Last summer, in this seminar, I introduced a dynamical system called "complex billiards" that extends the classical real billiards map to the setting of curves over algebraically closed fields. The...
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I will discuss the action induced by Adams operations on V \otimes THH(\ell), where V is a type 2 complex.
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Studying orientifold string theories on elliptic curves or abelian varieties motivates studying the derived category of coherent sheaves on a genus one curve or a torsor over an abelian variety...
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Materials that increase in size offer intriguing possibilities for shape morphing applications. Here, we explore two such systems—swelling polyacrylamide hydrogels and expanding polyurethane foams. The hydrogels swell by absorbing water...
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The derived category of a variety is an important and difficult invariant. In this talk, I discuss a purely convex-geometric and combinatorial approach to these categories for toric varieties. Along...
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Please see website for more details: www.math.harvard.edu/~ctm/sem.
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A fundamental motivating problem in homotopy theory is the study of the stable homotopy groups of spheres. The mathematical object that binds stable homotopy groups together is a spectrum. In...
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Joint with the MIT number theory seminar, note the special time and location When does a nice curve $X$ over a number field $k$ have infinitely many closed points of...
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Classical Schubert calculus analyzes the geometry of the flag variety, namely the space of nested subspaces $V_1 \subseteq V_2 \subseteq \cdots \subseteq \mathbb{C}^n$, asking enumerative questions about intersections of linear...
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Expanding the work of arXiv:1504.08040, we show that black holes obey a second law for linear perturbations to bifurcate Killing horizons, in any covariant higher curvature gravity coupled to scalar...
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