Periods and Algebraicity

This is the webpage of the research project ‘‘Periods and Algebraicity’’ supported by the São Paulo Research Foundation (FAPESP) Young Investigator Grant #2020/15804-1 (October 2021 – September 2026), hosted at IMECC–Unicamp.

Team:

• Tiago J. Fonseca (PI) - Unicamp
• Otávio Cunha Oliveira (PhD student) - Unicamp
• Nelson P. P. Serrano (PhD student) - Unicamp
• Mario Raúl Ruiz Córdova (PhD student) - Unicamp
• Otávio Casagrande Ferrari (master’s student) - Unicamp
• Henrique de Cristo Fonseca (undergraduate research student) - Unicamp
• Laura Torquato Rangel (undergraduate research student) - Unicamp
• Izabella Calais Fernandes (undergraduate research student) - Unicamp

External collaborators:

• Francis Brown - Oxford
• Nils Matthes

Publications:

• F. Brown, T. J. Fonseca - Single-valued periods of meromorphic modular forms and a motivic interpretation of the Gross-Zagier conjecture. Preprint. [arXiv]
• T. J. Fonseca, N. Matthes - Elliptic KZB connections via universal vector extensions. Algebra Number Theory 19 (2025), no. 7, 1369–1425. [arXiv]
• T. J. Fonseca, N. Matthes - A note on the Gauss-Manin connection for abelian schemes. Rend. Semin. Mat. Univ. Padova 152 (2024), 117–131. [arXiv]

Master’s dissertations:

• Mario Raúl Ruiz Córdova - Períodos de variedades algébricas: Equivalências, motivos e conjecturas. Unicamp, 2026.
• Nelson P. P. Serrano - Grupos fundamentais em geometria algébrica. Unicamp, 2024. [pdf]
• João Gabriel Oliveira de Jesus - Propriedades aritméticas do j-invariante. Unicamp, 2023. [pdf]

Ongoing theses:

• Otávio Cunha Oliveira - Algebraic differential equations on Shimura varieties. PhD (FAPESP fellowship).
• Nelson P. P. Serrano - Tannakian formalism of unipotent fundamental torsors and applications. PhD.
• Otávio Casagrande Ferrari - Aritmética dos períodos e quase-períodos de formas modulares. Master’s (FAPESP fellowship).

Events:

• Segunda Semana de Encontros Aritméticos (II SemEAr), IMECC–Unicamp, 24–27/02/2026. Supported by FAPESP (grant #2025/21023-6).

Some talk videos or slides:

• T. J. Fonseca - A motivic approach to the Gross–Zagier conjecture. Séminaire AGATA, Université de Montpellier, 2026.
• T. J. Fonseca - Elliptic KZB equations via the universal vector extension. Workshop ‘‘Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights’’, INI Cambridge, 2022.
• T. J. Fonseca - From multiple polylogarithms to the universal vector extension of an elliptic curve. Fields Number Theory Seminar, 2022.

Outreach:

• T. J. Fonseca - Como calcular trilhões de dígitos de π usando apenas papel, caneta e um supercomputador (slides). Seminário Bolachinha, IMECC-Unicamp, 10/03/2026.
• Izabella Calais Fernandes - Números congruentes e a conjectura BSD. Won the top prize at the 2nd Semana Nacional de Iniciação Científica (II SENIC-SBM).