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Garrett Alston

Publications and source records attributed to Garrett Alston.

7 recordsLinked to original sources
arXiv2026

Data center cooling choices shift water impacts across the grid: An integrated water-energy model for sustainable data center development

Data centers are being developed at an unprecedented pace, yet their energy and water impacts, and the spatial and temporal distribution of these impacts, remain poorly characterized. Data centers consume water for cooling (direct) and through electricity generation (indirect). Decisions on siting and cooling technology result in water-energy trade-offs that extend impacts beyond the facility's location. Existing assessment frameworks rely on facility efficiency metrics and average grid water intensity factors, suppressing the temporal impacts of data center load and generation availability. They also attribute indirect consumption to the facility's location rather than to the generators (and corresponding hydrologic regions) that respond to the added load, misattributing spatial impacts. To close this gap, we develop a computational model of the data center-energy-water nexus that links facility cooling and electricity demand with hourly economic dispatch, generator-level water consumption, and monthly subbasin depletion. Built on open-source data, the model resolves where and when water is consumed, and where this consumption compounds existing water risk or creates new risk. Using the model, we study different cooling configurations and proposed developments in the state of Michigan. Air-cooled data centers halve total water consumption relative to evaporative cooling, but increase electricity demand and raise indirect water consumption by one-third, shifting the water footprint from the facility to generators. Mapping these changes to subbasins reveals depletion increases beyond the data center sites, in regions that facility-level reporting may overlook. These results show that data center water and energy impacts cannot be assessed in isolation, motivating the need for integrated modeling to inform siting, design, and reporting practices.

eess.SY↗
arXiv2021

Immersed Lagrangian Floer cohomology via pearly trajectories

We define Lagrangian Floer cohomology over $\mathbb Z_2$-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy certain positivity condition on the index of the non-embedded points, and show that it is an invariant of the Lagrangian immersion under Hamiltonian deformations. We also show that it is naturally isomorphic to the Hamiltonian perturbed version of Lagrangian Floer cohomology as defined in [4]. As an application, we prove that the number of non-embedded points of such a Lagrangian in $\mathbb C^n$ is no less than the sum of its Betti numbers.

math.SG↗
arXiv2015

Exact, graded, immersed Lagrangians and Floer theory

We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians with clean self-intersection using Seidel's setup. A positivity assumption on the index of the self intersection points is imposed to rule out certain (but not all) disc bubbles. This allows the Lagrangians to be included in the exact Fukaya category. We also study quasi-isomorphism of Lagrangians under certain exact deformations which are not Hamiltonian.

math.SG↗
arXiv2013

Floer cohomology of immersed Lagrangian spheres in smoothings of $A_N$ surfaces

We calculate the self-Floer cohomology with Z/2 coefficients of some immersed Lagrangian spheres in the affine symplectic submanifolds of C^3 that are smoothings of A_N surfaces. The immersed spheres are exact and graded. Moreover, they satisfy a positivity assumption that allows us to calculate the Floer cohomology as follows: Given auxiliary data a Morse function on S^2 and a time-dependent almost complex structure, the Floer cochain complex is the Morse complex plus two generators for each self-intersection point of the Lagrangian sphere. The Floer differential is defined by counting combinations of Morse flow lines and holomorphic strips. Using a Lefschetz fibration allows us to explicitly calculate all holomorphic strips and describe the Floer differential. For most of the immersed spheres the Floer differential is zero (with Z/2-coefficients).

math.SG↗
arXiv2011

Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds

In this article, we consider the Floer cohomology (with $\Z_2$ coefficients) between torus fibers and the real Lagrangian in Fano toric manifolds. We first investigate the conditions under which the Floer cohomology is defined, and then develop a combinatorial description of the Floer complex based on the polytope of the toric manifold. We show that if the Floer cohomology is defined, and the Floer cohomology of the torus fiber is non-zero, then the Floer cohomology of the pair is non-zero. We use this result to develop some applications to non-displaceability and the minimum number of intersection points under Hamiltonian isotopy.

math.SG↗
arXiv2010

Floer cohomology of real Lagrangians in the Fermat quintic threefold

Let X be the Fermat quintic threefold. The set of real solutions L forms a Lagrangian submanifold of X. Multiplying the homogeneous coordinates of X by various fifth roots of unity gives automorphisms of X; the images of L under these automorphisms defines a family of 625 different Lagrangian submanifolds, called real Lagrangians. In this paper we try to calculate the Floer cohomology between all pairs of these Lagrangians. We are able to complete most of the calculations, but there are a few cases we cannot do. The basic idea is to explicitly describe some low energy moduli spaces and then use this knowledge to calculate the differential on the E_2 page of the standard spectral sequence for Floer cohomology. It turns out that this is often enough to calculate the cohomology completely. Several techniques are developed to help describe these low energy moduli spaces, including a formula for the Maslov index, a formula for the obstruction bundle, and a way to relate holomorphic strips and discs to holomorphic spheres. The real nature of the Lagrangians is crucial for the development of these techniques.

math.SG↗