Edray H Goins
Number Theory Seminar
Last updated on June 28, 2017.Summer 2017
The seminar is being run as MA 59800-65-12039: Introduction to Algebraic Geometry. We will meet on Mondays, Wednesdays, and Fridays from 3:30 PM - 4:30 PM in MATH 215. We will cover Chapter 1 of Hartshorne's Algebraic Geometry (113 MB). I am assuming that each of you has a solid background in commutative algebra, especially those topics in Atiyah-Macdonad's Introduction to Commutative Algebra (13 MB) and Zariski-Samuel's Commutative algebra, Vol. I (31 MB). As supplemental reading to Hartshorne, I recommend Shafarevich's Basic Algebraic Geometry 1 (9 MB).
- Week 1 (6/12 - 6/16): Affine Varieties
- Week 2 (6/19 - 6/23): Projective Varieties
- Week 3 (6/26 - 6/30): Morphisms
- Week 4 (7/3 - 7/7): Rational Maps
- Week 5 (7/10 - 7/14): Nonsingular Varieties
- Week 6 (7/17 - 7/21): Nonsingular Curves
- Week 7 (7/24 - 7/28): Intersections in Projective Space
- Week 8 (7/31 - 8/4): What is Algebraic Geometry?
Week 1 | June 12 | Edray Herber Goins |
Organizational Meeting | |
June 14 | Daniel Shankman |
Zariski Topology (pgs. 1 - 4) | ||
June 16 | Tyler Billingsley |
Affine Varieties (pgs. 4 - 7) | ||
Week 2 | June 19 | Warren Katz |
Solutions to Exercises (1.5, 1.6, 1.7, 1.8, 1.9) | |
June 21 | Vinh Nguyen |
Projective Varieties (pgs. 8 - 11) | ||
June 23 | Alex Porter |
Solutions to Exercises (2.1, 2.2, 2.3, 2.4, 2.5) | ||
Week 3 | June 26 | Matt Weaver |
Regular Functions (pgs. 14 - 16) | |
June 28 | Kelsey Walters |
Morphisms Between Varieties (pgs. 17 - 20) | ||
June 30 | Clinton Bradford |
Solutions to Exercises (2.6, 2.7, 3.1, 3.3, 3.8) | ||
Week 4 | July 3 | -- | 4th of July Holiday | |
July 5 | Nathanael Cox |
Rational, Birational, and Dominant Maps (pgs. 24 - 27) | ||
July 7 | Frankie Chan |
Blowing Up (pgs. 27 - 30) | ||
Week 5 | July 10 | Matt Weaver |
Solutions to Exercises (3.11, 3.12, 4.1, 4.2, 4.4) | |
July 12 | Alison Rosenblum |
Non-Singularity and Jacobian Matrices (pgs. 31 - 33) | ||
July 14 | Clinton Bradford |
Local Rings and their Completions (pgs. 33 - 35) | ||
Week 6 | July 17 | Miscellaneous |
Solutions to Exercises (4.5, 4.7, 4.9, 5.1, 5.2) | |
July 19 | Matt Weaver |
Non-Singular Curves and Dedekind Domains (pgs. 39 - 42) | ||
July 21 | TBA |
DVRs and Abstract Non-Singular Curves (pgs. 42 - 46) | ||
Week 7 | July 24 | TBA |
Solutions to Exercises (5.3, 5.4, 5.8, 5.9, 6.1) | |
July 26 | TBA |
Bezout's Theorem (pgs. 47 - 49) | ||
July 28 | Sarah Percival |
Hilbert Polynomials I (pgs. 49 - 52) | ||
Week 8 | July 31 | Frankie Chan |
Hilbert Polynomials II (pgs. 52 - 54) | |
August 2 | TBA |
Solutions to Exercises (6.3, 6.4, 6.6, 7.2) | ||
August 4 | Edray Herber Goins |
What is Algebraic Geometry? (pgs. 55 - 59) |
Fall 2016
Talks were held on Thursdays in MATH 731 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
December 8 | Abhishek Parab |
Duality between S_{k} and GL_{n}(C) | |
November 17 | Tyler Billingsley |
Characters of GL_{n}(C) | |
October 6 | Alex Barrios |
Mackey Theory | |
September 29 | Jeremy Fuller |
Induced Characters and Frobenius Reciprocity | |
September 22 | Frankie Chan |
Character Theory | |
September 8 | Tyler Billingsley |
Wedderburn's Theorem | |
September 1 | Edray Herber Goins |
Group Rings |
Summer 2016
Talks were held on Tuesdays and Thursdays in MATH 731 from 3:30 PM - 4:20 PM. We read through Diamond and Shurman's A First Course in Modular Forms .
July 28 | Mohammad Hadi Hedayatzadeh |
Congruences between modular forms | |
July 26 | Rachel Davis |
Galois Representations | |
July 21 | Dongming She |
L-series and functional equations | |
July 19 | Alex Barrios |
Jacobians and Abelian Varieties | |
July 14 | Abhishek Parab |
Ramanujan's Conjecture and growth of coefficients | |
July 12 | Daniel Shankman |
Hecke Operators | |
July 7 | Justin Katz |
Eisenstein Series | |
July 5 | Tyler Billingsley |
Modular Curves as Riemann Surfaces | |
June 30 | Frankie Chan |
Modular Forms, Elliptic Curves, and Modular Curves | |
June 28 | Edray Herber Goins |
Generating Functions, Partitions, and q-series: An Introduction to Classical Modular Forms |
Fall 2014
Talks were held on Thursdays in MATH 731 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
December 11 | Pamela Harris |
Generalizing Zeckendorf's Theorem: The Kentucky Sequence | |
October 30 | Jeremy Fuller |
Genus Theory for Quadratic Forms Revisited: The Genus Field | |
October 2 | Alex Barrios |
Hilbert and Ring Class Fields: From Quadratic Forms to Ideals in Number Fields | |
September 25 | Jeremy Fuller |
Genus Theory for Quadratic Forms | |
September 18 | Edray Herber Goins |
Gauss' Composition of Quadratic Forms | |
TBA | Abhishek Parab |
Bhargava's Reinterpretation of Gauss' Composition Laws | |
TBA | Rachel Davis |
Higher Composition Laws and Applications |
Fall 2013
Talks were held on Fridays in MATH 731 from 4:30 PM - 5:20 PM.
December 5 | Ben McReynolds |
A Curious Geometrically Motivated Algebraic Bijection | |
November 14 | Kevin Mugo |
Brauer Groups, Part II | |
November 7 | Kevin Mugo |
Brauer Groups, Part I | |
October 31 | Jeremy Fuller |
The Brauer-Manin Obstruction | |
October 17 | Jamie Weigandt |
The Cassels-Tate Pairing | |
September 26 | Rachel Davis |
The Shafarevich-Tate Group of Elliptic Curves | |
September 19 | Abhishek Parab |
Hilbert's Theorem 90 and Generalizations | |
September 12 | Alex Barrios |
Artin-Schreier Theory and Kummer Theory | |
September 5 | Edray Goins |
The Weil Pairing on Elliptic Curves, Part II | |
August 29 | Edray Goins |
The Weil Pairing on Elliptic Curves, Part I |
Spring 2013
Talks were held on Fridays in MATH 215 from 4:30 PM - 5:20 PM.
April 30 | Noam Elkies |
How many elliptic curves can have the same prime conductor? | |
April 26 | Kevin Mugo |
On the ABC Conjecture and Diophantine Approximation by Rational Points | |
April 5 | Abhishek Parab |
ABC Implies no "Siegel Zeros" for L-Functions of Characters with Negative Discriminant | |
March 8 | Jamie Weigandt |
The ABC-Theorem, Davenport's Inequality and Elliptic Surfaces | |
March 1 | Alex Barrios |
On Some Consequences of the ABC Conjecture in Arithmetic and Logic | |
February 22 | Alejandra Alvarado |
Congruence ABC implies ABC | |
February 15 | Kevin Mugo |
Lang's Height Conjecture and Szpiro's Conjecture | |
February 1 | Jeffrey A. Oaks |
Polynomials and Equations in Medieval Algebra and in Diophantus | |
January 25 | Jeremy Fuller |
Questions about Number | |
January 18 | Alejandra Alvarado |
Questions About Powers of Numbers |
Fall 2012
Talks were held on Fridays in MATH 215 from 4:30 PM - 5:20 PM.
December 7 | Kevin Mugo |
A 60,000 digit prime number of the form x^{2} + x + 41 | |
November 30 | Jeremy Fuller |
The Bruhat Decomposition | |
November 16 | Edray Goins |
Ranks of Elliptic Curves via Class Groups of Number Fields | |
November 2 | Jamie Weigandt |
The Fifteen Theorem and Generalizations, Part II | |
October 26 | Jamie Weigandt |
The Fifteen Theorem and Generalizations, Part I | |
October 19 | Alex Barrios |
Elasticity of Factorization in Number Fields, Part II | |
October 5 | Alex Barrios |
Elasticity of Factorization in Number Fields, Part I | |
September 28 | Alejandra Alvarado |
Belyi Maps and Dessins d'Enfants | |
September 21 | Alejandra Alvarado |
Belyi's Theorem | |
September 14 | Abhishek Parab |
The ABC Conjecture for Polynomials | |
September 7 | Edray Goins |
From Klein's Platonic Solids to Kepler's Archimedean Solids: Elliptic Curves and Dessins d'Enfants, Part II | |
August 31 | Edray Goins |
From Klein's Platonic Solids to Kepler's Archimedean Solids: Elliptic Curves and Dessins d'Enfants, Part I |
Spring 2012
Talks were held on Fridays in MATH 215 from 3:30 PM - 4:20 PM.
April 6 | Alex Barrios |
Mill's Prime Representing Function | |
March 30 | Kevin Mugo |
Noether's Problem for A_{5}, Part II | |
March 23 | Kevin Mugo |
Noether's Problem for A_{5}, Part I | |
March 2 | David Chapman |
An Algebraic Approach to Greenberg's Question | |
February 24 | Alejandra Alvarado |
On Square Values of Quadratics | |
February 17 | Alain Togbe |
Diophantine Equations with Products of Consecutive Values of a Quadratic Polynomial | |
February 10 | Jeremy Fuller |
Class Number Formulas via 2-Isogenies of Elliptic Curves, Part II | |
February 3 | Jeremy Fuller |
Class Number Formulas via 2-Isogenies of Elliptic Curves, Part I | |
January 27 | Jamie Weigandt |
Selmer's Conjecture and Families of Elliptic Curves |
Fall 2011
Talks were held on Thursdays in MATH 215 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
November 30 REC 114 |
Jeremy Fuller |
Modular Forms via Quaternion Algebras: Some Explicit Examples | ||
November 11 MATH 211 |
Ted Chinburg |
Small Generators for Arithmetic Groups | ||
November 10 | Jamie Weigandt |
Computing Modular Forms on Definite Quaternion Algebras, Part II | ||
October 20 | Jamie Weigandt |
Computing Modular Forms on Definite Quaternion Algebras, Part I | ||
October 6 | Edray Goins |
Mazur's Control Theorem, Part III | ||
September 29 | Edray Goins |
Mazur's Control Theorem, Part II | ||
September 22 | Edray Goins |
Mazur's Control Theorem, Part I | ||
September 15 | Kevin Mugo |
Lambda-Modules in Iwasawa Theory, Part II | ||
September 8 | Kevin Mugo |
Lambda-Modules in Iwasawa Theory, Part I | ||
September 1 | Edray Goins |
An Introduction to Iwasawa Theory for Elliptic Curves, Part II | ||
August 25 | Edray Goins |
An Introduction to Iwasawa Theory for Elliptic Curves, Part I |
Spring 2009
All talks will be held on Thursdays in MATH 215 from 4:30 PM - 5:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
April 30 BRNG B247 at 3:30 PM |
Ling Long |
Noncongruence Modular Forms and Modularity | |
April 9 | Alain Togbe |
On Families of Diophantine Triples | |
March 12 | Alfred Noël |
Algorithmic and Theoretical Considerations for Computing Generators of the Centralizer of K in U(g) | |
February 12 | Tong Liu |
Lattices in semi-stable representations | |
January 15 | Lloyd Kilford |
An Introduction to Overconvergent Modular Forms |
Spring 2008
Talks were held on Thursdays in BRNG 1248 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
February 7 | Ning Shang |
Low Genus Curves and Cryptography | |
January 31 MATH 731 |
Edray Goins |
Distributions of 2-Selmer Ranks for Elliptic Curves, Part III | |
January 24 MATH 731 |
Edray Goins Purdue University |
Distributions of 2-Selmer Ranks for Elliptic Curves, Part II | |
January 17 MATH 731 |
Edray Goins |
Distributions of 2-Selmer Ranks for Elliptic Curves, Part I |
Spring 2007
Talks were held on Thursdays in MATH 731 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
May 3 | Brad Lucier |
Recently (re)discovered algorithms for large integer arithmetic | |
March 29 | Florian Luca |
Fibonacci Numbers with the Lehmer Property | |
March 28 MATH 817 |
Andreas Stein |
Zeta Function Approximation in Function Fields | |
March 22 | Lloyd Kilford |
A Jacquet-Langlands Correspondence in Weight 1 | |
February 8 | Louis de Branges |
Theta Functions of Modular Forms |
Fall 2006
Talks were held on Thursdays in MATH 731 from 3:30 PM - 4:20 PM, following a break after the Automorphic Forms and Representation Theory Seminar .
December 14 REC 113 |
Mahdi Asgari |
On Generic Representations of p-adic GSp(4) | |
November 30 | David Whitehouse |
On the Weighted Fundamental Lemma for Twisted Endoscopy of GL(n) | |
November 16 | Jennifer Johnson-Leung |
The Equivariant Main Conjecture of Iwasawa theory for Imaginary Quadratic Fields | |
November 8 BRNG 2280 |
Michael Larsen |
Functoriality and the Inverse Galois Problem |
Spring 2006
Most talks were held on Wednesdays in BRNG B255 from 4:30 PM - 5:20 PM, immediately following the Working Algebraic Geometry Seminar.
April 12 | Alain Togbe |
On the Solutions of a Family of Quartic Thue Equations | |
April 5 | Anthanasios Pheidas |
A Survey on Hilbert's Tenth Problem | |
March 22 BRNG 1238 |
James Cogdell |
Sums of Three Squares |