IISER Pune, India)
TIFR, Mumbai, India (19.12.2019--17.01.2020)
Motives in Tokyo
Asia-Australia Algebra Conference, Sydney
2018: Haramura Workshop 2018
Voevodsky Memorial
Motives in St. Petersburg (1st week)
Motivic homotopy theory and enumerative geometry (Essen)
Motives in Tokyo 2018 (Shuji Saito 60)
LinkedIn: linkedin.com/in/wataru-kai-6084542b
ORCID: https://orcid.org/0000-0002-4920-8043
科研費データベース: https://nrid.nii.ac.jp/ja/nrid/1000000804296/
若手研究「数体における加法的整数論」2022-2026 (合計416万円 = approx. 27,000 USD in total)
JSPS KAKENHI grant JP22K13886
若手研究「モジュラス付きChern類と代数的サイクルの高次の構造」2018-2023 (合計315万円 = approx. 20,000 USD in total)
JSPS KAKENHI grant JP18K13382
JSPS海外特別研究員: https://www.jsps.go.jp/j-ab/ab_list/list_r2.html
Links to some arXiv pages:
https://arxiv.org/list/math.AG/recent
https://arxiv.org/list/math.AT/recent
https://arxiv.org/list/math.CT/recent
https://arxiv.org/list/math.KT/recent
https://arxiv.org/list/math.NT/recent
https://arxiv.org/help/faq/whytex#comments (how to automatically delete embarrassing comments from a LaTeX file)
Lists of upcoming conferences
Ravi Vakil's https://math.stanford.edu/~vakil/conferences.html
Kiran Kedlaya's: https://mathweb.ucsd.edu/~kedlaya/cgi-bin/confs.cgi
London Math Soc's calendar: https://www.lms.ac.uk/events/calendar
Hiro Lee Tanaka's: https://www.hiroleetanaka.com/index.php?pageID=conferences
AMS's calender: https://www.ams.org/cgi-bin/mathcal/mathcalendar.pl
COMS: https://conference-service.com/conferences/mathematics.html
Number Theory Conferences, new and old: http://www.numbertheory.org/ntw/N3.html
London School of Economics: http://www.maths.lse.ac.uk/Personal/jan/conferences.html#other
Oxford Number Theory Seminar: https://www.maths.ox.ac.uk/groups/number-theory
GeCo Ged (complex and diff. geometry)i: https://gecogedi.dimai.unifi.it