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Visual recognition is essential for most everyday tasks including navigation, reading and socialization. Visual pattern recognition is also important for many engineering applications such as automatic analysis of clinical images, face recognition by computers, security tasks and automatic navigation. In spite of the enormous increase in computational power over the last decade, humans still outperform the most sophisticated engineering algorithms in visual recognition tasks. In this course, we will examine how circuits of neurons in visual cortex represent and transform visual information. The course will cover the following topics: functional architecture of visual cortex, lesion studies, physiological experiments in humans and animals, visual consciousness, computational models of visual object recognition, computer vision algorithms. Video lectures are from 2019.
Gabriel Kreiman | Fall 2023 | Harvard University
This course introduces basic concepts of mathematical biology and evolutionary dynamics: reproduction, selection, mutation, genetic drift, quasi-species, finite and infinite population dynamics, game dynamics, evolution of cooperation, language, spatial models, evolutionary graph theory, infection dynamics, virus dynamics, somatic evolution of cancer.
Martin Nowak | Fall 2023 | Harvard University
Maxwell's equations in macroscopic media, conservation laws, Green's functions, time-dependent solutions and radiation, scattering and diffraction, and gauge invariance. Time permitting: geometrical optics and caustics, negative refractive index materials and radiation from rapidly accelerating charges.
Subir Sachdev | Spring 2020 | Harvard University
Introduction to modern atomic physics. The fundamental concepts and modern experimental techniques will be introduced. Topics will include: Two-state systems, magnetic resonance, interaction of radiation with atoms, transition probabilities, spontaneous and stimulated emission, dressed atoms, trapping, laser cooling. Structure of simple atoms, coupling to fields, light scattering. Fundamental symmetries and introduction to molecules and artificial atoms. Selected experiments. The first of a two-term subject sequence that provides the foundations for contemporary research.
Susanne Yelin | Fall 2023 | Harvard University
This interdisciplinary course will explore the physical interactions that underpin life: the interactions of molecules, macromolecular structures, and cells in warm, wet, squishy environments. Topics will include Brownian motion, diffusion in a potential field, continuum mechanics of polymers, rods, and membranes, low Reynolds number flow, interfacial forces, electrostatics in solution. The course will also cover recently developed biophysical tools, including laser tweezers, superresolution microscopies, and optogenetics. Numerical simulations in Matlab will be used extensively.
Adam Cohen | Fall 2022 | Harvard University
Covering spaces and fibrations. Simplicial and CW complexes, Homology and cohomology, universal coefficients and Künneth formulas. Hurewicz theorem. Manifolds and Poincaré duality.
Hana Jia Kong | Fall 2023 | Harvard University
Arithmetic statistics can be thought of as the study sequences of arithmetic interest, such as the number of divisors of integers or the number of points on an elliptic curve over finite fields. In this course we'll encode these sequences in “automorphic forms'' and then extract statistical information using techniques from analytic number theory. We'll focus primarily on explicit calculations involving the spectral decomposition of weight 0 GL2 forms to study shifted convolutions.
Alex Cowan | Fall 2023 | Harvard University
A continuation of Mathematics 22a.
Oliver Knill | Spring 2019 | Harvard University
Smooth manifolds (vector fields, differential forms, and their algebraic structures; Frobenius theorem), Riemannian geometry (metrics, connections, curvatures, geodesics), Lie groups, principal bundles and associated vector bundles with their connections, curvature and characteristic classes. Other topics if time permits.
Fan Ye | Fall 2022 | Harvard University
An interactive introduction to problem solving with an emphasis on subjects with comprehensive applications. Each class will be focused around a group of questions with a common topic: logic, information, number theory, probability, and algorithms.
Joe Harris and Yusheng Luo | Spring 2019 | Harvard University
This class is an introduction to algebraic geometry. Some topics we will cover include Hilbert's Nullstellensatz, affine and projective varieties, plane curves, Bézout's Theorem, morphisms of varieties, divisors and linear systems on curves, Riemann-Roch Theorem.
Brooke Ullery | Spring 2020 | Harvard University
Introduction to relativistic quantum field theory. Topics include path integral, perturbation theory, Feynman diagrams, renormalization, Green functions, scattering theory, spinor particle and fields, vector boson and gauge fields, quantum electrodynamics.
Xi Yin | Fall 2022 | Harvard University
A continuation of Physics 253a. Topics include: resonances, implications of analyticity and unitarity, infrared divergence, the renormalization group, epsilon expansion, non-Abelian gauge theories, asymptotic freedom and confinement, spontaneous symmetry breaking, chiral perturbation theory and anomalies.
Xi Yin | Spring 2023 | Harvard University
An introduction to conformal field theories: conformal bootstrap via the conformal block expansion and semidefinite optimization, the Ising model in 2 and 3 dimensions, and the maximally supersymmetric Yang-Mills theory in four dimensions.
Xi Yin | Fall 2023 | Harvard University
All classes are licensed under the CC-BY-NC-SA license.
