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Venice, 2014
What is a mathematician?
What is a mathematician?
I am a senior researcher at QSMS (Center for Quantum structures in Modules and Spaces), Seoul National University (Sep 2021 ~ current).
I was an associate professor at Department of Mathematics, Postech from Sep 2014 to Aug 2021 at Department of Mathematics, Postech (an assistant professor from July 2010 to Aug 2014). I was a postdoctoral fellow at Department of Mathematics and Statistics, McGill University (postdoc mentors: Henri Darmon and Adrian Iovita) from Sep 2007 to July 2010. I had been appointed as a Clay liftoff fellow during the summer of 2007. I earned my PhD at Boston University in May 2007 under the guidance of Glenn Stevens with the thesis "p-adic family of half-integral weight modular forms and its arithmetic applications". I obtained my Bachelor degree at Seoul National University in Feb 2001.
My research areas are number theory, arithmetic algebraic geometry, and their connections with physics (physical mathematics). More precisely, my works are concentrated on following 3 specific subjects:
arithmetic gauge theory (arithmetic Dijkgraaf-Witten theory, arithmetic Chern-Simons theory, and arithmetic BF theory);
B-side Frobenius manifolds and flat F-manifolds for algebraic varieties;
motivic and p-adic Eisenstein cocycles and their number-theoretic applications.
In general, I am interested in understanding the structural interactions between invariants of arithmetic schemes (algebraic varieties) and invariants in quantum field theory and the p-adic (arithmetic and analytic) structures and higher (homotopy) structures in number theory and algebraic geometry. Sometimes I like to describe myself as "a structure hunter".
Research key words: algebraic operads, algebraic varieties, arithmetic gauge theory (arithmetic Chern-Simons theory and arithmetic BF theory), Batalin-Vilkovisky formalism, dGBV algebras, Eisenstein cohomology, flat F-manifolds, Frobenius manifolds, homotopy Lie algebras, Iwasawa theory, Milnor K-theory, modular forms, modular symbols, p-adic zeta functions, p-adic theta correspondence, toric varieties, quantum field theory, Shintani cocycles, and totally real fields.
Email: jpark.math (at) gmail.com
Address: Jeehoon Park, QSMS, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, South Korea 08826
Publications:
Modular symbols with values in Beilinson-Kato distributions (with Cecilia Busuioc, Owen Patashnick, Glenn Stevens), to appear in the Transactions of the American Mathematical Society (2025), https://arxiv.org/abs/2311.14620
Comparison of Frobenius algebra structures on Calabi-Yau toric hypersurfaces (with Philsang Yoo), to appear in Journal of Pure and Applied Algebra (2025), http://arxiv.org/abs/2504.06694
BF path integrals for elliptic curves and p-adic L-functions (with Junyeong Park) to appear in Osaka Journal of Mathematics (2025), http://arxiv.org/abs/2312.05587
Period integrals of smooth projective complete intersections as exponential periods Journal of Pure and Applied Algebra, Volume 229, Issue 1 (Jan 2025), 107836, https://doi.org/10.1016/j.jpaa.2024.107836.
Entanglement entropies in the abelian arithmetic Chern-Simons theory (with Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Hwajong Yoo) Communications in Number theory and Physics, Volume 18 (2024) Number 3, pp. 579-609. https://dx.doi.org/10.4310/CNTP.240904011422
Path integrals and p-adic L-functions (with Magnus Carlson, Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Hwajong Yoo) Bulletin of the London Mathematical Society, Volume 56, Issue 6, Pages 1951-1966 (June 2024). https://doi.org/10.1112/blms.13036
Arithmetic Chern-Simons theory with real places (with Jungin Lee) Journal of Knot Theory and Its ramifications Vol. 32, No. 04, 2350027 (2023), https://doi.org/10.1142/S021821652350027X
A basis of algebraic de Rham cohomology of complete intersections over a characteristic zero field (with Junyeong Park) Communications in Algebra 50 (2022), no. 4, 1372–1388. https://doi.org/10.1080/00927872.2021.1981359
An algorithm for a lifted triple Massey product of a smooth projective plane curve (with Younggi Lee, Junyeong Park, Jaehyun Yim) International Journal of Algebra and Computation, Volume No 30, Issue No. 08 (2020), pp. 1651-1669, https://doi.org/10.1142/S0218196720500587, pdf
Arithmetic Chern-Simons theory II (with Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Hwajong Yoo) pages 81-128, "p-adic Hodge theory (editors: Bhatt, Bhargav; Olsson, Martin 2020)", ISBN 978-3-030-43844-9, Simons Symposia. pdf
Abelian arithmetic Chern-Simons theory and arithmetic linking numbers (with Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Georgios Pappas, Hwajong Yoo) International Mathematics Research Notices, Volume 2019, Issue 18, September 2019, Pages 5674–5702, https://doi.org/10.1093/imrn/rnx271. pdf
The Koszul-Tate type resolution for Gerstenhaber-Batalin-Vilkovisky algebras (with Donggeon Yhee) Journal of Homotopy Related Structures, June 2019, Volume 14, Issue 2, pp 455–475, https://doi.org/10.1007/s40062-018-0218-2. pdf
Differential Gerstenhaber-Batalin-Vilkovisky algebras for Calabi-Yau hypersurface complements (with Dokyoung Kim, Yesule Kim) Mathematika 64 (2018) Pages 637-651. pdf
Inverse values of the modular j-invariant and homotopy Lie theory (with Kwang-Hyun Kim, Yesule Kim) Proceedings of the American Mathematical Society, Volume 146, Number 8, August 2018, 3295-3305. pdf
The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes (with Byoung Du Kim) Acta Arithmetica 181 (2017), no. 3, 209–238. pdf
Milnor K_2 and p-adic zeta functions for real quadratic fields Annales mathématiques du Québec, Volume 41 (2017), Number 1, Pages 3-25. pdf
Enhanced homotopy theory for period integrals of smooth projective hypersurfaces (with Jae-Suk Park) Communications in Number theory and Physics, Volume 10 (2016), Number 2, Pages 235-337. pdf
On Teitelbaum type L-invariant of Hilbert modular forms attached to definite quaternions (with Masataka Chida, Chung Pang Mok) Journal of Number Theory, Volume 147, February 2015, Pages 633-665. pdf
Plus/minus p-adic L-functions for Hilbert modular forms (with Shahab Shahabi) Journal of Algebra, Volume 342, Issue 1, 15 September 2011, Pages 197-211. pdf
Another look at Gross-Stark units for the number field Q International Journal of Number Theory, Volume 7, Issue5 (2011), Pages 1379-1393. pdf
The Darmon-Dasgupta units over genus fields and the Shimura Correspondence Journal of Number Theory, Volume 130, Issue 11, November 2010, Pages 2610-2627. pdf
p-adic family of half-integral weight modular forms via overconvergent Shintani lifting Manuscripta Mathematica, Volume 131, Numbers 3-4 / March (2010), 355-384. pdf
Prepublications:
The arithmetic BF theory and the Cassels-Tate pairing (with Junyeong Park), submitted.
L^2-Hodge theory of hybrid Landau-Ginzburg models for Calabi-Yau complete intersections (with Jaewon Yoo), submiteed https://arxiv.org/pdf/2505.24218
A remark on L^2-Hodge theoretic construction of Frobenius manifolds for Calabi-Yau smooth projective hypersurfaces (with Jaewon Yoo), submitted https://arxiv.org/pdf/2505.18489
Twisted de Rham complex for toric Calabi-Yau complete intersections and flat F-manifold structures (with Junyeong Park), submitted http://arxiv.org/abs/2312.17144
Modular symbols with values in circular distributions (with Glenn Stevens)
A perturbative algorithm for flat F-manifolds associated to Landau-Ginzburg models (with Jaewon Yoo)
Polynomial realizations of period matrices of projective smooth complete intersections and their deformation (with Yesule Kim, Junyeong Park) https://arxiv.org/abs/2101.03488
The Milnor K-theory and the Shintani cocycle (with Sung Hyun Lim ) https://arxiv.org/abs/1909.03450
Batalin-Vilkovisky formalism in the p-adic Dwork theory (with Dohyeong Kim, Junyeong Park) https://arxiv.org/abs/1906.06564v2
Infinity is the most useful human mind's invention to understand the finite world; Questions are at the boundary of beauty and understanding is at the heart of beauty. -JP.
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