Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have...
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Khovanov homology can be upgraded to an invariant of pairs (K,V) where K is a framed knot and V is an object of the annular Bar-Natan category (ABN). In this...
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4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the...
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String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black...
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This seminar will take place in SC 507 at 3:30pm.
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One of the first deep things we learned in elementary school is the act of taking negatives of numbers. I'll explain the geometry that underlies this activity, which leads to...
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Over the past few decades, significant progress has been made in arithmetic statistics by the following two-step process: (1) parametrize arithmetic objects of interest in terms of the integral orbits...
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Feedforward neural networks with ReLU activation are a class of parameterized functions that have proven remarkably successful in supervised learning tasks. They do so even in regimes where classical notions...
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Brill-Noether theory answers the question of whether a general curve of genus $g$ admits $g^r_d$, a linear system of rank $r$ and degree $d$. A refined Brill-Noether theory hopes to...
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