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CMSA Math-Science Literature Lecture: Area-minimizing integral currents and their regularity

Virtual

Camillo De Lellis (IAS) Title: Area-minimizing integral currents and their regularity Abstract: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has […]

CMSA-New-Technologies-in-Mathematics-09.23.20

Self-induced regularization from linear regression to neural networks

Virtual

https://youtu.be/bjRqmlI_SFs Speaker: Andrea Montanari, Departments of Electrical Engineering and Statistics, Stanford Title: Self-induced regularization from linear regression to neural networks Abstract: Modern machine learning methods --most noticeably multi-layer neural networks-- require to fit highly non-linear models comprising tens of thousands to millions of parameters. Despite this, little attention is paid to the regularization mechanism to […]

CMSA Math-Science Literature Lecture: Hodge structures and the topology of algebraic varieties

Virtual

Claire Voisin (Collège de France) Title: Hodge structures and the topology of algebraic varieties Abstract: We review the major progress made since the 50’s in our understanding of the topology of complex algebraic varieties. Most of the results  we will discuss  rely on Hodge theory, which  has some analytic aspects giving the Hodge and Lefschetz decompositions, and […]

CMSA-New-Technologies-in-Mathematics-09.16.20-1

Graph Representation Learning: Recent Advances and Open Challenges

Virtual

Speaker: William Hamilton, McGill University and MILA Title: Graph Representation Learning: Recent Advances and Open Challenges Abstract: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial if we want systems that can learn, reason, and generalize from this kind of […]

Lecture_Lian-pdf

CMSA Math-Science Literature Lecture: From string theory and Moonshine to vertex algebras

Virtual

Bong Lian (Brandeis) Title: From string theory and Moonshine to vertex algebras Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as […]

Lecture_Manolescu-pdf

CMSA Math-Science Literature Lecture: Four-dimensional topology

Virtual

Ciprian Manolescu (Stanford) Title: Four-dimensional topology Abstract: I will outline the history of four-dimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the Seiberg-Witten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the […]

CMSA Math-Science Literature Lecture: My life and times with the sporadic simple groups

Virtual

Robert Griess (University of Michigan) Title: My life and times with the sporadic simple groups Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 1965-1975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad […]

Lecture_Bieri-pdf

CMSA Math-Science Literature Lecture: Black Hole Formation

Virtual

Lydia Bieri (University of Michigan) Title: Black Hole Formation Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the […]

Lecture_Etingof-pdf

CMSA Math-Science Literature Lecture: Quantum Groups

Virtual

Pavel Etingof (MIT) Title: Quantum Groups Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum Yang-Baxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as […]

Lecture_Harris_updated-pdf

CMSA Math-Science Literature Lecture: Rationality questions in algebraic geometry

Virtual

Joe Harris (Harvard) Title: Rationality questions in algebraic geometry Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension […]