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I completed my Ph.D. degree in August 2020 on regularity theory for many PDE models, under the direction of Prof. Edgard Pimentel. During my Ph.D. I held a Visiting Student position at UCF, Florida (Dec. 2018 - Nov. 2019), in collaboration with Prof. Eduardo Teixeira who became my co-advisor. From Oct. 2020 to July 2021, I held a postdoctoral position at the Centro de Investigación en Matemáticas (CIMAT) under the supervision of Prof. Héctor Chang-Lara, where we worked on regularity theory for porous medium-type equations. I also held a postdoctoral position at the University of São Paulo, ICMC-USP (Aug. 2021 - Feb. 2022) under the supervision of Prof. Ederson Moreira dos Santos. I also held a postdoctoral position at Instituto Superior Técnico - Lisbon, under the supervision of Prof. Hugo Tavares working on existence and regularity in shape optimization problems. Currently, I hold a junior research position at the Center for Mathematical Studies, University of Lisbon.
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Identification

Personal identification

Full name
Makson Sales Santos

Citation names

  • Santos, Makson
  • Santos, Makson S.

Author identifiers

Ciência ID
8C1D-9578-684A
ORCID iD
0000-0002-6933-2199

Email addresses

  • msasantos@ciencias.ulisboa.pt (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
Education
Degree Classification
2017/03/01 - 2020/08/20
Concluded
 Mathematics (Doctor)
Major in Partial differential equations
Pontifícia Universidade Católica do Rio de Janeiro, Brazil

University of Central Florida, United States
"Mostly regularity theory: interfaces and free boundaries" (THESIS/DISSERTATION)
2013/03 - 2015/08/15
Concluded
 Mathematics (Master)
Major in Differential geometry
Universidade Federal de Sergipe, Brazil
"Métricas com Q-curvatura constante via um fluxo não local e um princípio do máximo para o operador de Paneitz" (THESIS/DISSERTATION)
2009/03 - 2012/12
Concluded
 Mathematics (Bachelor)
Universidade Federal de Sergipe, Brazil
"O Paradoxo de Banach-Tarski" (THESIS/DISSERTATION)
Affiliation

Science

Category
Host institution 		Employer
2024/09/01 - Current Researcher (Research) Universidade de Lisboa Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Portugal
Universidade de Lisboa Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Portugal
2022/03/01 - 2024/08/31 Postdoc (Research) Universidade de Lisboa Instituto Superior Técnico, Portugal
Universidade de Lisboa Instituto Superior Técnico, Portugal
2021/08/01 - 2022/02/28 Postdoc (Research) Universidade de São Paulo Instituto de Ciências Matemáticas e de Computação, Brazil
Universidade de São Paulo Instituto de Ciências Matemáticas e de Computação, Brazil
2020/10/01 - 2021/07/28 Postdoc (Research) Centro de Investigacion en Matemáticas, Mexico
Centro de Investigacion en Matemáticas, Mexico
Projects

Contract

Designation Funders
2021/03/01 - 2025/02/28 Nonlinear Dispersive and Elliptic Systems - new horizons in regularity, dynamics and asymptotic analysis
PTDC/MAT-PUR/1788/2020
10.54499/PTDC/MAT-PUR/1788/2020
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Universidade de Lisboa Grupo de Física Matemática, Portugal

Universidade de Lisboa Instituto Superior Técnico, Portugal

FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal

Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
Fundação para a Ciência e a Tecnologia
Ongoing
Outputs

Publications

Book chapter
  1. Edgard A. Pimentel; Makson S. Santos. "Asymptotic Methods in Regularity Theory for Nonlinear Elliptic Equations: A Survey". 167-194. Springer International Publishing, 2018.
    10.1007/978-3-030-01947-1_8
Journal article
  1. Andrade, Pêdra D. S.; Moreira dos Santos, Ederson; Santos, Makson S.; Tavares, Hugo. "Spectral Partition Problems with Volume and Inclusion Constraints". SIAM Journal on Mathematical Analysis 56 6 (2024): 7136-7169. https://doi.org/10.1137/23m161553x.
    10.1137/23m161553x
  2. da Silva, João Vitor; Santos, Makson S.. "Schauder and Calderón–Zygmund type estimates for fully nonlinear parabolic equations under “small ellipticity aperture” and applications". Nonlinear Analysis 246 (2024): 113578. http://dx.doi.org/10.1016/j.na.2024.113578.
    Published • 10.1016/j.na.2024.113578
  3. Andrade, Pêdra D. S.; da Silva, João Vitor; Rampasso, Giane C.; Santos, Makson S.. "Sharp Regularity Estimates for a Singular Inhomogeneous (m, p)-Laplacian Equation". Potential Analysis (2024): https://doi.org/10.1007/s11118-024-10164-2.
    10.1007/s11118-024-10164-2
  4. Andrade, Pêdra D S; dos Prazeres, Disson S; Santos, Makson S. "Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy". Nonlinearity 37 4 (2024): 045009. http://dx.doi.org/10.1088/1361-6544/ad2c22.
    Published • 10.1088/1361-6544/ad2c22
  5. Héctor A. Chang-Lara; Makson S. Santos. "Hölder regularity for non-variational porous media type equations". Journal of Differential Equations 360 (2023): 347-372. http://dx.doi.org/10.1016/j.jde.2023.02.055.
    10.1016/j.jde.2023.02.055
  6. Edgard A. Pimentel; Makson Santos. "Fully nonlinear free transmission problems". Interfaces and Free Boundaries 25 3 (2023): 325-342. http://dx.doi.org/10.4171/ifb/489.
    10.4171/ifb/489
  7. Andrade, P. D. S.; Makson S. Santos. "Improved regularity for the parabolic normalized p-Laplace equation". Calculus of Variations and Partial Differential Equations 61 5 (2022): http://dx.doi.org/10.1007/s00526-022-02291-8.
    10.1007/s00526-022-02291-8
  8. Edgard Pimentel; Makson S. Santos; Eduardo V. Teixeira. "Fractional Sobolev regularity for fully nonlinear elliptic equations". Communications in Partial Differential Equations 47 8 (2022): 1539-1558. http://dx.doi.org/10.1080/03605302.2022.2059676.
    10.1080/03605302.2022.2059676
  9. Pêdra D. S. Andrade; Giane C. Rampasso; Santos, Makson. "Geometric regularity theory for a time-dependent Isaacs equation". Nonlinear Differential Equations and Applications NoDEA 29 2 (2022): http://dx.doi.org/10.1007/s00030-022-00752-9.
    10.1007/s00030-022-00752-9
  10. Edgard A. Pimentel; Makson S. Santos. "Improved regularity for the porous medium equation along zero level sets". Israel Journal of Mathematics 245 1 (2021): 135-151. http://dx.doi.org/10.1007/s11856-021-2208-z.
    10.1007/s11856-021-2208-z
  11. Raimundo Leitão; Edgard A. Pimentel; Makson S. Santos. "Geometric regularity for elliptic equations in double-divergence form". Analysis & PDE 13 4 (2020): 1129-1144. http://dx.doi.org/10.2140/apde.2020.13.1129.
    10.2140/apde.2020.13.1129
  12. Edgard Pimentel; Giane C Rampasso; Makson S Santos. "Improved regularity for the p-Poisson equation". Nonlinearity 33 6 (2020): 3050-3061. http://dx.doi.org/10.1088/1361-6544/ab7d21.
    10.1088/1361-6544/ab7d21
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2024 Spectral partition problems with volume constraint One day in free boundary problems and related topics
(Campinas, Brazil)
2024 From fully nonlinear elliptic equations to the fractional Laplacian UFS summer school
(Aracaju, Brazil)
2024 Regularity theory for fully nonlinear nonlocal equations Webinar in Analysis and Differential Equations
(Lisboa, Portugal)
2024 Regularity properties for spectral partition problems with volume and inclusion constraints Free boundary problems - Theory and applications
(João Pessoa, Brazil)
2023 Variational methods for an optimal partition problem with volume constraint LYMC 2023 – Lisbon Young Mathematicians Conference
Universidade Aberta (Lisbon, Portugal)
2023 Regularity for fully nonlinear elliptic equations via the fractional Laplacian CMUC Analysis Seminar
Universidade de Coimbra (Coimbra, Portugal)
2023 Optimal partition problems with volume constraint 34o Colóquio Brasileiro de Matemática
(Rio de Janeiro, Brazil)
2023 Regularity theory through approximation methods Ciclo de Palestras
(Aracaju, Brazil)
2023 From fully nonlinear elliptic equations to the fractional Laplacian Atlantic Conference in Nonlinear PDEs
(Lisboa, Portugal)
2023 Spectral partition problems with volume constraint Seminario di matematica applicata
(Pavia, Italy)
2022 Optimal partition problems with volume constraint 8th Workshop on Analysis and PDEs - UFS
Universidade federal de Sergipe (São Cristovão, Brazil)
2022 Improved regularity for the parabolic normalized p-Laplace equation Workshop on nonuniformly elliptic problems conference
Institute of Mathematics of the Polish Academy of Sciences (Varsóvia, Poland)
2022 Fractional Sobolev Regularity for fully nonlinear elliptic equations CMM PDE Seminar
Universidade do chile (Santiago (online), Chile)
2022 Improved regularity for the parabolic normalized p-Laplace equation Three Nonlinear Days in Coimbra
Universidade de Coimbra (Coimbra, Portugal)
2022 Fractional Sobolev Regularity for fully nonlinear elliptic equations Portugal-Italy Conference on Nonlinear Differential Equtions and Applications
Universidade de Évora (Évora, Portugal)
2022 Regularity theory for a non-variational porous medium equation Lisbon Young Mathematicians Conference
Faculdade de Ciências (Lisboa, Portugal)
2022 A non-variational approach to the porous medium approach XI Escola de Verão em Matemática
Universidade Federal de Sergipe (São Cristovão (online), Brazil)
2021 A non-variational approach to the porous medium approach CMUC Learning Seminar on Analysis of PDEs
Universidade de Coimbra (Coimbra (online), Portugal)
2021 Geometric regularity theory for a time-dependent Isaacs equation Webinar of young researchers in PDE and applied mathematics,
Universidade Federal Fluminense (Niterói (online), Brazil)
2021 A fully nonlinear free transmission problem Analysis and PDEs From the South
Universidade Federal de Rio de Janeiro (Rio de janeiro (online), Brazil)
2020 Improved regularity for the porous medium equation along zero level-sets ICMC Summer Meeting on Differential Equations 2020 Chapter
Universidade de São Paulo - ICMC (São carlos, Brazil)
2020 Improved regularity for the porous medium equation along zero level-sets IX Escola de Verão em Matemática - UFS
Universidade federal de Sergipe (São Cristovão, Brazil)
2020 Sobolev Regularity Theory for Degenerate Fully Nonlinear Elliptic Equations Rio Summer School on PDEs
Universidade Federal do Rio de Janeiro (Rio de janeiro, Brazil)
2018 Geometric regularity for elliptic equations in double-divergence form The International Workshop on Partial Differential Equations and Complex Analysis
Universidade Federal de São carlos - UFSCar (São Carlos, Brazil)
2018 Geometric regularity for elliptic equations in double-divergence form Workshop for Women in Differential Equations - ICM
Universidade Federal do ABC (Santo André, Brazil)

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2024/08/29 - 2024/08/29 Organizer of a thematic session at the Free boundaries - theory and applications (2024/08/29 - 2024/08/29)
Conference (Co-organisor)
2024/07/18 - 2024/07/18 Organizer of a satellite conference of the European Congress of Mathematics - Regularity theory and free boundary problems: from PDE to interfaces (2024/07/18 - 2024/07/18)
Congress (Co-organisor)
2021/10/01 - 2022/03/19 We organized with Edgard Pimentel (UC) a mini-symposium on PDEs at the SIAM Conference on Analysis of Partial Differential Equations 2022, focusing on regularity theory and free boundaries. (2022/03/14 - 2022/03/22)
Symposium (Co-organisor)
 Society for Industrial and Applied Mathematics, United States
2020/01 - 2020/08 We organized with Juliana Fernades and Edgard Pimentel weekly seminars (online) on partial differential equations. (2020/01 - 2020/10)
Seminar (Co-organisor)
 Pontifícia Universidade Católica do Rio de Janeiro, Brazil

Event participation

Activity description
Type of event 		Event name
Institution / Organization
2022 - 2022 ICMC Summer Meeting on Differential Equations 2022 Chapter (Online Event)
Meeting
 ICMC Summer Meeting on Differential Equations 2022 Chapter (Online Event)
Universidade de São Paulo Câmpus de São Carlos, Brazil
2022 - 2022 XIV Workshop de Verão em Matemática - MAT/UnB (Online Event)
Workshop
 XIV Workshop de Verão em Matemática - MAT/UnB
Universidade de Brasília, Brazil
2022 - 2022 Shape Optimization, related topics and applications
Workshop
 Shape Optimization, related topics and applications
Station Biologique de Roscoff, France
2021 - 2021 ICMC Summer Meeting on Differential Equations 2021 Chapter (Online Event)
Meeting
 ICMC Summer Meeting on Differential Equations 2021 Chapter
Universidade de São Paulo Câmpus de São Carlos, Brazil
2021 - 2021 XIII Workshop de Verão em Matemática - MAT/UnB (Online Event)
Workshop
 XIII Workshop de Verão em Matemática - MAT/UnB
Universidade de Brasília, Brazil
2021 - 2021 I Workshop de Pesquisadores Jovens em Análise e EDP (Online Event)
Workshop
 I Workshop de Pesquisadores Jovens em Análise e EDP
Universidade de Brasília, Brazil
2021 - 2021 33 Colóquio Brasileiro de Matemática - IMPA (Online Event)
Conference
 33 Colóquio Brasileiro de Matemática - IMPA
Instituto Nacional de Matemática Pura e Aplicada, Brazil
2018 - 2018 Satellite Conference - ICM 2018
Conference
 The Mathematics of Games in the Applied Sciences
Universidade Federal Fluminense, Brazil
2018 - 2018 Summer School and scientific visiting ICTP
Conference
 International School on Extrinsic Curvature Flows — smr 3209
Abdus Salam International Centre for Theoretical Physics, Italy
2018 - 2018 International Congress of Mathematicians
Congress
 International Congress of Mathematicians - 2018
International Mathematical Union, Germany
Distinctions

Other distinction

2023 Selected to participate in the 10th Heidelberg Laureate Forum
2021 Postdoctoral Fellowship FAPESP
Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil
2018 Doctoral scholarship ARQUIMEDES
Pontifícia Universidade Católica do Rio de Janeiro, Brazil
2018 Travel Grant for the participation in the International School on Extrinsic Curvature Flows
Abdus Salam International Centre for Theoretical Physics, Italy