Prof. Tiago Henrique Picon

             Professor Doutor I
                Departamento de Computação e Matemática (DCM)
                Faculdade de Filosofia, Ciência e Letras de Ribeirão Preto (FFCLRP)
                Universidade de São Paulo (USP) 

                     
Address: Av. Bandeirantes, 3900 - Monte Alegre, Ribeirão Preto. São Paulo, Brasil. CEP 14040-901.

Email: picon @ ffclrp dot usp dot br     Horário:  II Semestre 2019    Curriculum (full cv): Currículo Lattes    

 


Disciplinas I Semestre de 2020

Complementos de Álgebra Linear (Bacharelado em Matemática Aplicada a Negócios - FFCLRP)

Geometria Diferencial (Bacharelado em Matemática Aplicada a Negócios - FFCLRP)

Geometria Analítica (Programa de Pós Graduação - PROFMAT)

Semestres Anteriores

 


Research interests : Linear PDEs and Harmonic Analysis

·         A priori estimates for ellipitic systems of complex vector fields;

·         L^1 estimates for elliptic operators; Div-curl estimates; 

·         Pseudodifferential and singular integral operators ;

·         Hardy spaces;

·         Multiplier operators and hyperbollic PDEs;

Current research projects:

(1)  “Algumas Equações Diferenciais Parciais de evolução em espaços singulares”, Projeto Universal CNPq (proc. 409306/2016-9)

(2)  Estimativas a priori para operadores elíticos e aplicações, Jovem Pesquisador em Centro Emergente II – Fapesp  (proc.: 2018/15484-7);

 

 

Completed research projects:

(1)  ”Resolubilidade contínua local para EDPs associada a operadores e complexos elípticos”, Auxílio Professor Visitante Fapesp

 (proc.: 17/17804-6); collaborator: Laurent Moonens (Unniversité Paris/Sud);

(2)  Estimativas a priori para complexos elíticos e aplicações, Jovem Pesquisador em Centro Emergente – Fapesp  (proc.: 2013/17636-5);

(3)  “Estimativas L^1 para sistemas elíticos de campos vetoriais complexos”, Programa de Apoio aos Novos Docentes USP (proc.: 13.1.1601.59.2 ).

(4)  “A priori estimates for semilinear hyperbolic and pseudo-hyperbolic equations”,  AUCANI – USP Santander; collaborator: Marcello D`Abbicco (University of Bari – Italy);

 

 


Publications:

Published papers:

1.    J. Hounie and T. Picon, “Local Gagliardo-Nirenberg Estimates for Elliptic Systems of Vector Fields”, Mathematical Research Letters, v. 18, p. 791-804, 2011.

2.    J. Hounie and T. Picon, “Local L^1 estimates for elliptic systems of complex vector fields”, Proceedings of American Mathematical Society, v. 143, p. 1501-1514, 2015.

3.    G. Hoepfner, J. Hounie and T. Picon, “Div-curl type estimates for elliptic systems of complex vector fields”, Journal of Mathematical Analysis and Applications, v. 429, 2, p. 774-799, 2015.

4.    M. D`Abbicco, M. Ebert and T. Picon, “Long time decay estimates in real Hardy spaces for evolution equations with structural dissipation”, Journal of Pseudo-Differential Operators and Applications, v. 7, p. 261-293, 2016.

5.    M. Ebert, R. Kapp and T. Picon, “L^1 – L^p estimates for radial solutions of the wave and application”, Annali di Matematica Pura ed Applicata, v. 195, p. 1081-1091, 2016.

6.    J. Hounie and T. Picon, “L^1 Sobolev estimates for (pseudo)-differential operators and applications”, Mathematische Nachrichten, v. 289, p. 1838-1854, 2016.

7.    M. D`Abbicco, M. Ebert and T. Picon, “Global existence of small data solutions to the semilinear fractional wave equation”, New Trends in Analysis and Interdisciplinary Applications, Pei Dang et alter (eds), Trends in Mathematics, Springer International Publishing AG, p. 465-471, 2017.

8.    L. Moonens and T. Picon, “Continuous solution for divergence-type equations associated to elliptic systems of complex vector fields”, Journal of Function Analysis, vol 275, 5, 1073-1099, 2018.

9.     L. Moonens and T. Picon, “Solving the equation div u=f in C_0(R^n,R^n)”, Proceedings of the Edinburgh Mathematical Society, v. 61, 1055-1061, 2018.

10.  C. Perez, T. Picon, O. Saari and M. Sousa, “Regularity of maximal functions on Hardy-Sobolev spaces”; Bulletin of the London Mathematical Society, v.50, 1007-1015, 2018. 

11.  M. D`abbicco, M. Ebert and T. Picon, “The critical exponent(s) for the semilinear fractional diffusive equation”, Journal of Fourier Analysis and Applications, v. 25, 3, 696-731, 2019;

 

 

Submitted papers:

12.  G. Hoepfner, R. Kapp and T. Picon, “On the continuity and compactness of pseudodifferential operators on localizable Hardy spaces”.

13.  J. Hounie and T. Picon, “Local Hardy-Littlewood--Sobolev inequalities for canceling elliptic differential operators”.

14.  L. Moonens and T. Picon, “Local continuous solutions for canceling and elliptic  linear differential operators”.

 

Others:

     Doctoral  thesis (in portuguese) Estimativas locais para complexos elíticos” ,  2011 (advisor: Prof. Jorge Hounie);

     Master dissertation  (in portuguese) Uma extensão da desigualdade de Gagliardo-Nirenberg”, 2008 (advsior: Prof. Ruidival dos Santos Filho);

 


Schedule:

2020

1.    University of Joseph Fourier , Grenoble, France (collaborator: Emmanuel Russ), February 17-20;

2.    Ludwig Maximilian University of Munich, Germany (collaborator: Mateus Sousa) January 25-Februaruy 01;

 

2019

3.    ICMC Summer Meeting on Differential Equations – Chapter 2019, University of São Paulo, São Carlos, Brazil, February 4-6;

4.    Federal University of Sergipe, Brazil, (collaborator: Marcelo Fernandes de Almeida) March 07-16;

5.    Seminários em Análise Harmônica, Federal University of Rio Grande do Sul, May 26-31;

6.    1st Joint Meeting Brazil-France in Mathematics, IMPA, Brazil, July 15-19;

7.    31th Brazilian Colloquium of Mathematics – Session: Harmonic Analysis and Applications, IMPA, July 29 – August 02;

8.    10 Workshop in Several Complex Variables and Partial Differential Equations, Serra Negra, Brazil, August 04-10;

9.    ICTP, Trieste - Italy, (collaborator: Emanuel Carneiro) November 04-19;

10.  Université  Paris/ Sud - Orsay France (supervisor: Prof. Guy David), December 01 – March 07;

 

 2018

11.  ICMC Summer Meeting on Differential Equations – Chapter 2018, University of São Paulo, São Carlos, Brazil, February 5-7;

12.  South American Workshop on Integral and Differential Equations, University of São Paulo, São Paulo, Brazil, February 26-28;

13.  ICM Satellite Conference -Harmonic Analysis, Porto Alegre, Brazil, July 24-29;

14.  International Congress of Mathematicians – ICM 2018, Rio de Janeiro, Brazil, August 1-9;

15.  ICM Satellite Conference -International Workshop on Harmonic Analysis and Partial Differential Equations, UFSCar, August 13-17;

16.  Symposium in Harmonic Analysis and Geometric Measure Theory, Ribeirão Preto, Brazil, August 20-22;

17.  VI Encontro Hotel de Hilbert EHH, Florianópolis, Brazil, November 20-25;

18.  Université  Paris/ Sud - Orsay France (collaborator: Laurent Moonens), December 06-29;

2017

19.  ICMC Summer Meeting on Differential Equations, University of São Paulo, Brazil, February 6-8;

20.  Workshop na UNB – Session: Análise, University of Brasilia, Brazil, February 13-15;

21.  Post-doctoral Summer Program, IMPA, Brazil, February  20-22;

22.  Federal University of Sergipe, Brazil, (collaborator: Marcelo Fernandes de Almeida) June 26-30;

23.  31th Brazilian Colloquium of Mathematics – Session: Harmonic Analysis and Approximation Theory, IMPA, July 31 – August 04;

24.  Workshop in Several Complex Variables and Partial Differential Equations, Serra Negra, Brazil, August 07-11;

25.  11th ISAAC congress – Session: Recent progress in evolution equations, University of Växjö, Sweden, August 14-18;

26.  University of Paris Sud - Orsay, France (collaborator: Laurent Moonens), September 27th to October 17th;

27.  Harmonic Analysis and Geometric Measure Theory, Marseille, France, October 02-06;

28.  5th WorkShop in Analysis and PDEs, UFS, Sergipe, Brazil, November 21-24;

2016

29.  IX Jornada de Equações Diferenciais Parciais – Conference on Analysis of PDEs, Federal University of São Carlos, Brazil, January 18-20;

30.  ICMC Summer Meeting on Differential Equations, University of São Paulo, Brazil, February 01-03;

31.  University of São Paulo, IME-USP (collaborator: Pedro Tavares), Brazil March;

32.  NonLinear PDEs@IMPA, IMPA, Rio de Janeiro, Brazil, June 20-24;

33.  4th WorkShop in Analysis and PDEs, UFS, Sergipe, Brazil, September 08-09;

34.  University of Bari, Italy (collaborator: Marcello D`Abbicco) October 31th to November 14th;

2015

35.  ICMC Summer Meeting on Differential Equations, University of São Paulo, Brazil, February 02-04;

36.  VIII Jornada de Equações Diferenciais Parciais, Federal University of São Carlos, Brazil, January 26-28;

37.  X Americas Conference on  Differential Equations and Nonlinear Analysis, University of Buenos Aires, Argentina, February 09-20;

38.  Special Program: Nonlinear Dispersive Equations,IMPA, Rio de Janeiro, Brazil, June

39.  Workshop in Several Complex Variables and Partial Differential Equations, Serra Negra, Brazil, August 03-07;

40.  International Conference on Current Trends in Analysis and Partial Differential Equations, IMPA, Rio de Janeiro, Brazil, August 17-21;

41.  Workshop in NonLinear PDE’s, Université Libre de Bruxelles, Brussel, September 07-11;

2014

42.  ICMC Summer Meeting on Differential Equations, University of São Paulo, Brazil, February 03-07;

43.  VII Jornada de Equações Diferenciais Parciais, Federal University of São Carlos, Brazil, January 20-22;

44.  AMS Fall Western Sectional Meeting – Recent Progress in Harmonic Analysis and Several Complex Variables, San Francisco, USA, October 25-26;

45.  Fourth Workshop on Fluids and PDE, IMPA, Rio de Janeiro, Brazil, May 26-30;

46.  Seminário de EDP, IMEEC-UNICAMP, Campinas, Brazil;

 

2013

47.  II Colóquio Brasileiro de Matemática da Região Sudeste, ICMC, University of São Paulo, Brazil, January 21-26;

48.  III Colóquio Brasileiro de Matemática da Região Centro Oeste, Federal University of Goias, Brazil, November 18-23;

49.  Symposium in Real Analysis XXXVII, ICMC, University of São Paulo, Brazil, June 03-06;

50.  VII Workshop in Several Complex Variables and Partial Differential Equations, Serra Negra, Brazil, August 05-09;

 

Citações: Google Scholar     Others: Genealogia Matemática

   

Visiting researchers

2019

Lucas Oliveira (UFRGS) - February 7-9;

Laurent  Moonens (Université Paris/Sud) – July 01-13;

Antonin Monteil (Université Catholique de Louvain) – July 05-12;

Pablo De Nápoli (Universidad de Buenos Aires ) -  July 21-27;

 

2018

Event: Symposium in Harmonic Analysis and Geometric Measure Theory - Link

Laurent  Moonens (Université Paris/Sud) – February to September;

Pablo De Nápoli (Universidad Buenos Aires) August 19-25;

Others

   

Academic Advisory

Phd`s thesis

1.       Victor Hugo Falcão Francheto (CAPES),”Espaços de Hardy radiais” (co-advisor in collaboration with Prof. Gustavo Hoepfner );

 

Master`s thesis

1.       Claudio Henrique Machado Vasconcelos Filho (CNPq), “Operadores de Calderón-Zygmund, Pseudo-Diferenciais e Espaços de Hardy”, March 2018;

2.       Thaysa Fernanda Elias (CAPES), “Uma nova caracterização dos espaços de Sobolev W^{1,p}(R^n)”, April 2018;

3.       Victor Sandrin Biliatto (Fapesp), “Resolubilidade e singularidades removíveis para equação divergente”, August 2019;

4.       Raphael Hoshijima (CAPES), “Uma estimativa L1 para o potencial de Riesz , August 2019”;

 

 

Master`s thesis: professional

5.       Clodoaldo Bevilaqua Avelar, “O fantástico mundo dos números complexos”, 2016.

6.       Caio Martins Raíz, “Transformações de Mobius e projeção na esfera de Riemann”, 2018.

7.       Jorge Silva, “Um estudo sobre cônicas: equações do segundo grau”, 2019.

 

Current

Ph.D 

2.       Claudio Henrique Machado Vasconcelos Filho (CAPES);

3.       Victor Sandrin Biliatto (CAPES);

4.       Raphael Hoshijima (CAPES);

 

Master

5.       Ana Catarina Bruxellas

 

 

Scientific Initiation 

6.       Catarina Barbosa (Fapesp ).

 


Others

Membro da Sociedade Brasileira de Matemática

Life membership of ISSAC Society (2018) – International Society for Analysis, its Applications and Computation