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

Purdue University

Organizational Meeting
June 14 Daniel Shankman

Purdue University

Zariski Topology (pgs. 1 - 4)
June 16 Tyler Billingsley

Purdue University

Affine Varieties (pgs. 4 - 7)
Week 2 June 19 Warren Katz

Purdue University

Solutions to Exercises (1.5, 1.6, 1.7, 1.8, 1.9)
June 21 Vinh Nguyen

Purdue University

Projective Varieties (pgs. 8 - 11)
June 23 Alex Porter

Purdue University

Solutions to Exercises (2.1, 2.2, 2.3, 2.4, 2.5)
Week 3 June 26 Matt Weaver

Purdue University

Regular Functions (pgs. 14 - 16)
June 28 Kelsey Walters

Purdue University

Morphisms Between Varieties (pgs. 17 - 20)
June 30 Clinton Bradford

Purdue University

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

Purdue University

Rational, Birational, and Dominant Maps (pgs. 24 - 27)
July 7 Frankie Chan

Purdue University

Blowing Up (pgs. 27 - 30)
Week 5 July 10 Matt Weaver

Purdue University

Solutions to Exercises (3.11, 3.12, 4.1, 4.2, 4.4)
July 12 Alison Rosenblum

Purdue University

Non-Singularity and Jacobian Matrices (pgs. 31 - 33)
July 14 Clinton Bradford

Purdue University

Local Rings and their Completions (pgs. 33 - 35)
Week 6 July 17 Miscellaneous

Purdue University

Solutions to Exercises (4.5, 4.7, 4.9, 5.1, 5.2)
July 19 Matt Weaver

Purdue University

Non-Singular Curves and Dedekind Domains (pgs. 39 - 42)
July 21 TBA

Purdue University

DVRs and Abstract Non-Singular Curves (pgs. 42 - 46)
Week 7 July 24 TBA

Purdue University

Solutions to Exercises (5.3, 5.4, 5.8, 5.9, 6.1)
July 26 TBA

Purdue University

Bezout's Theorem (pgs. 47 - 49)
July 28 Sarah Percival

Purdue University

Hilbert Polynomials I (pgs. 49 - 52)
Week 8 July 31 Frankie Chan

Purdue University

Hilbert Polynomials II (pgs. 52 - 54)
August 2 TBA

Purdue University

Solutions to Exercises (6.3, 6.4, 6.6, 7.2)
August 4 Edray Herber Goins

Purdue University

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

Purdue University

Duality between Sk and GLn(C)
November 17 Tyler Billingsley

Purdue University

Characters of GLn(C)
October 6 Alex Barrios

Purdue University

Mackey Theory
September 29 Jeremy Fuller

Purdue University

Induced Characters and Frobenius Reciprocity
September 22 Frankie Chan

Purdue University

Character Theory
September 8 Tyler Billingsley

Purdue University

Wedderburn's Theorem
September 1 Edray Herber Goins

Purdue University

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

Purdue University

Congruences between modular forms
July 26 Rachel Davis

Purdue University

Galois Representations
July 21 Dongming She

Purdue University

L-series and functional equations
July 19 Alex Barrios

Purdue University

Jacobians and Abelian Varieties
July 14 Abhishek Parab

Purdue University

Ramanujan's Conjecture and growth of coefficients
July 12 Daniel Shankman

Purdue University

Hecke Operators
July 7 Justin Katz

Purdue University

Eisenstein Series
July 5 Tyler Billingsley

Purdue University

Modular Curves as Riemann Surfaces
June 30 Frankie Chan

Purdue University

Modular Forms, Elliptic Curves, and Modular Curves
June 28 Edray Herber Goins

Purdue University

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

United States Military Academy

Generalizing Zeckendorf's Theorem: The Kentucky Sequence
October 30 Jeremy Fuller

Purdue University

Genus Theory for Quadratic Forms Revisited: The Genus Field
October 2 Alex Barrios

Purdue University

Hilbert and Ring Class Fields: From Quadratic Forms to Ideals in Number Fields
September 25 Jeremy Fuller

Purdue University

Genus Theory for Quadratic Forms
September 18 Edray Herber Goins

Purdue University

Gauss' Composition of Quadratic Forms
TBA Abhishek Parab

Purdue University

Bhargava's Reinterpretation of Gauss' Composition Laws
TBA Rachel Davis

Purdue University

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

Purdue University

A Curious Geometrically Motivated Algebraic Bijection
November 14 Kevin Mugo

Purdue University

Brauer Groups, Part II
November 7 Kevin Mugo

Purdue University

Brauer Groups, Part I
October 31 Jeremy Fuller

Purdue University

The Brauer-Manin Obstruction
October 17 Jamie Weigandt

Purdue University

The Cassels-Tate Pairing
September 26 Rachel Davis

Purdue University

The Shafarevich-Tate Group of Elliptic Curves
September 19 Abhishek Parab

Purdue University

Hilbert's Theorem 90 and Generalizations
September 12 Alex Barrios

Purdue University

Artin-Schreier Theory and Kummer Theory
September 5 Edray Goins

Purdue University

The Weil Pairing on Elliptic Curves, Part II
August 29 Edray Goins

Purdue University

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

Harvard University

How many elliptic curves can have the same prime conductor?
April 26 Kevin Mugo

Purdue University

On the ABC Conjecture and Diophantine Approximation by Rational Points
April 5 Abhishek Parab

Purdue University

ABC Implies no "Siegel Zeros" for L-Functions of Characters with Negative Discriminant
March 8 Jamie Weigandt

Purdue University

The ABC-Theorem, Davenport's Inequality and Elliptic Surfaces
March 1 Alex Barrios

Purdue University

On Some Consequences of the ABC Conjecture in Arithmetic and Logic
February 22 Alejandra Alvarado

Purdue University

Congruence ABC implies ABC
February 15 Kevin Mugo

Purdue University

Lang's Height Conjecture and Szpiro's Conjecture
February 1 Jeffrey A. Oaks

University of Indianapolis

Polynomials and Equations in Medieval Algebra and in Diophantus
January 25 Jeremy Fuller

Purdue University

Questions about Number
January 18 Alejandra Alvarado

Purdue University

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

Purdue University

A 60,000 digit prime number of the form x2 + x + 41
November 30 Jeremy Fuller

Purdue University

The Bruhat Decomposition
November 16 Edray Goins

Purdue University

Ranks of Elliptic Curves via Class Groups of Number Fields
November 2 Jamie Weigandt

Purdue University

The Fifteen Theorem and Generalizations, Part II
October 26 Jamie Weigandt

Purdue University

The Fifteen Theorem and Generalizations, Part I
October 19 Alex Barrios

Purdue University

Elasticity of Factorization in Number Fields, Part II
October 5 Alex Barrios

Purdue University

Elasticity of Factorization in Number Fields, Part I
September 28 Alejandra Alvarado

Purdue University

Belyi Maps and Dessins d'Enfants
September 21 Alejandra Alvarado

Purdue University

Belyi's Theorem
September 14 Abhishek Parab

Purdue University

The ABC Conjecture for Polynomials
September 7 Edray Goins

Purdue University

From Klein's Platonic Solids to Kepler's Archimedean Solids: Elliptic Curves and Dessins d'Enfants, Part II
August 31 Edray Goins

Purdue University

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

Purdue University

Mill's Prime Representing Function
March 30 Kevin Mugo

Purdue University

Noether's Problem for A5, Part II
March 23 Kevin Mugo

Purdue University

Noether's Problem for A5, Part I
March 2 David Chapman

Valparaiso University

An Algebraic Approach to Greenberg's Question
February 24 Alejandra Alvarado

Purdue University

On Square Values of Quadratics
February 17 Alain Togbe

Purdue University - North Central

Diophantine Equations with Products of Consecutive Values of a Quadratic Polynomial
February 10 Jeremy Fuller

Purdue University

Class Number Formulas via 2-Isogenies of Elliptic Curves, Part II
February 3 Jeremy Fuller

Purdue University

Class Number Formulas via 2-Isogenies of Elliptic Curves, Part I
January 27 Jamie Weigandt

Purdue University

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

Purdue University

Modular Forms via Quaternion Algebras: Some Explicit Examples
November 11

MATH 211

Ted Chinburg

University of Pennsylvania

Small Generators for Arithmetic Groups
November 10 Jamie Weigandt

Purdue University

Computing Modular Forms on Definite Quaternion Algebras, Part II
October 20 Jamie Weigandt

Purdue University

Computing Modular Forms on Definite Quaternion Algebras, Part I
October 6 Edray Goins

Purdue University

Mazur's Control Theorem, Part III
September 29 Edray Goins

Purdue University

Mazur's Control Theorem, Part II
September 22 Edray Goins

Purdue University

Mazur's Control Theorem, Part I
September 15 Kevin Mugo

Purdue University

Lambda-Modules in Iwasawa Theory, Part II
September 8 Kevin Mugo

Purdue University

Lambda-Modules in Iwasawa Theory, Part I
September 1 Edray Goins

Purdue University

An Introduction to Iwasawa Theory for Elliptic Curves, Part II
August 25 Edray Goins

Purdue University

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

Iowa State University

Noncongruence Modular Forms and Modularity
April 9 Alain Togbe

Purdue University - North Central

On Families of Diophantine Triples
March 12 Alfred Noël

University of Massachusetts, Boston

Algorithmic and Theoretical Considerations for Computing Generators of the Centralizer of K in U(g)
February 12 Tong Liu

Purdue University

Lattices in semi-stable representations
January 15 Lloyd Kilford

University of Bristol

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

Purdue University

Low Genus Curves and Cryptography
January 31
MATH 731
Edray Goins

Purdue University

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

Purdue University

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

Purdue University

Recently (re)discovered algorithms for large integer arithmetic
March 29 Florian Luca

Instituto de Matemáticas, Unidad Morelia

Fibonacci Numbers with the Lehmer Property
March 28

MATH 817

Andreas Stein

University of Wyoming

Zeta Function Approximation in Function Fields
March 22 Lloyd Kilford

Merton College, Oxford

A Jacquet-Langlands Correspondence in Weight 1
February 8 Louis de Branges

Purdue University

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

Oklahoma State University

On Generic Representations of p-adic GSp(4)
November 30 David Whitehouse

Institute for Advanced Study

On the Weighted Fundamental Lemma for Twisted Endoscopy of GL(n)
November 16 Jennifer Johnson-Leung

Brandeis University

The Equivariant Main Conjecture of Iwasawa theory for Imaginary Quadratic Fields
November 8

BRNG 2280

Michael Larsen

Indiana University

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

Purdue University - North Central

On the Solutions of a Family of Quartic Thue Equations
April 5 Anthanasios Pheidas

Purdue University - West Lafayette

A Survey on Hilbert's Tenth Problem
March 22

BRNG 1238

James Cogdell

Ohio State University

Sums of Three Squares