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 alumni.
Bounds on the Cardinality of Maximal Sidon Sets
Projective Geometry
An Introduction to the Nash Equilibrium
Prime and Shine
Fun with Catalan Numbers and Motivating Generating Functions
Is this a polynomial function?
Fractal Dimensions
Geometry on Surfaces
Complexity, or why solving one problem solves them all
Combinatorical Games
Fractal Design
Averaging and inequality
Tour of Philosophy of Science
Factoring Large Numbers
Algebraic Dynamic Programming
PROMYS 2020 T-Shirt Talk
Algebraic Number Theory I
Algebraic Number Theory II
Algebraic Number Theory III
Algebraic Number Theory IV
Algebraic Topology I
Algebraic Topology II
Algebraic Topology III
Algebraic Topology IV
Affine Algebraic Sets
The Zariski Topology
Hilbert’s Nullstellensatz
Geometric Spaces and Spectrum of a Ring
Localization
Sheaves and Ringed Spaces
Morphisms of Ringed Spaces
An Overview of Schemes
Compactness in Metric Spaces I
Compactness in Metric Spaces II
Compactness in Metric Spaces III
Complex Analysis I
Complex Analysis II
Complex Analysis III
Riemann Sphere and Moebius Transformations
Group Presentations and Cayley Graphs
Quasi-Isometries and the Milnor-Svarc Theorem
Milnor-Svarc Theorem and Ping-Pong Lemma
Groups acting on Trees
Ends of Groups
Classification
Non-linearity
Generalization
Neural Networks
Definitions and Examples
Untilting and Finite Extensions
(phi, Gamma) - modules
Outlook on Perfectoid Spaces
Quantum Computation I
Quantum Computation II
Quantum Computation III
Quantum Computation IV
Period Finding
Shor’s Algorithm
Biases and Products of Two Primes
Vector Calculus, Laplace’s Equation and Hodge Theory
Introduction to the P-Adics
Curves on Surfaces and Mapping Class Groups
Group Cohomology and Grothendieck Topologies
Model Theory
Perfect Dice
Mittag-Leffler Problems
Curves of Constant Width - Arya Vadnere
Ramsey Numbers - Lizzie Pratt
Applying Information Theory to Combinatorics - Kenz Kallal
Voting Theory - Samuel Marks
Unnecessary Proofs of the Infinitude of Primes - Kevin Chang
Frisbee minicourse - (various)
Tropical Geometry - Yuhan Jiang
Triternions - Jessie Tan
Influence in Referendum Elections - Lee Trent
Elliptic Curves - Chris Zhu
Markov Chains and Hidden Markov Model - Eileen Zhang
Partition Functions - Adit Vishnu
Rings and Ideals - Hugo Jenkins
Soddy-Gosset Theorem - Devansh Sehta
How many proofs of AM-GM is too many? - Natalie Merson
Homogeneous Polynomials over Finite Fields - Joye Chen
T-shirt Talk: Geometry and Splitting of Primes - Samuel Marks
The Fundamental Group - Kevin Chang
The Seifert Van-Kampen Theorem - Ishan Levy
Covering Spaces and Galois Correspondence - Kevin Chang
Covering Spaces - Arya Vadnere
Brown Representability Theorem - Kevin Chang
Quadratic Forms - Ishan Levy
Group Cohomology - Alec Leng
Global Statements of Class Field Theory - Ishan Levy
Quadratic Forms, Lattices, and Ideals - Ishan Levy
Complex Analysis, Part I - Kenz Kallal
Complex Analysis, Part II - Vijay Srinivasan
Complex Analysis, Part III - Kenz Kallal
Complex Analysis, Part IV - Vijay Srinivasan
Dirichlet’s Theorem on Primes in Arithmetic Progressions - Kenz Kallal
The Prime Number Theorem, Part I - Kenz Kallal
The Prime Number Theorem, Part II - Kenz Kallal
A Dip into Linear Algebra - Arya Vadnere
Introduction to Differential Forms - Kevin Chang
Pullbacks and Integrating Forms - Arya Vadnere
Zabrieko’s Lemma and Corollaries - Vijay Srinivasan
Extending Linear Functionals - Vijay Srinivasan
The Weak Topology and L^p spaces - Vijay Srinivasan
Introduction to Lambda Calculus - Eileen Zhang
The Church-Rosser Theorem - Eileen Zhang
Combinatory Algebra - Eileen Zhang
Introduction to Modular Forms - Adit Vishnu
The Ramanujan Congruences - Adit Vishnu
Algebraic Relations between Partition Functions and the j-function - Adit Vishnu
The Basics of Class Field Theory - Adam Block
Discrete Time Stochastic Processes - Adam Block
Brownian Motion and the Random Walk - Adam Block
Stochastic Calculus - Adam Block
Brownian Motion and Partial Differential Equations - Adam Block
Basic Categories - Jackson Markey
Local/Global Principle for nth powers - Ishan Levy
Pathological Functions - Philip Lamkin
Philosophies in Mathematics - Lee Trent
Introduction to Hopf Algebras - Yuhan Jiang
p-adic Numbers - Alex Rodriguez
Introduction to Algebraic Number Theory - Yuhan Jiang
Introduction to Coq - David Jao
Proving Theorems in Coq - David Jao
Introduction to Mapping Class Groups - Arya Vadnere
Congruences between Modular Forms - Sam Mundy
The Empirical and the Formal - Justin Yim
p-adic Analysis - Alex Rodriguez
Structure Theorem for Finitely Generated Modules over a PID - Philip Lamkin
The Laplacian and Number Fields - Ishan Levy
Farey Sequences (Distribution and Extension) - Lee Trent
Dividing Squares Into Triangles of Equal Area - Adam Block
Linear Algebra and Face Recognition - Soumen Ghosh
Metropolis-Hastings Algorithm - Levi Borodenko
The Inscribed Rectangle Problem - Chris Zhang
The Dehn Invariant - Dylan Pentland
Introduction to Smooth Manifolds - Arya Vadnere
Crossing Numbers of Alternating Knots - Ishan Levy
The 5-Color Theorem - Linda Gutsche
Random Walks - Seraphina Lee
Burnside’s Lemma - Mirilla Zhu
LaTeX Minicourse – Leon Ochmann
The AKS Primality Test - Adit Vishnu
Frisbee Rules and Strategy - Chris Zhang and Ishan Levy
Visualizing Polytopes in 4D - Neelima Borade
Period Three Implies Chaos - Lisa Lokteva
ABC Conjecture and its Consequences - Sabir Shaik
Doodles - Jeremy Taylor
Introduction to Special Relativity and Group Theory - Tarang Saluja
The Skolem-Mahler-Lech Theorem - Adam Block
T-Shirt Minicourse: Families - Kevin Lin
Riemann Surfaces: Example Sheet 0 Problem Session – Kevin Lin
Riemann Surfaces: Elliptic Integrals – Kevin Lin
Riemann Surfaces: Example Sheet 1 Problem Session – Kevin Lin
Riemann Surfaces: Topology of Riemann Surfaces - Chris Zhang
Riemann Surfaces: Example Sheet 2 Problem Session – Kevin Lin
Riemann Surfaces: The Klein Quartic - Alyosha Latyntsev
Riemann Surfaces: Sheaves and Analytic Continuation – Kevin Lin
Galois Theory and Riemann Surfaces – Ishan Levy
Riemann Surfaces: Example Sheet 3 Problem Session – Kevin Lin
Form and Function - Alyosha Latyntsev
Riemann Surfaces: The Riemann-Roch Theorem – Kevin Lin
Riemann Surfaces: Questions Session - Alyosha Latyntsev
Riemann Surfaces: The Abel-Jacobi Theorem - Alyosha Latyntsev
Riemann Surfaces: Modular Curves – Kevin Lin
What is Algebraic Geometry? – Ishan Levy
Divisors and Intersections – Ishan Levy
Dimension and Moduli- Ishan Levy
Gröbner Bases – Ishan Levy
Algebraic Number Theory I - Jeremy Taylor
Algebraic Number Theory II - Jeremy Taylor
Algebraic Number Theory III - Jeremy Taylor
Algebraic Number Theory IV - Jeremy Taylor
Artin Reciprocity I – Alec Leng
Artin Reciprocity II – Alec Leng
Iwasawa Theory I - Sam Mundy (alum)
Iwasawa Theory II - Sam Mundy (alum)
Iwasawa Theory III - Sam Mundy (alum)
Introduction to Elliptic Curves – Alec Leng
Points of Order 13 on Elliptic Curves – Kevin Lin
Hasse Bound for Elliptic Curves – Seraphina Lee
Morse Theory and Handles – Ishan Levy
Heegaard Splittings and Knots on the Torus – Ishan Levy
Dehn Surgery and Kirby Calculus – Ishan Levy
The Poincaré Homology Sphere – Ishan Levy
Dehn’s Lemma and an Application - Lisa Lokteva
Multi-Jet Transversality and Classification of Stable Immersions - Lisa Lokteva
Representation Theory of Finite Groups I - Hugo Jenkins
Representation Theory of Finite Groups II - Hugo Jenkins
Intersection Theory in Algebraic Geometry I – Adam Block
Intersection Theory in Algebraic Geometry II – Adam Block
Intersection Theory in Algebraic Geometry III – Adam Block
Introduction to Commutative Algebra – Caitlyn Booms
Introduction to Minimal Free Resolutions – Caitlyn Booms
Linear Resolutions of Edge Ideals – Caitlyn Booms
Introduction to Measure Theory – Luya Wang
Ergodic Theory and Continued Fractions I – Chris Zhang
Ergodic Theory and Continued Fractions II – Chris Zhang
Borel Measures – Alex Rodriguez
Random Matrix Theory I – Roger Van Peski
Random Matrix Theory II – Roger Van Peski
Representation Theory of the Symmetric Group I – Adam Block
Representation Theory of the Symmetric Group II – Roger Van Peski
Representation Theory of the Symmetric Group II – Adam Block
Matrix Lie Groups I – Yichi Zhang
Matrix Lie Groups II – Yichi Zhang
Rigidity Theory I - Rebecca Rohrlich
Rigidity Theory II - Rebecca Rohrlich
Tannaka Duality I – Oron Propp
Tannaka Duality II – Oron Propp
An Introduction to Logic - Lisa Lokteva
Introduction to p-Adics – Alec Leng
Chemistry and Representation Theory - Alyosha Latyntsev
Holomorphic Functions and Complex Integration- Levi Borodenko
Singular Value Decomposition - Hugo Jenkins
Complex Analysis – Adit Vishnu
Probability and Expectation – Kevin Lin
An Overview of the Proof of the Prime Number Theorem – Adit Vishnu
Hearing the Shape of a Manifold - Alyosha Latyntsev
SL(2,Z) – Kevin Lin
p-Adic Modular Forms – Sam Marks (alum)
A Quick Introduction to Linguistics - Lisa Lokteva
Groups and Zeta Functions – Dylan Pentland
Review of Galois Theory - Alyosha Latyntsev
Shnirel'man’s Theorem - Stanislav Atanasov
Infinite Dimensional Topologies - Mendel Keller
Fermat’s Last Theorem for Polynomials - Adam Block
Fundamental Groups and Covering Spaces - Ishan Levy
What is R? - Sam Marks
Hyperplane Separation Theorem and Intro to Convex Analysis - Hedi Xia
Let’s Talk About Sets, Baby! - Kat Hall
Hyperplane Arrangement - Yibo Gao
LaTeX Minicourse - Various
Frisbee Minicourse - Various
Extending Platonic Solids - Philip Lamkin
Quantum Computing - Vandana Agarwala
General Relativity - Alyosha Latyntsev
Special Relativity - Olivia Cannon
Sharkovsky’s Theorem - Vaughan McDonald
Sylow Theorem and Unique Groups of Order n - Samira le Grand
Linear Algebra and Face Recognition - Soumen Ghosh
Introduction to Measure Theory - Yuxi Han
Goodstein’s Theorem - Sabir Shaik
An Introduction to Generating Functions - Max Hlavacek
T-Shirt Minicourse: The j –Invariant - Daniel Li
Affine Varieties - Sam Marks
But dat Nullstellensatz tho - Ishan Levy
Projective Varieties - Max Hlavacek
Morphisms: Putting the “Fun” in “Function” - Larsen Linov
Coordinate Rings and Rational Functions - Sam Marks
Rational Maps and Blowups: Getting Mor Out of Morphisms - Larsen Linov
Localizations and Nakayama’s Lemma - Stanislav Atanasov
Review Session - Various
Nonsingular Varieties - Adam Block
Curves - Kevin Lin
Divisors and Linear Systems - Kevin Lin
Embeddings into Projective Space - Kevin Lin
The Riemann-Roch Theorem - Kevin Lin
Riemann-Hurwitz and Applications - Adam Block
Reducing Elliptic Curves Modulo p , I - Daniel Li
Reducing Elliptic Curves Modulo p , II - Daniel Li
An Overview of the Proof of Fermat’s Last Theorem - Glenn Stevens
Holomorphic Functions and Contour Integrals - Sam Marks
Cauchy’s Theorem - Sam Marks
Cauchy’s Integral Formulas and Applications - Sam Marks
Some Complex Theorems and Simple Analysis - Ishan Levy
The Residue Theorem and Applications - Vaughan McDonald
Vector Bundles - Kevin Lin
Stiefel-Whitney Classes - Kevin Lin
The Euler Class and the Thom Isomorphism - Kevin Lin
Chern Classes - Kevin Lin
The Chern-Weil Homomorphism - Kevin Lin
Categories and Functors - Ishan Levy
Natural Transformations, Duality, and Equivalences - Ishan Levy
Duality, Equivalences - Ishan Levy
Representable Functors and the Yoneda Lemma - Ishan Levy
Universals and Limits - Ishan Levy
Adjunctions - Ishan Levy
Representation Theory and Combinatorics, I - Adam Block
Representation Theory and Combinatorics, II - Adam Block
Riemann Surfaces, I - Alyosha Latyntsev
Riemann Surfaces, II - Alyosha Latyntsev
Riemann Surfaces, III - Alyosha Latyntsev
Ping Pong and Quasi-Isometry - Larsen Linov
The Word Problem and Hyperbolic Groups - Robert Huben (’15)
The Ordinal Numbers - Mendel Keller
Monstrous Moonshine - Roger Van Peski (’15) & Neekon Vafa (’14)
Diophantine Approximations and Schmidt Subspace Theorem - Stanislav Atanasov
Uniform Spaces - Yuxi Han
Propositional Logic and Stone Duality - Sam Marks
Beginnings of Functional Analysis - Srivatsav Kunnawalkam Elayavalli
Hilbert Spaces - Ben Bruce
Resolvent & Spectra of Bounded Linear Operators - Leila Sloman
Examples of Spectra, Holomorphic Functions, and the Spectral Radius - Daniel Dore
Compact Operators - Sam Zbarsky
Compact Operators Part. 2; SelfAdjoint Operators - Steven Kwon
The Spectra of Bounded SelfAdjoint Operators - Daniel Dore
Proof of Spectral Theorem and Unbounded Operators - Sam Zbarsky
Linear Operators in Quantum Mechanics - Leila Sloman
Fredholm Alternative - Sam Zbarsky
Combinatorial Game Theory - Sam Zbarsky
An Interesting Hat Problem - Srivatsav Kunnawalkam Elayavalli
Ergodic Theorem for Markov Chains - Ishan Levy
Hex and the Brouwer Fixed Point Theorem - Sam Marks
What are Elliptic Curves and Why Do We Care? - Tim Ratigan
Göodel & the Halting Problem - Shakthi Shrima
Löb’s Theorem - Jack Gurev
How to Play Ultimate - Larsen Linov, Sam Marks, David Amirault, Ishan Levy
Covering Spaces - Art Waeterschoot
Unique Prime Factorization of Knots - Josh Wang
Cubic Curves and Bezout’s Theorem - Daniel Dore
Lucas’ Theorem and its Applications - Cailan Li
Kirchhoff ’s MatrixTree Theorem - Kevin Lin
The Fundamental Group - Roshan Padaki
ABC Conjecture and its Consequences - Sabir Shaik
Brownian Motion and Liouville’s theorem - Vanshika Jain
A Dip into Galois Theory - Vineet Gupta
T-shirt talk (Dedekind sums) - Art Waeterschoot
A Historical Introduction to Representation Theory: The Group Determinant - Daniel Dore
Introduction to Representation Theory; Maschke’s Theorem - Steven Kwon
Characters - Alyosha Latyntsev
Tensor Products and Induced Representations - Sam Zbarsky
Review of Concepts - Vineet Gupta
Calculating Character Tables - Kevin Lin
The TensorHom Adjunction - Kevin Lin
Burnside’s Theorem - Ben Bruce
Irreducible Representations of Sn - Vineet Gupta
The Mackey Criterion and Frobenius Groups - Daniel Dore
Lie Groups, Lie Algebras, and Their Representations - Steven Kwon
A survey of the SchurWeyl Duality and Schur Polynomials - Vineet Gupta
SchurWeyl Duality - Kevin Lin
Schur Polynomials - Vineet Gupta
The PeterWeyl Theorem - Steven Kwon
Complex Multiplication Part 0 - Sam Marks
Forcing and the Continuum Hypothesis, I - Kevin Lin
An Invitation to Extremal Set Theory - Srivatsav Kunnawalkam Elayavalli
Forcing and the Continuum Hypothesis, II - Kevin Lin
Intro to Mapping Class Groups - Larsen Linov
Chromatic Graph Theory - Art Waeterschoot
Matrix Decompositions - Jack Gurev
Forcing and the Continuum Hypothesis, III - Kevin Lin
Complex Multiplication, Part 1 (Elliptic Curves) - Art Waeterschoot
Differential Topology - Lisa Lokteva
Green’s Functions - Claudia Feng, Kevin Lin
Forcing and the Continuum Hypothesis, IV - Kevin Lin
Morse Theory, Part 1 - Alyosha Latyntsev
Normal Number Theorem - Ben Bruce
Complex Multiplication, Part 2 - Jack Gurev
Random Matrices - Chris Zhang
Complex Multiplication, Part 3 (LFunctions and Distribution of Primes) - Daniel Dore
Morse Theory, Part 2 - Alyosha Latyntsev
A Brief History of Cyclotomic Fields - Sam Mundy
The Magic Queendom of Standard Young Tableaux - Lisa Lokteva
Complex Multiplication, Part 4 - Tim Ratigan
Spectra and Representability of Cohomology - Sam Mundy
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
Recitation
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
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
Modular Forms I – Joe Stahl
Modular Forms II – Sam Mundy
Hecke Operators – Joe Stahl
Eichler-Shimura Theory – Sam Mundy
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
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
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
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
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
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
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
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
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
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
Gerbelli-Gauthier
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
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
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
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
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
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
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
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
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
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
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)