Methods - Publications - Faculty & Research

Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details

Keywords: COVID-19; Mathematical Methods

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How Much Should We Trust Staggered Difference-In-Differences Estimates?

By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang

We explain when and how staggered difference-in-differences regression estimators, commonly applied to assess the impact of policy changes, are biased. These biases are likely to be relevant for a large portion of research settings in finance, accounting, and law that... View Details

Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods

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Oracle Efficient Private Non-Convex Optimization

By: Seth Neel, Aaron Leon Roth, Giuseppe Vietri and Zhiwei Steven Wu

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it.... View Details

Keywords: Machine Learning; Algorithms; Objective Perturbation; Mathematical Methods

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Aztec Castles and the dP3 Quiver

By: Megan Leoni, Gregg Musiker, Seth Neel and Paxton Turner

Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 (dP3) quiver and geometric properties of its corresponding brane tiling. In... View Details

Keywords: Brane Tiling; Del Pezzo 3 Lattice; Dimer Model; Mathematical Methods

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1990
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Refinement of Nash Equilibrium: The Main Ideas

By: E. Kohlberg

Keywords: Mathematical Methods

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Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80

By: Noam D. Elkies and Scott Duke Kominers

We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms... View Details

Keywords: Mathematical Methods

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