Activities/Talks
Activities/Services:
- Algebra Seminar Group
- Spring Problem Session and
Fall Putnam
Seminar
Recent Talks:
- Mar, 2008: Introduction to Arithmetic-Algebraic Geometry.,
Hudson Colloquia, AASU
- Nov, 2008: The Birch and Swinnerton Dyer Conjecture and
Quadratic Twists of an Elliptic Curve,
Hudson Colloquia, AASU
- Mar, 2009: Reflections on the Putnam Competition.,
Hudson Colloquia, AASU
- Apr, 2009: Maximizing the minimum mutual distance,
Hudson Colloquia, AASU
- Oct, 2009: The equal circle packing problem,
Hudson Colloquia, AASU
Talk(s) coming:
- Reflection on the 70th Putnam Competition,
Spring, 2010, Hudson Colloquia, AASU
- Diophantine Approximation,
Spring, 2010, Hudson Colloquia, AASU
- Mathematics and Music,
Hudson Colloquia, AASU
Slides:
- Oct,2005:
Algebra/Geometry/Topology Seminar, Geogia Tech;
Quadratic Twists of Elliptic Curves:
Slide.
- Sep,Oct,2005: Hudson Colloquia/Research Seminar, AASU;
- Nov,2006: Hudson Colloquia, AASU;
The Equations That Couldn't Be Solved:
Slide.
- Apr,2007: Hudson Colloquia, AASU;
- Oct,2007: Hudson Colloquia, AASU;
The arithmetic of elliptic curves:
Slide.
- Mar,2008: Hudson Colloquia, AASU;
The intro to arithmetic algebraic geometry:
Slide.
- Nov,2008: Hudson Colloquia, AASU;
The Birch and Swinnerton Dyer Conjecture and Quadratic Twists of an Elliptic Curve:
Slide.
- Mar,2009: Hudson Colloquia, AASU;
Reflections on the Putnam Competition:
Slide.
- Apr,2009: Hudson Colloquia, AASU;
Maximizing the minimum mutual distance:
Slide.
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Research/Teaching
Teaching in Spring 2010: Precalculus, Differnetial Equations, Linear Algebra • Course websites are set up at
Vista
• Look up your Vista ID at
Pirates' Cove
Research: The equal circle packing problem
Publications
- Paper, 2009:
The equal circle packing problem, in prep.
- Animation, 2009: Taylor Polynomials Approximated by Interpolations,
demonstrations.wolfram.com.
- Paper, 2008:
Quadratic twists of an elliptic curve with small Selmer rank, Acta Arith 141 (2010) 345--367.
- Paper, 2005:
On the arithmetic of twists of superelliptic curves,
Acta Arith 124 (2006) 371--389.
[AMS Review by Bjorn Poonen]
- Paper, 2005:
Note on the rank of quadratic twists of Mordell equations,
J. Number Theory 118 (2006) 53--61.
[AMS Review by Pavlos Tzermias]
- Technical Report, 2003:
Implementation of the 3-descent on a Mordell's elliptic curve,
selmer3.html.
Article Reviews
- N. Bruin:
The arithmetic of Prym varieties in genus 3, Compos. Math. 144, No. 2, 317-338 (2008).
- D. Poulakis:
On the rational points of the curve
f(X,Y)q=h(X) g(X,Y), Can. Math. Bull. 52, No. 1, 117-126 (2009).
- M. Stoll:
Finite descent obstructions and rational points on curves, Algebra & Number Theory, No. 1, 349-391 (2007).
- K. Miyake:
Twists of Hessian elliptic curves and cubic fields, Ann. Math. Blaise Pascal 16, No. 1, 27-45 (2009).
- E.V. Flynn:
Homogeneous spaces and degree 4 del Pezzo surfaces, Manuscr. Math. 129, No. 3, 369-380 (2009).
Projects:
- Verification of Birch and Swinnerton-Dyer Conjecture for quadratic twists of elliptic curves.
- Generalization of my thesis: twists on cyclic covering of curves of positive genus.
- Quadratic reciprocity on Galois conjugates
- Finding a curve over the rationals with arbitrarily large genus with MW rank 0
Things to read: [This portion shall be moved to a facebook network]
Expository Articles
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