Counselor Talks

The counselors both contribute to and benefit from the mathematically rich environment at PROMYS in many ways including by doing their own research and by designing and participating in a wide range of seminars both for students and for each other.  Counselors also invite their peers, undergraduate and graduate students at top math programs, to speak to the PROMYS community.  Often these peers are also PROMYS alums.  

2013 Minicourses, Counselor Seminars (Algebraic Geometry and Elliptic Curves), and Miscellaneous Counselor Talks

2013 Minicourses

July 3

       Tropical Geometry – Joe Stahl and Dylan Yott

July 8

       Knot Theory – Robert Huben

July 9

      Cubic and Quartic and Galois – David Corwin

July 10

      Generating Functions – Michael Greenberg

July 10

      Topology of Cell Complexes – Ian Frankel

July 13

      Reciprocals of the Binary Generating Function for the Sum of Divisors
      – Sandy Neal

July 15

     Group Theory and Cayley Graphs – Mathilde Gerbelli-Gauthier and Olivier Martin

July 24

      Field Theory and Trisecting the Angle – Tony Feng

      Sylow Theorems – Andrew Ardito

July 25

      Hyperbolic Geometry and Continued Fractions – Krishna Dasaratha

July 29

      Introduction to LaTeX – Eva Belmont

July 30

      A Reduced Inventory for Geometry – Jenny Yeon

July 31

      The Mystery of the Prime Races – Lucy Mocz

August 1

      Hall's Theorem – Tomer Reiter

August 5

      Origami vs. Straight-Edge and Compass – Sarah Trebat-Leder

August 9

      Frieze Groups and Crystallographic Groups – Elena Slobodyan

      Eisenstein Integers (T-shirt Talk) – Lucy Mocz

      p-adic Numbers – David Corwin

2013 Algebraic Geometry Counselor Seminars

July 3

      Basic Notions in Topology – Dylan Yott

July 9

      An Introduction to Homology – Krishna Dasaratha

July 11

     Homology and the Inverse Function Theorem – Ian Frankel '07, '11-12

July 16

      Cohomology – Eva Belmont

July 18

     CW Complexes and the Eilenberg-Steenrod Axioms – Olivier Martin

July 24

       Constructions in Homotopy Theory – Will Perry

July 30

       Generalized Cohomology Theories and Spectra – Eva Belmont

August 1

      Characteristic Classes – Will Perry

August 7

       Formal Group Laws and Generalized Cohomology – Eva Belmont

2013 Elliptic Curves Counselor Seminars

July 3

      Introduction to Elliptic Curves – Tony Feng

July 10

      Isogenies of Elliptic Curves – Eva Belmont

July 13

      Elliptic Curves over Finite Fields and the Weil Conjectures – Olivier Martin

July 17

      Elliptic Curves over C – Lucy Mocz

July 23

      The Mordell-Weil Theorem: An Overview – Sarah Trebat-Leder

July 25

       Computing the Rank of the Mordell-Weil Group – Sarah Trebat-Leder

July 31

     The Congruent Number Problem – Glenn Stevens

August 5

       The Modularity Theorem – Lucy Mocz

August 6

       Computing Special Values of L-Functions of Elliptic Curves
       – Glenn Stevens

2013 Miscellaneous Counselor Talks

June 29

      The Ergodic Theorem in Number Theory – Dylan Yott

July 3

      The Thurston Norm – Dani Alvarez-Gavela '11

July 4

      Topological Quantum Field Theories – Will Perry

July 7

      Counting Antichains in Dimension 2 Posets – Sandy Neal

July 8

      Galois Groups and Fundamental Groups – David Corwin

July 14

      Mapping Class Group – Jifeng Shen (Visitor)

      The Étale Fundamental Group pt. 1 – David Corwin

July 15

      Patching over Fields and Inverse Galois Theory – Susan Xia

July 20

       A Bijective Proof of Cayley's Tree Theorem – Sandy Neal

      Riemann Roch Theory in Number Fields pt. 1 – Sam Mundy

July 21

       The Five-Color Theorem – Andrew Ardito

       Recursive Sequences – Robert Huben

July 26

       Complex Multiplication – Lucy Mocz

      The Étale Fundamental Group pt. 2 – David Corwin

      Riemann-Roch Theory in Number Fields pt. 2 – Sam Mundy

July 27

       Simplicial Sets and Infinity Categories – Eva Belmont

       Quadratic Forms and the Local-Global Principle – Jon Hanke '90-95

July 28

       The Weil Conjectures for Curves – Tony Feng

      A Crash Course in Modular Forms – Joe Stahl and Andrew Ardito

July 29

      3-Manifolds and Dehn Twists – Lucas Culler '02, '04-06, '08-09

August 3

      Ramanujan Congruences – Sarah Trebat-Leder

      Modular Forms mod p and Serre's Conjectures – Mathilde
      Gerbelli-Gauthier

August 4

      p-adic Integration and Bernoulli Functions – Dylan Yott

      Arithmetic Functions – Michael Greenberg

      Cohomology of Modular Twists on the Selmer Bundle – Joe Stahl,
      Will Perry, Dylan Yott, Sam Mundy, Andrew Ardito, Tomer Reiter

2012 Minicourses, Reviews, Counselor Seminars (Algebraic Number Theory and Lie Theory), and Minicourses for Counselors

2012 Minicourses

July 6

Möbius Functions: Applications to Geometry - Senia Sheydvasser, alumnus

July 9

Combinatorial Game Theory - Erick Knight

July 10

Compactness - Dylan Yott

July 11

Counting Colorings Cleverly - Zev Chonoles

July 12

Walks on Graphs - Qiaochu Yuan

July 16

Coloring Maps - Eva Belmont

July 23

Cryptography - Andrew Ardito

July 24

P vs NP - Tomer Reiter

July 26

Polynomials - Derek Hollowood

July 27

How to Beat RSI at Frisbee - Andrew Ardito and Ian Frankel

July 30

The Basel Problem - Michael Dunn-Goekjian

Watch Charlotte do LaTeX on the Board with her Left Hand - Charlotte Chan

July 31

Math and Chess - Kate Thompson

August 2

Algebraic Music Theory - Joe Stahl

The p-adic Numbers - Ian Frankel

August 10

The Earth is Spherical: Truth or Belief? - Jenny Yeon

The T-shirt Talk - Ian Frankel

Mini-mini-marathon - all counselors

2012 Reviews

July 17

Chain of Reasoning - Djordjo Milovic, William Perry

Numericals - Joe Stahl, Dylan Yott

July 18

Rigor - Andrew Ardito, Charlotte Chan, Ian Frankel

July 19

Miscellaneous - miscellaneous counselors

August 8

Numericals - Andrew Ardito, Djordjo Milovic

Circle of i - Michael Greenberg, Qiaochu Yuan

August 9

QR - Eva Belmont, Erick Knight

Continued Fractions - Andrew Ardito, Ian Frankel

August 10

Miscellaneous - miscellaneous counselors

2012 Algebraic Number Theory Counselor Seminars

July 3

Introduction to Algebraic Number Theory - Erick Knight

July 6

Rings of Integers, Dedekind Domains, etc. - Kate Thompson

July 10

Dedekind Domains - Djordjo Milovic

July 11

Dedekind Domains - Djordjo Milovic

July 18

Recap: Intro to the Class Group - Kate Thompson

July 23

Finiteness of the Class Number - Kate Thompson

July 26

Galois Actions on Number Fields - Erick Knight

August 1

Discriminants - Djordjo Milovic

August 2

Algebraic Number Theory Recitation Session - Erick Knight

August 6

The Minkowski Bound - Kate Thompson 

2012 Lie Theory Counselor Seminars

July 12

Introduction to Lie Theory - Ian Frankel

July 13

Representation Theory of Compact Groups - Qiaochu Yuan

July 17

The Peter-Weyl Theorem - Eva Belmont

July 19

Representations of S1 - Djordjo Milovic

July 24

The Story of sl(2) and its Representations - Charlotte Chan

July 27

SU(2), SO(3) and the quaternions - Qiaochu Yuan

July 31

SO(4) and Plücker relation - Lucas Culler, alumnus

August 7

Tensor Products of Representations - Qiaochu Yuan

August 8

Representations of sl(3) - Ian Frankel

2012 Counselor Guest Lectures and Minicourses for Counselors

July 3

The Spectral Theorem - Ian Frankel

July 5

Riemann Surfaces - Tim Holland

July 6

Multilinear Algebra - Qiaochu Yuan

July 7

Mathematical Foundations of Quantum Mechanics - Senia Sheydvasser, alumnus

July 27

Minimal Surfaces - Daniel Alvarez-Gavela, alumnus

 

2011 Minicourses, Review Sessions, Counselor Seminars, Counselor Guest Lectures, and Minicourses for Counselors

2011 Minicourses

July 7

Eulerian Graphs – Daniel Alvarez-Gavela

The Limits of Computation – Jeremy Booher

July 8

Extremal Combinatorics – Corina Panda

SETs and Anti-SETs: The Math Behind the Game of SET – Charlotte Chan

July 11

Point-Set Topology – Zev Chonoles

Matrices, Endomorphisms, Eigenvalues, and Hobbits – Daniel Alvarez-Gavela

July 12

The Probabilistic Method – Andy Zucker

The Fundamental Group – William Perry

July 14

Constructing the Reals – Ian Frankel

Frisbee Minicourse – Ian Frankel, William Perry, Andrew Ardito

July 18

Constructing the Integers – Jeremy Booher

LaTex and eMacs Minicourse – Alan Chang, Andrew Ardito

July 25

Convergence of Sequences; Points and Functions – Daniel Alvarez-Gavela

July 26

To Infinity and Beyond – The Reverend Senia Sheydvasser

Linear Programming – Michael Greenberg

July 28

An Introduction to Fractals – Robyn Fielder, Khrystyna Nechyporenko

Random Polynomials – Djordjo Milovic

August 1

Graph Planarity: Kuratowski’s Theorem – Elaine Liew

Probability Distributions and the Central Limit Theorem – Richard Zhang

Combinatorial Game Theory – Alan Chang

August 3

What is the “Right” Right Triangle – The Reverend Senia Sheydvasser

Frivolous Applications of Linear Algebra – Irving Dai

Sylow Theorems – Andrew Ardito

August 4

Compass and Straightedge Constructions – William Perry

Number Theory in Cryptography – Robyn Fielder, Jeremy Booher

Computational Complexity – Jason Bland

August 12

The 2011 T-Shirt: Cubic Reciprocity – Jeremy Booher

Rubik’s Cube – Alan Chang 

2011 Review Sessions

July 19

Rigor – Charlotte Chan, Corina Panda, Djordjo Milovic

July 20

Chain of Reasoning – Ian Frankel, Andy Zucker

Numericals – Andrew Ardito, Jeremy Booher

July 21

Miscellaneous – Miscellaneous counselors

August 8

Numericals – Alan Chang, Richard Zhang

Continued Fractions – Jeremy Booher, Andrew Ardito

August 9

Circle of i – Yoana Gyurova, Zev Chonoles

Quadratic Reciprocity – Daniel Alvarez-Gavela, Andy Zucker

August 10

Miscellaneous – Miscellaneous counselors

2011 Counselor Seminars - Representation Theory

July 9

Introduction to Representation Theory and First Examples – Charlotte Chan

July 15

Characters as an Orthonormal Basis – Ian Frankel

July 16

Semisimplicity – Jason Bland

July 24

Induced Representations and Frobenius Reciprocity – Djordjo Milovic

July 26

Brauer’s Theorem – Djordjo Milovic

July 30

Character Tables or Solving Representation Theory Sudoku – Corina Panda

July 31

Representations of the Symmetric Group via Young Tableaux, Part 1 – Jeremy Booher

August 7

Representations of the Symmetric Group via Young Tableaux, Part 2 – Jeremy Booher

Modular Representations of Symmetric Groups – Charlotte Chan

2011 Counselor Seminars - Differential Geometry and Topology

July 9

Introduction to Differential Topology – Zev Chonoles

July 15

Regular Values – Daniel Alvarez-Gavela

July 16

Applications of Regular Values – William Perry

July 17

Tangent Vectors – William Perry

July 29

Vector Bundles – Zev Chonoles

Degree Theory – Daniel Alvarez-Gavela

August 5

Vector Fields – Daniel Alvarez-Gavela

August 6

The Magic of the Euler Characteristic – Daniel Alvarez-Gavela

2011 Counselor Minicourses and Counselor Guest Lectures

July 10

Category Theory, Part 1 – William Perry, Zev Chonoles

July 12

Category Theory, Part 2 – William Perry, Zev Chonoles

July 17

The Probabilistic Method – Andy Zucker

July 19

Transcendental Numbers – Jeremy Booher

July 27

Modularity of CM Elliptic Curves – Erick Knight (Princeton University)

August 1

Banach Spaces, Part 1 – Ian Frankel

August 2

Banach Spaces, Part 2 – Ian Frankel

K-Theory – William Perry

August 4

The Schoenflies Conjecture and Morse Theory – Lucas Culler (MIT)

K-Theory – Daniel Alvarez-Gavela

August 6

A Gentle Introduction to Algebraic Number Theory Through Cyclotomic Fields – Carl Erickson (Harvard University)

August 7

Hamiltonian Mechanics – The Reverend Senia Sheydvasser

August 8

K-Theory – William Perry, Daniel Alvarez-Gavela

August 10

K-Theory – Andres Larrain Hubach (Boston University)