Calendar

TITLE: K-theory and characteristic classes in topology and complex geometry (a tribute to Atiyah and Hirzebruch)

ABSTRACT: We will discuss the K-theory of complex vector bundles on
topological spaces and of holomorphic vector bundles on complex
manifolds. A central question is the relationship between K-theory
and cohomology. This is done in topology by constructing
characteristic classes, but other constructions appear in the

holomorphic or algebraic context. We will discuss the Hirzebruch-
Riemann-Roch formula, the Atiyah-Hirzebruch spectral sequence, the

role of complex cobordism, and other tools developed later on, like
the Bloch-Ogus spectral sequence.

Talk chair: Baohua Fu

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

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We will present some rigorous results about Relative entropy in QFT, motivated in part by recent physicists’ work which however depends on heuristic arguments such as introducing cut off and using path integrals. In the particular case of CFT, we will discuss interesting relations between relative entropy, central charge and global dimension of conformal net

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Title: New Structures in Gravitational Waves

Abstract: Mathematical General Relativity (GR) explores the structures and resulting dynamics of gravitational systems. These are described by the Einstein equations, which can be written as a system of nonlinear, hyperbolic partial differential equations. Recent years have seen fruitful interactions between physical questions and geometric analysis, sparking new breakthroughs, in particular related to gravitational radiation. Gravitational waves transport information from faraway regions of the Universe. They were observed for the first time by Advanced LIGO in 2015. So far, most studies in GR have been devoted to sources like binary black hole mergers or generally to sources that are stationary outside of a compact set. However, when extended neutrino halos are present, the situation changes.  Mathematically, we describe these systems by asymptotically-flat manifolds solving the Einstein equations. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields fall off more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects (permanent change of the spacetime) that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations.

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Information visualizations are an efficient means to support the users in understanding large amounts of complex, interconnected data; user comprehension. Previous research suggests that user-adaptive information visualizations positively impact the users’ performance in visualization tasks. This study aims to develop a computational model to predict the users’ success in visual search tasks from eye gaze data and thereby drive such user-adaptive systems. State-of-the-art deep learning models for time series classification have been trained on sequential eye gaze data obtained from 40 study participants’ interaction with a circular and an organizational graph. The results suggest that such models yield higher accuracy than a baseline classifier and previously used models for this purpose. In particular, a Multivariate Long Short Term Memory Fully Convolutional Network (MLSTM-FCN) shows encouraging performance for its use in on-line user-adaptive systems. Given this finding, such a computational model can infer the users’ need for support during interaction with a graph and trigger appropriate interventions in user-adaptive information visualization systems.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

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