The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of...
The goal of this thesis is to prove that topological restriction homology, TR, is locally even in the quasi-syntomic topology in characteristic p. This local evenness was already known for the other main trace theories, but is more subtle for TR.
Laser powder-blown directed energy deposition (DED) is an additive manufacturing process that utilizes a co-axial nozzle and laser to melt metal powders onto a substrate in a line-by-line fashion. This coupling gives rise to interactions between the laser, powder, and melt pool. To address fundamental process understanding, physical models were...
We study the complexification of Laplace Eigenfunctions on the Grauert tube of a compact real analytic manifold. Our main results concern scaling asymptotics of Fourier coefficients of the Szego kernel on the Grauert tube boundary in a Heisenberg frequency scaled neighborhood of the geodesic flow. We show that in the...
We prove the Rigidity Conjecture of Goette and Igusa, which states that, after rationalizing, there are no stable exotic smoothings of manifold bundles with closed even dimensional fibers. The key ingredients of the proof are fiberwise Poincaré–Hopf theorems generalizing earlier such results about the Becker–Gottlieb transfer. These theorems show how...