报告题目1：Bifurcation Phenomena in Geometric Variational Problems

报告人：Paolo Piccione，University of São Paulo

报告时间：2023年10月10日（周二）14:00

报告地点：20-200

报告摘要：I will provide an overview of classical Bifurcation Theory, followed by an exploration of its contemporary applications in Riemannian Geometry. Topics covered will include minimal and constant mean curvature surfaces, as well as the Yamabe problem.

报告人简介：Paolo Piccione, Graduated in Mathematics from the University of Rome La Sapienza (Italy, 1987), and Ph.D. in Mathematics from Pennsylvania State University (USA, 1994), holds a Livre Docência at the University of São Paulo (1998). Served for three consecutive terms (2017-2023) as the President of the Brazilian Mathematical Society, and currently holding the position of Full Professor (MS-6) at the University of São Paulo. A full member of the Brazilian Academy of Sciences since May 2012, and a member of the Executive Committee of the International Mathematical Union (IMU) for a second term (2023-2025), as well as a member of the Special Committee on Work Regimes (CERT) at USP, and part of the Coordination of Area - Mathematics and Statistics at Fapesp. Admitted to the National Order of Scientific Merit in the rank of Commander, in the field of Mathematical Sciences, in 2018.
    He has served as a member of the Advisory Board in Mathematics for the Brazilian Ministry Of Science and Technology, President of the Research Committee of  the Institute of Mathematics and Statistics of the University of Sao Paulo (USP), member of the Research Council of USP, and member of the Sectoral Assessment Committee (CAS) for Mathematics and Statistics at the University of São Paulo. His mathematical specialty is Differential Geometry, primarily engaged in the following topics: Calculus of Variations and Geometric Variational Problems, Bifurcation Theory, Global Riemannian and Lorentzian Geometry, Morse Theory, Symplectic Geometry, and Hamiltonian Systems. He coordinates the Fapesp Thematic Project Algebraic, Topological, and Analytical Techniques in Differential Geometry and Geometric Analysis. Since March 2017, he has held the status of Researcher 1A of the Brazilian National Committee for Research.
    His contributions to the Brazilian Mathematical Society (SBM) encompass participation in the Evaluation Committee for the IMPA-SBM Journalism Prize, coordination of the SBM Prize Jury, and involvement in the editorial committees of the journals: Revista Matemática Universitária (Chief Editor), Matemática Contemporânea (Associate Editor), and the SBM Newsletter.

报告题目2：Classification results for critical sixth order PDEs with applications to conformal geometry

报告人：João Henrique Andrade，University of British Columbia

报告时间：2023年10月10日（周二）15:30

报告地点：20-200

报告摘要：We are concerned with classifying entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely, we show that when the origin is a non-removable singularity, solutions are given by a singular radial factor times a periodic solution to a sixth order ODE with constant coefficients. On the technical level, we combine integral sliding methods and qualitative analysis of ODEs, based on the conservation of energy result, to perform a topological two-parameter shooting technique. Furthermore, we present applications of this classification theorem to study some classical problems in conformal geometry, namely compactness and bifurcation results for GJMS equations.

报告人简介：João Henrique Andrade , received a doctor degree in Mathematics from Federal University of Paraíba in 2020(with visiting period at Princeton University). Currently holding the postdoctoral position in the Department of Mathematics of University of British Columbia, and the Institute of Mathematics and Statistics of University of São Paulo. Attended seminars at multiple internationally renowned universities, including College University of New York, University of British Columbia, Federal University of Paraíba, University of Brasília, University of Wuerzburg and Princeton University. Published papers in international journals such as Nonlinearity and Int. Math. Res. Not. IMRN.