On the symplectic eightfold associated to a Pfaffian cubic fourfold

We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points.Comment: 9 pages. Minor changes; to appear in Crelle as an appendix to 1305.017

Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. These two notions of having an associated K3 should coincide. We prove that they coincide generically: Hassett's cubics form a countable union of irreducible Noether-Lefschetz divisors in moduli space, and we show that Kuznetsov's cubics are a dense subset of these, forming a non-empty, Zariski open subset in each divisor.Comment: 37 pages. Applications to algebraic cycles added, and other improvements following referees' suggestions. This is a slightly expanded version of the paper to appear in Duke Math

Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way we produce a derived equivalence between two compact hyperkaehler 2g-folds that are not birational, for every g >= 2. We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived-equivalent.Comment: 28 pages. typos corrected. final version to appear in JLM

Design of a Folded Cascode Operational Amplifier in a 1.2 Micron Silicon-Carbide CMOS Process

This thesis covers the design of a Folded Cascode CMOS Operational Amplifier (Op-Amp) in Raytheon’s 1.2-micron Silicon Carbide (SiC) process. The use of silicon-carbide as a material for integrated circuits (ICs) is gaining popularity due to its ability to function at high temperatures outside the range of typical silicon ICs. The goal of this design was to create an operational amplifier suitable for use in a high temperature analog-to-digital converter application. The amplifier has been designed to have a DC gain of 50dB, a phase margin of 50 degrees, and a bandwidth of 2 MHz. The circuit’s application includes input ranging from 0 volts to 8 volts so a PMOS input differential pair was selected to allow the input range down to the VSS rail. The circuit has been designed to work over a temperature range of 25°C to 300°C

The Pfaffian-Grassmannian equivalence revisited

We give a new proof of the 'Pfaffian-Grassmannian' derived equivalence between certain pairs of non-birational Calabi-Yau threefolds. Our proof follows the physical constructions of Hori and Tong, and we factor the equivalence into three steps by passing through some intermediate categories of (global) matrix factorizations. The first step is global Knoerrer periodicity, the second comes from a birational map between Landau-Ginzburg B-models, and for the third we develop some new techniques.Comment: Improved exposition, minor corrections. 32 page