We want to announce the new IMSA's Frontiers in Mathematics Lecture Series. This lecture series aims to highlight outstanding recent achievements in mathematics, with a particular emphasis on those of female mathematicians from Latin America or working in Latin America.
The lectures consist of a week-long visit to IMSA during which the awardee will deliver two in-person lectures. There will be a live broadcast at IMSAC institutions and other universities worldwide. The lectures should give a general mathematical audience explanation of the speaker's oeuvre.
Frontiers Seminar
Carolina Benedetti, University of Los Andes, Bogotá, Colombia
Wednesday, November 15 & Thursday, November 16, 2023
Frontiers Seminar
Carolina Araujo, Instituto Nacional de Matematica Pura e Aplicada, Rio de Janeiro, Brazil
Wednesday, May 3, 2023, 5:00pm
Lakeside Village Auditorium, University of Miami
Title: The Calabi problem - from a birational geometer’s viewpoint I - Video
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Thursday, May 4, 2023, 4:00pm
Lakeside Village Auditorium, University of Miami
Title: The Calabi problem - from a birational geometer’s viewpoint II - Video
Abstract: A formidable problem in the confluence of differential and algebraic geometry is to determine which compact complex manifolds admit a Kähler-Einstein metric. This problem has received great attention since advertised by Eugenio Calabi in his 1954 ICM lecture.
A necessary condition for the existence of a Kähler-Einstein metric on a compact complex manifold is that its curvature has a definite sign. For manifolds with zero or negative curvature, the Calabi problem was solved by Yau and Aubin/Yau in the 1970s. They confirmed Calabi's prediction, showing that these manifolds always admit a Kähler-Einstein metric. This result has had profound consequences both in differential and algebraic geometry.
On the other hand, for complex manifolds with positive curvature, called “Fano manifolds”, the problem is much more subtle: Fano manifolds may or may not admit a Kähler-Einstein metric. The Calabi problem for Fano manifolds has attracted much attention in the last decades, resulting in the famous Yau-Tian-Donaldson conjecture. The conjecture, which is now a theorem, states that a Fano manifold admits a Kähler-Einstein metric if and only if it satisfies a sophisticated algebro-geometric condition, called “K-polystability”. In the last few years, tools from birational geometry have been used with great success to investigate K-polystability, yielding enormous progress and unforeseen new research directions.
In this series of lectures, I will present an overview of the Calabi problem, describing some of the important recent developments in connection with birational geometry.
Carolina Araujo is a world known algebraic geometer. She comes from a top scientific lineage being a student of J. Kollár at Princeton. She is well known for her work on rational curves of minimal degrees and the minimal model program. Araujo won the L'Oreal Award for Women in Science in 2008 and Araujo was awarded the 2020 Ramanujan Prize from the International Centre for Theoretical Physics. Carolina is a researcher at the Instituto Nacional de Matemática Pura e Aplicada in Brazil (IMPA). Since 2023, Araujo has been an elected member of the Brazilian Academy of Sciences and serves as chair of the Committee for Women in Mathematics at the International Mathematical Union.
Frontiers Seminar
Jacqueline Godoy Mesquita, Professor at the Department of Mathematics at the University of Brasilia, Brazil
Tuesday, March 28, 2023, 5:00pm
Click here to view video
Title: An introduction to delay differential equations: motivation and applications
Abstract: In this talk, I will present an introduction to delay differential equations, describing the main applications and motivation to investigate these types of equations. Also, I will present open and developing problems in the field.
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Wednesday, March 29, 2023, 5:30pm
Click here to view video
Title: Linearized instability for neutral functional differential equations with state-dependent delays
Abstract: In this talk, I will present the recent results concerning the linearized instability principle for neutral functional differential equations with state-dependent delays. This is a joint work with Professor Bernhard Lani-Wayda from Justus-Liebig University in Giessen, Germany.
Ungar Building, Room 402
Jaqueline Godoy Mesquita is a Brazilian mathematician specializing in dynamical systems and functional differential equations. She is a professor of mathematics at the University of Brasília. In 2021 she was elected vice president of the Brazilian Mathematical Society. Mesquita became a member of the Brazilian Academy of Sciences in 2018. In 2019 she was awarded the L'Oréal-UNESCO Award for Women in Sciences.
General Audience Seminar
Maria Amelia Salazar Pinzon, Assistant Professor at the Departamento de Matematica Aplicada of the Universidade Federal Fluminense, Brazil
University of Miami & IMSA
Fundamentals of Lie Groupoids and Algebroids
Monday, January 23, 2023, 5:00pm
Lakeside Village, Auditorium
Click here for Video
Abstract: In recent years, Lie groupoids and algebroids have come to the fore because of their versatility in describing seemingly distinct geometric structures, ranging from foliations and group actions, to Poisson bivectors and generalized complex structures. Intuitively, Lie groupoids and algebroids can be thought of as finite-dimensional geometric objects that encode certain infinite dimensional Lie groups and Lie algebras. The aim of this talk is to provide a gentle introduction to the Lie theory of these objects, illustrating the various definitions and properties with examples. Time permitting, we will state a few fundamental questions for Lie groupoids and algebroids that are the analogs of the corresponding ones for finite dimensional Lie groups and Lie algebras.
Research Seminar
Maria Amelia Salazar Pinzon, Assistant Professor at the Departamento de Matematica Aplicada of the Universidade Federal Fluminense, Brazil
University of Miami & IMSA
On Local Integration of Lie Brackets
Tuesday, January 24, 2023, 5:00pm
Lakeside Village, Auditorium
Click here for Video
Abstract: The foundation of Lie theory is Lie's three theorems that provide a construction of the Lie algebra associated to any Lie group; the converses of Lie's theorems provide an integration, i.e. a mechanism for constructing a Lie group out of a Lie algebra. The Lie theory for groupoids and algebroids has many analogous results to those for Lie groups and Lie algebras, however, it differs in important respects: one of these aspects is that there are Lie algebroids which do not admit any integration by a Lie groupoid. In joint work with Cabrera and Marcut, we showed that the non-integrability issue can be overcome by considering local Lie groupoids instead. In this talk I will explain a construction of a local Lie groupoid integrating a given Lie algebroid and I will point out the similarities with the classical theory for Lie groups and Lie algebras.
