This talk is on work in preparation with Ali Daemi. I will explain why Kim Froyshov's mod 2 instanton invariant q_3 gives information about indefinite 4-manifolds: if H_1(W;Z/2) = 0...
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Understanding the geometry of The Mandelbrot set, which records dynamical information about every quadratic polynomial, has been a central task in holomorphic dynamics over the past forty years. Near parabolic...
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Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution,...
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We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a...
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This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 21st. Please see the seminar page for more details: https://math.harvard.edu/~ctm/sem/.
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For more information, please see: https://cmsa.fas.harvard.edu/tech-in-math/
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A metric graph is a graph---a finite network of vertices and edges---together with a prescription of a positive real length on each edge. I'll use the term ``moduli space of...
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The adaptive immune system is able to learn from past experiences to better fit an unforeseen future. This is made possible by a diverse and dynamic repertoire of cells expressing unique antigen...
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Just as moments of a distribution of real numbers are a powerful tool that (if they are not too large) determine the distribution uniquely, we can consider certain averages as...
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We prove that the categories of coherent (or, equivalently, of quasi-coherent) sheaves over two noetherian non-commutative schemes X and Y are equivalent if and only if there centers C(X) and...
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