Rachel Lawrence

Rachel Lawrence

Cambridge, England, United Kingdom
586 followers 500+ connections

About

I am an AI researcher at Microsoft Research Cambridge, with the goal of improving the…

Activity

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Experience

  • Microsoft Research

    Cambridge, England, United Kingdom

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    Berkeley, CA

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    Seattle, Washington, United States

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    Palo Alto, CA

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    New York, NY

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    New Haven, CT

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    New Haven, CT

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    New Haven, CT

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    New Haven, CT

Education

Publications

  • Counting Arcs in Projective Planes via Glynn's Algorithm

    Journal of Geometry

    An n-arc in a projective plane is a collection of n distinct points in the plane, no three of which lie on a line. Formulas counting the number of n-arcs in any finite projective plane of order q are known for n≤8. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted 9-arcs in the projective plane over a finite field of order q and showed that this count is a quasipolynomial function of q. We present a formula for the number of 9-arcs in any projective plane of order q, even those that are…

    An n-arc in a projective plane is a collection of n distinct points in the plane, no three of which lie on a line. Formulas counting the number of n-arcs in any finite projective plane of order q are known for n≤8. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted 9-arcs in the projective plane over a finite field of order q and showed that this count is a quasipolynomial function of q. We present a formula for the number of 9-arcs in any projective plane of order q, even those that are non-Desarguesian, deriving Iampolskaia, Skorobogatov, and Sorokin's formula as a special case. We obtain our formula from a new implementation of an algorithm due to Glynn; we give details of our implementation and discuss its consequences for larger arcs.

    Other authors
    • Nathan Kaplan
    • Susie Kimport
    • Luke Peilen
    • Max Weinreich
    See publication

Courses

  • Abstract Algebra

    MATH 350

  • Advanced Matrix Computations

    MATH 221

  • An Algorithmist's Toolkit

    CPSC 665

  • Beyond Worst Case Analysis

    CS 294

  • Combinatorial Algorithms and Data Structures

    CS 270

  • Computational Complexity

    CPSC 468

  • Data Analysis

    AMTH 361

  • Data Structures and Programming Techniques

    CPSC 223

  • Design and Analysis of Algorithms

    CPSC 365

  • Discrete Mathematics

    MATH 244

  • Machine Learning in Social Dynamics

    CS 294

  • Ordinary and Partial Differential Equations

    APHY 194

  • Randomized Algorithms

    CPSC 469

  • Randomness and Computation

    CS 271

  • Real Analysis

    MATH 300

  • Security in Computer Systems

    CS 261

  • Statistical Learning Theory

    CS C281A

  • Stochastic Processes

    MATH 251

  • Sums of Squares

    CS 294

  • Systems Programming and Computer Organization

    CPSC 323

  • Theoretical Challenges in Network Science

    ENAS 962

  • Vector Analysis

    MATH 250

  • Vector Calculus and Linear Algebra

    MATH 230

Honors & Awards

  • National Physical Science Consortium Fellowship

    United States Department of Defense

    National fellowship supporting duration of graduate study, sponsored by the US Department of Defense

  • SUMRY Fellowship

    Yale College

    Awarded for 10-week intensive summer research program at the Yale Department of Mathematics

  • Davenport College Richter Fellowship

    Yale College

    Yale College fellowship awarded for independent study and research.

  • Yale College Dean's Research Fellowship

    Yale College

    Research fellowship awarded for undergraduate work in STEM. Received twice, in 2013 and 2014.

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