August 22 : Organizational Meeting
August 29 : Elliptic Curves and Modularity, Sandra Nair. Download notes here.
September 5 : p-adic Numbers and Geometry, Jeff Achter
September 12 : Moduli of Abelian Varieties, Rachel Pries
September 19 : Newton polygons (or Newton stratification) and p-divisible groups, Sandra Nair. Download notes here.
September 26 : Arboreal Galois representations, Daniel Tedeschi
October 3 : Cayley Bacharach theorem, Chloe Stewart
October 10 : p-rank of curves and the Hasse-Witt matrix of curves, Rachel Pries
October 17 : Hilbert Functions, Jake Kettinger
October 24 : Maximum number of points on an algebraic set over finite field, Deepesh Singhal
October 31: No talk
November 7: Cigole Thomas
November 14 : CSU Math Day, No Seminar
November 21:
November 28 : Thanksgiving Break
December 5 : Coffee
January 24: Organizational Meeting
January 31: Rachel Pries
February 7: Jake Kettinger, Dynamics of Iterated Hesse Derivatives
February 14: Chloe Stewart, Elliptic Curves and Complex Multiplication
February 21: Emily Varney, Dynatomic Polynomials and Periodic Points
February 28: No talk at the regular time. May attend Kelly and Amie's defense.
March 6: Not meeting (Arizona Winter School)
March 13: Spring Break
March 20: Sandra Nair, Chloe Stewart, Daniel Tedeschi, post Arizona Winter School mini-talks
March 27: Jamie Juul and Cigole Thomas Dynamical irreducibility of certain families of polynomials
April 3: Daniel Tedeschi
April 10: Jeff Achter, Algebraic Cocycles
April 17: Sandra Nair, Weyl group coset
April 24: Jamie Juul, Specializations of Iterated Galois Groups of PCF Rational Functions
May 1: Coffee
August 22: Organizational Meeting
August 29: Rachel Pries
September 5: Jeff Achter
September 12: Cigole Thomas and Sandra Nair
September 19: Amie Bray and Kelly O'Connor
September 26: Jamie Juul, The Dedekind-Kummer Theorem
October 3: Jeff Achter
October 10: Sandra Nair
October 17: Dusan Dragutinovic (Utrecht University)
October 24: Coffee
October 31: Vlad Sworski, An Exploration of Superspecial 2-Isogeny Graphs in Genus 2
November 7: Jamie Juul, Introduction to height functions
November 14: Amie Bray
November 28: Sandra Nair
December 5: End of semester coffee
January 26: Organizational Meeting
February 2: p-adic numbers (discussion) - Kristina Moen (notes)
February 9: p-adic numbers discussion continued - Amie Bray
February 16 : p-adic numbers discussion
February 23: Introduction to Arithmetic Dynamics - Cigole Thomas
March 2 : Didn't meet (MMARGS by Erin Dawson on Elliptic Curves)
March 9 : Naïve enumeration of small degree polynomials up to PGL2 - Everett Howe
March 30: Coffee Break!
April 6: Introduction to Modular Forms - Chloe Stewart
April 13: Amie Bray
April 20: Jeff Achter
April 27: Rachel Pries
May 4: Arithmetic Dynamics over Local Fields - Daniel Tedeschi
May 11 : Coffee
September 1: Jeff Achter, What is a public key cryptosystem?
September 8: Kelly Emmrich, What is an elliptic curve?
September 15: Rachel Pries, What is a supersingular elliptic curve over a finite field?
September 22: Amie Bray, What are isogenies of elliptic curves and isogeny graphs?
September 29: Vlad Sworski, What is an isogeny-based cryptosystem?
October 6: No talk due to FRAGMENT seminar on 6th and Number Theory Day on Oct 8th
October 13: William Scarboro, Efficient Ring Operations,
(Paper: "Multidigit Multiplication for Mathematicians." Daniel Bernstein. 2001. https://www.semanticscholar.org/author/D.-Bernstein/2175374)
October 20: Rachel Pries, Reed-Solomon Codes
October 27: Jeff Achter, Lattice Based Cryptography
November 3 : Cigole Thomas, Markoff Triples
December 8: Jamie Juul, Shapes of Number Fields