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.   

2015 Algebraic Topology Seminars, Minicourses, Mini-Seminars in Algebraic Number Theory, Mini-Seminars in Modular Forms, and One-Off Counselor Talks

2015 Algebraic Topology Seminars

Point Set Topology I – Tomer Reiter

Point Set Topology II – Ashwin Iyengar

Point Set Topology III – Larsen Linov

Fundamental Groups I – Luya Wang, Ben Bruce

The Seifert van Kampen Theorem – Kevin Lin

Induced Maps and More – Larsen Linov

Covering Spaces – Ashwin Iyengar

Simplicial Homology – Katy Weber

Singular Homology – Kevin Lin

Exact Sequences – Kevin Lin

Cellular Homology – Kevin Lin

Eilenberg-Steenrod Axioms – Sam Mundy


de Rham Cohomology and Introduction to Singular Cohomology – Yingying Wang

Singular Cohomology and Universal Coefficient Theorem – Yingying Wang

The Cup Product and Ring Structure on Cohomology – Joseph Stahl

Guest Lecture – Will Perry

2015 Minicourses

Quotient Maps – Chris Zhang

Probabilistic Method – Steven Kwon

Exact Sequences – Robert Huben

Lebesgue Integrals – Ashwin Iyengar

Cayley Graphs – Hannah Turner

Linear Algebraic Methods in Combinatorics – Arjun Khandelwal

Mandelbrot Set – Joe Zurier

Infinite Graphs – Kevin Lin

Knot Theory – Sam Zbarsky

An Introduction to Topology – Larsen Linov

Topology and the Intermediate Value Theorem – Tim Ratigan

Planar Graphs and the Three Cottages Puzzle – Ben Bruce

Introduction to Special Relativity – Claudia Feng

Group Actions – Chris Zhang

Game Theory – Yael Goldstein

Schur Polynomials and Quadratic Reciprocity – Roger van Peski

Arrow’s Impossibility Theorem – Luya Wang

Matrix Methods in Population Dynamics – Claudia Feng

Introduction to Representation Theory – Vineet Gupta

T-shirt Talk: The Arithmetic of Pell Conics – Joe Stahl

Origami Constructions – Tony Qiao

2015 Mini-Seminars in Algebraic Number Theory

Motivation for Algebraic Number Theory – Vineet Gupta

Rings of Integers and Class Groups – Sam Mundy

Prime Splitting in Number Fields – Joe Stahl

Finiteness of Class Number – Sam Mundy

2015 Mini-Seminars in Modular Forms

Modular Forms I – Joe Stahl

Modular Forms II – Sam Mundy

Hecke Operators – Joe Stahl

Eichler-Shimura Theory – Sam Mundy

2015 One-Off Counselor Talks

Riemannian Geometry – Chris Zhang

Introduction to Classical Algebraic Geometry – Anastasia Prokudina

Introduction to Modern Algebraic Geometry – Yingying Wang

Elementary Consequences of the Prime Number Theorem – Steven Kwon

Representation Theory – Vineet Gupta

Extensions of Locally Compact Abelian Groups – Sam Mundy

The Birch and Swinnerton-Dyer Conjecture – Tomer Reiter

The Antigeneric Blow-Up of the Category of Trimmed Artin Symbols – Sam Mundy, Tomer Reiter, and Yingying Wang

Nets, Ultrafilters, and Tychnoff’s Theorem – Ashwin Iyengar

Infinite Graphs – Kevin Lin

Structure Theorem of Finitely Generated Modules over PIDs – Roger van Peski

Kähler Manifolds – Yingying Wang

Morse Theory – Sam Mundy

Inverse Limits – Robert Huben

Schur Polynomials – Vineet Gupta and Roger van Peski

Classical Algebraic Geometry Part 2 – Anastasia Prokudina


2014 Minicourses, Counselor Seminars (Class Field Theory and Geometric Group Theory), and Miscellaneous Counselor Talks

2014 Minicourses

Hats – Dylan Yott 

Schur Polynomials, Gelfand-Tsetlin Patterns & Tokuyama’s Formula – Vineet Gupta 

Lie Algebras and Representations of SL (C)–Uthsav Chitra   

Generating Functions – Michael Greenberg 

Fundamental Groups – Akhil Mathew 

Axiom of Choice – Henry Swanson 

Pathological Functions – Wentong Zhang       

Fundamental Theorem of Algebra – Robert Huben 

Category Theory – Lucas Mann 

Riemann Surfaces – Yingying Wang 

Incompleteness Theorems – Raffael Singer    

An Introduction to Graph Theory – Amelie Dougherty 

2014 Class Field Theory Counselor Seminars 

Algebraic Number Theory – Joe Stahl 

Galois + QR – Raffael Singer 

Frobenius Elements – Dylan Yott 

The Artin Map – Sam Mundy 

Elliptic Functions – Dylan Yott 

Orders in Imaginary Quadratic Fields – Sam Mundy 

Elliptic Curves and Ring Class Fields – Sam Mundy 

2014 Geometric Group Theory Counselor Seminars

Group Presentations – Akhil Mathew 

More on Presentations – Akhil Mathew 

Cayley Graphs – Hanna Astephan 

Coxeter Groups – Mathilde Gerbelli-Gauthier 

The Word Problem – Hanna Astephan 

Roots Systems – David Mehrle 

Dynkin Diagrams and Lie Algebras – David Mehrle 

When is a Group Free? – Akhil Mathew 

Amalgams – Mathilde Gerbelli-Gauthier 

Ends of Groups & Stalling’s Theorem – Akhil Mathew 

2014 Miscellaneous Counselor Seminars

Grobner Bases – David Merhle 

Adeles and Ideles – Sam Mundy 

The Gross Zagier Formula – Dylan Yott 

Tate’s Thesis – Sam Mundy 

Closed Surfaces – Jason Marsh 

Galois Theory – Raffael Singer 

Ramsey Theory – Alexander Neal Riasanovsky 

Number and String Theory – Yingying Wang 

Categories for the Working Counselor – Joe Stahl 

Smooth Manifolds – Jason Marsh 

Elliptic Curves and String Theory – Yingying Wang 

Queueing Theory – Michael Greenberg 

Szemeredi Regularity Lemma – Tomer Reiter 

Whitney Embedding Theorem – Jason Marsh 

Shor’s Algorithm – Chen Xie 

Stable Homotopy Theory – Akhil Mathew 


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

2013 Minicourses

       Tropical Geometry – Joe Stahl and Dylan Yott

       Knot Theory – Robert Huben

      Cubic and Quartic and Galois – David Corwin

      Generating Functions – Michael Greenberg

      Topology of Cell Complexes – Ian Frankel

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

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

      Field Theory and Trisecting the Angle – Tony Feng

      Sylow Theorems – Andrew Ardito

      Hyperbolic Geometry and Continued Fractions – Krishna Dasaratha

      Introduction to LaTeX – Eva Belmont

      A Reduced Inventory for Geometry – Jenny Yeon

      The Mystery of the Prime Races – Lucy Mocz

      Hall's Theorem – Tomer Reiter

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

      Frieze Groups and Crystallographic Groups – Elena Slobodyan

      Eisenstein Integers (T-shirt Talk) – Lucy Mocz

      p-adic Numbers – David Corwin

2013 Algebraic Topology Counselor Seminars

      Basic Notions in Topology – Dylan Yott

      An Introduction to Homology – Krishna Dasaratha

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

      Cohomology – Eva Belmont

      CW Complexes and the Eilenberg-Steenrod Axioms – Olivier Martin

      Constructions in Homotopy Theory – Will Perry

      Generalized Cohomology Theories and Spectra – Eva Belmont

      Characteristic Classes – Will Perry

      Formal Group Laws and Generalized Cohomology – Eva Belmont

2013 Elliptic Curves Counselor Seminars

      Introduction to Elliptic Curves – Tony Feng

      Isogenies of Elliptic Curves – Eva Belmont

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

      Elliptic Curves over C – Lucy Mocz

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

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

      The Congruent Number Problem – Glenn Stevens

      The Modularity Theorem – Lucy Mocz

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

2013 Miscellaneous Counselor Talks

      The Ergodic Theorem in Number Theory – Dylan Yott

      The Thurston Norm – Dani Alvarez-Gavela '11

      Topological Quantum Field Theories – Will Perry

      Counting Antichains in Dimension 2 Posets – Sandy Neal

      Galois Groups and Fundamental Groups – David Corwin

      Mapping Class Group – Jifeng Shen (Visitor)

      The Étale Fundamental Group pt. 1 – David Corwin

      Patching over Fields and Inverse Galois Theory – Susan Xia

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

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

      The Five-Color Theorem – Andrew Ardito

      Recursive Sequences – Robert Huben

      Complex Multiplication – Lucy Mocz

      The Étale Fundamental Group pt. 2 – David Corwin

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

      Simplicial Sets and Infinity Categories – Eva Belmont

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

      The Weil Conjectures for Curves – Tony Feng

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

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

      Ramanujan Congruences – Sarah Trebat-Leder

      Modular Forms mod p and Serre's Conjectures – Mathilde

      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

Möbius Functions: Applications to Geometry
- Senia Sheydvasser, alumnus

Combinatorial Game Theory - Erick Knight

Compactness - Dylan Yott

Counting Colorings Cleverly - Zev Chonoles

Walks on Graphs - Qiaochu Yuan

Coloring Maps - Eva Belmont

Cryptography - Andrew Ardito

P vs NP - Tomer Reiter

Polynomials - Derek Hollowood

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

The Basel Problem - Michael Dunn-Goekjian

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

Math and Chess - Kate Thompson

Algebraic Music Theory - Joe Stahl

The p-adic Numbers - Ian Frankel

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

The T-shirt Talk - Ian Frankel

Mini-mini-marathon - all counselors

2012 Reviews

Chain of Reasoning - Djordjo Milovic, William Perry

Numericals - Joe Stahl, Dylan Yott

Rigor - Andrew Ardito, Charlotte Chan, Ian Frankel

Miscellaneous - miscellaneous counselors

Numericals - Andrew Ardito, Djordjo Milovic

Circle of i - Michael Greenberg, Qiaochu Yuan

QR - Eva Belmont, Erick Knight

Continued Fractions - Andrew Ardito, Ian Frankel

Miscellaneous - miscellaneous counselors

2012 Algebraic Number Theory Counselor Seminars

Introduction to Algebraic Number Theory - Erick Knight

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

Dedekind Domains - 1 - Djordjo Milovic

Dedekind Domains - 2 - Djordjo Milovic

Recap: Intro to the Class Group - Kate Thompson

Finiteness of the Class Number - Kate Thompson

Galois Actions on Number Fields - Erick Knight

Discriminants - Djordjo Milovic

Algebraic Number Theory Recitation Session - Erick Knight

The Minkowski Bound - Kate Thompson 

2012 Lie Theory Counselor Seminars

Introduction to Lie Theory - Ian Frankel

Representation Theory of Compact Groups - Qiaochu Yuan

The Peter-Weyl Theorem - Eva Belmont

Representations of S1 - Djordjo Milovic

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

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

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

Tensor Products of Representations - Qiaochu Yuan

Representations of sl(3) - Ian Frankel

2012 Counselor Guest Lectures and Minicourses for Counselors

The Spectral Theorem - Ian Frankel

Riemann Surfaces - Tim Holland

Multilinear Algebra - Qiaochu Yuan

Mathematical Foundations of Quantum Mechanics
- Senia Sheydvasser, alumnus

Minimal Surfaces - Daniel Alvarez-Gavela, alumnus


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

2011 Minicourses

Eulerian Graphs – Daniel Alvarez-Gavela

The Limits of Computation – Jeremy Booher

Extremal Combinatorics – Corina Panda

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

Point-Set Topology – Zev Chonoles

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

The Probabilistic Method – Andy Zucker

The Fundamental Group – William Perry

Constructing the Reals – Ian Frankel

Frisbee Minicourse – Ian Frankel, William Perry, Andrew Ardito

Constructing the Integers – Jeremy Booher

LaTex and eMacs Minicourse – Alan Chang, Andrew Ardito

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

To Infinity and Beyond – The Reverend Senia Sheydvasser

Linear Programming – Michael Greenberg

An Introduction to Fractals – Robyn Fielder, Khrystyna Nechyporenko

Random Polynomials – Djordjo Milovic

Graph Planarity: Kuratowski’s Theorem – Elaine Liew

Probability Distributions and the Central Limit Theorem – Richard Zhang

Combinatorial Game Theory – Alan Chang

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

Frivolous Applications of Linear Algebra – Irving Dai

Sylow Theorems – Andrew Ardito

Compass and Straightedge Constructions – William Perry

Number Theory in Cryptography – Robyn Fielder, Jeremy Booher

Computational Complexity – Jason Bland

The 2011 T-Shirt: Cubic Reciprocity – Jeremy Booher

Rubik’s Cube – Alan Chang 

2011 Review Sessions

Rigor – Charlotte Chan, Corina Panda, Djordjo Milovic

Chain of Reasoning – Ian Frankel, Andy Zucker

Numericals – Andrew Ardito, Jeremy Booher

Miscellaneous – Miscellaneous counselors

Numericals – Alan Chang, Richard Zhang

Continued Fractions – Jeremy Booher, Andrew Ardito

Circle of i – Yoana Gyurova, Zev Chonoles

Quadratic Reciprocity – Daniel Alvarez-Gavela, Andy Zucker

Miscellaneous – Miscellaneous counselors

2011 Counselor Seminars - Representation Theory

Introduction to Representation Theory and First Examples – Charlotte Chan

Characters as an Orthonormal Basis – Ian Frankel

Semisimplicity – Jason Bland

Induced Representations and Frobenius Reciprocity – Djordjo Milovic

Brauer’s Theorem – Djordjo Milovic

Character Tables or Solving Representation Theory Sudoku – Corina Panda

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

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

Introduction to Differential Topology – Zev Chonoles

Regular Values – Daniel Alvarez-Gavela

Applications of Regular Values – William Perry

Tangent Vectors – William Perry

Vector Bundles – Zev Chonoles

Degree Theory – Daniel Alvarez-Gavela

Vector Fields – Daniel Alvarez-Gavela

The Magic of the Euler Characteristic – Daniel Alvarez-Gavela

2011 Counselor Minicourses and Counselor Guest Lectures

Category Theory, Part 1 – William Perry, Zev Chonoles

Category Theory, Part 2 – William Perry, Zev Chonoles

The Probabilistic Method – Andy Zucker

Transcendental Numbers – Jeremy Booher

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

Banach Spaces, Part 1 – Ian Frankel

Banach Spaces, Part 2 – Ian Frankel

K-Theory – William Perry

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

K-Theory – Daniel Alvarez-Gavela

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

Hamiltonian Mechanics – The Reverend Senia Sheydvasser

K-Theory – William Perry, Daniel Alvarez-Gavela

K-Theory – Andres Larrain Hubach (Boston University)