Pi Mu Epsilon - Mathematical Association of America

Thursday MAA Session #10 August 2, 2012
MAA Session #10
Room: Meeting Room N
2:00P.M. – 3:55P.M.
2:00–2:15
Studying Robotic Mobility Using Inverse Kinematics with Two Different Techniques
Melody Mone’t Wilson, Denetra Lynette Porties,
Kristen Danielle Edwards, and Chinae Edmonds
Central State University
The study of robot mobility is important in determining the full capacity in which a robot can
operate in any given space. Inverse kinematics in robotics uses an end-effector (robot hand) to
calculate the joint angles needed to obtain the position of the end-effector. This study uses inverse
kinematics to determine the joint angle mobility of a four degrees-of-freedom robot manipulator
using two techniques: Groebner Basis Theory and the Denavit-Hartenberg Matrix. The presenters
will use these techniques to analyze the geometry of the robot and solve for the unknown joint
angles of the waist, elbow, and shoulder. Since robotic movement is similar to human movement,
the presenters will discuss how these results can contribute to studies in human behavior.
2:20–2:35
Towards a Tropical Proof of the Gieseker-Petri Theorem - Part 1
Dat Pham Nguyen
SUNY Stony Brook
Tropical geometry allows for many of the properties of algebraic curves to be studied from a new
perspective. Specifically, tropical geometry reduces divisors on a Riemann surface to divisors on a
metric graph, which can be easier to work with. This technique has recently been used by Cools,
Draisma, Payne, and Robeva to prove the Brill-Noether Theorem (originally proven by Griffiths
and Harris) combinatorially. Our project uses the same technique as Cools et al. to provide a combinatorial
proof of the rank one case of the Gieseker-Petri Theorem, which was originally proven
by Gieseker in 1982.
This part of our talk details the background and motivation of our project.
2:40–2:55
Towards a Tropical Proof of the Gieseker-Petri Theorem - Part 2
Shalin Parekh
SUNY Stony Brook
Tropical geometry allows for many of the properties of algebraic curves to be studied from a new
perspective. Specifically, tropical geometry reduces divisors on a Riemann surface to divisors on a
metric graph, which can be easier to work with. This technique has recently been used by Cools,
Draisma, Payne, and Robeva to provide a combinatorial proof of the Brill-Noether Theorem (originally
proven by Griffiths and Harris). Our project uses the same technique as Cools et al. to provide
a combinatorial proof of the rank one case of the Gieseker-Petri Theorem, which was originally
proven by Gieseker in 1982.
In this part, we introduce the Gieseker-Petri theorem and our approach to a tropical proof of the
rank one case.
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