In this talk, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima, where the convolution product is modified by a virtual intersection. The resulting virtual...
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Given a grid diagram for a knot or link K in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy...
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In this talk, we determine when there is a Brill--Noether curve of given degree and given genus that passes through a given number of general points in any projective space....
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We use a relationship between Heegaard Floer homology and the symplectic Floer homology of surface diffeomorphisms to partially characterize knots with the same knot Floer homology as the torus knot T(2,5). We...
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It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. ...
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A real algebraic variety is the set of points in real Euclidean space that satisfy a system of polynomial equations. Metric algebraic geometry is the study of properties of real algebraic...
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How many rational preperiodic points can a degree d polynomial in Q[x] have? Conjecturally, there is some uniform bound B_d(Q) on the number of such preperiodic points -- but how...
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My lab is interested in the active and adaptive materials that underlie control of cell shape. This has centered around understanding force transmission and sensing within the actin cytoskeleton. I...
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Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global...
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Grothendieck's Section Conjecture posits that the set of rational points on a smooth projective curve Y of genus at least two should be equal to a certain "section set" defined purely in...
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