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 alumni.   

2021 Counselor Minicourses and Counselor Seminars on Algebraic Number Theory, Periods and Galois Representations in Algebraic Geometry and Arithmetic Commutative Algebra, Pósa Problem Solving, Algebraic Topology, Elliptic Curves: Geometry and Arithmetic, Graphs of Groups, Representation Theory of Lie Algebras, Probabilistic Combinatorics, Circle Method and Its Application to the Study of Rational Points, and One-Off topics.

2021 Counselor Minicourses

How to write a proof

Introduction to Mechanism Design

Ramsey Theory

Knot Theory

Measure Theory

Differential Equations and Recursion

Tropical Arithmetic


Languages and Automata

Axiom of Choice

Proof Assistants

Cutie Pi: Leibniz, Euler, and Warmth from Hugs

Construction of R

Cryptography is hard

Randomized computations

Continued Fractions

Metric Space and Topology

Riemann Integration

T-shirt Talk: Voronoi Diagram

How to find roots of polynomials mod p

Polynomial Statistics

Erdös Problems

Law of Large Numbers

2021 Counselor Seminars on Algebraic Number Theory

Cyclic Quartic Extensions of Fields


Dedekind Domains I

Dedekind Domains II

Galois Theory and Representation Theory

Dedekind Domains III

Extensions of Local Fields

Dedekind Domains IV

2021 Counselor Seminars on Periods and Galois Representations in Algebraic Geometry and Arithmetic

p-adic Hodge theory I

p-adic Hodge theory II

p-adic Hodge theory III

p-adic Hodge theory IV

Mumford-Tate groups/absolute Hodge classes I

Mumford-Tate groups/absolute Hodge classes II

p-adic Hodge theory V

Picard-Fuchs equations

Good reduction of abelian varieties

p-adic Hodge theory VI

2021 Counselor Seminars on Commutative Algebra

Manifesting Modules

Noetherian Rings

2021 Counselor Seminars on Pósa Problem Solving

Pósa Problem Solving I

Pósa Problem Solving II

Pósa Problem Solving III

Pósa Problem Solving IV

Pósa Problem Solving V

2021 Counselor Seminars on Algebraic Topology

Fundamental Groups

Seifert-Van Kampen Theorem I

Seifert-Van Kampen Theorem II

Covering Spaces I

Covering Spaces II

2021 Counselor Seminars on Elliptic Curves: Geometry and Arithmetic 

Riemann-Roch and Group Law of Elliptic Curves

Group Cohomology

Descent: Selmer and Sha

2021 Counselor Seminars on Graph of Groups

Graphs of Groups I

Graphs of Groups II

Graphs of Groups III

2021 Counselor Seminars on Representation Theory of Lie Algebras

Lie Algebras I

Lie Algebras II

Lie Algebras III

2021 Counselor Seminars on Probabilistic Combinatorics

Probabilistic Combinatorics I

Probabilistic Combinatorics II

2021 Counselor Seminars on The Circle Method and Its Application to the Study of Rational Points

Circle Method I

Circle Method II

2021 Counselor Seminars on One-Off Topics

How Not to Give a Talk

Quotients in Algebraic Geometry

Type Theory

Introduction to Hyperbolic Geometry

Dynamical Systems

Generating Functions

Motivating the Definition of a Modular Form

Classifying Spaces and Equivariant Cohomology

Derived Functors


Intro to Enumerative Geometry

Group Theory in Voting


2020 Counselor Minicourses and Counselor Seminars on Algebraic Number Theory, Algebraic Topology, Commutative Algebra and Algebraic Geometry, Compactness in Metric Spaces, Complex Analysis, Geometric Group Theory, Machine Learning, Perfectoid Fields, Quantum Computation and Miscellaneous Topics.

2020 Counselor Minicourses

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

2020 Counselor Seminars on Algebraic Number Theory

Algebraic Number Theory I

Algebraic Number Theory II

Algebraic Number Theory III

Algebraic Number Theory IV

2020 Counselor Seminars on Algebraic Topology

Algebraic Topology I

Algebraic Topology II

Algebraic Topology III

Algebraic Topology IV

2020 Counselor Seminars on Commutative Algebra and Algebraic Geometry

Affine Algebraic Sets

The Zariski Topology

Hilbert’s Nullstellensatz

Geometric Spaces and Spectrum of a Ring


Sheaves and Ringed Spaces

Morphisms of Ringed Spaces

An Overview of Schemes

2020 Counselor Seminars on Compactness in Metric Spaces

Compactness in Metric Spaces I

Compactness in Metric Spaces II

Compactness in Metric Spaces III

2020 Counselor Seminars on Complex Analysis

Complex Analysis I

Complex Analysis II

Complex Analysis III

Riemann Sphere and Moebius Transformations

2020 Counselor Seminars on Geometric Group Theory

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

2020 Counselor Seminars on Machine Learning




Neural Networks

2020 Counselor Seminars on Perfectoid Fields

Definitions and Examples

Untilting and Finite Extensions

(phi, Gamma) - modules

Outlook on Perfectoid Spaces

2020 Counselor Seminars on Quantum Computation

Quantum Computation I

Quantum Computation II

Quantum Computation III

Quantum Computation IV

Period Finding

Shor’s Algorithm

2020 Counselor Seminars on Miscellaneous Topics

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


2019 Counselor Minicourses and Counselor Seminars on Algebraic Topology, Class Field Theory, Complex Analysis and Analytic Number Theory, Differential Forms, Functional Analysis, Lambda Calculus, Modular Forms, Probability and Stochastic Processes, and Miscellaneous Topics.

2019 Counselor Minicourses

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

2019 Counselor Seminars on Algebraic Topology

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

2019 Counselor Seminars on Class Field Theory

Quadratic Forms - Ishan Levy

Group Cohomology - Alec Leng

Global Statements of Class Field Theory - Ishan Levy

Quadratic Forms, Lattices, and Ideals - Ishan Levy

2019 Counselor Seminars on Complex Analysis and Analytic Number Theory

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

2019 Counselor Seminars on Differential Forms

A Dip into Linear Algebra - Arya Vadnere

Introduction to Differential Forms - Kevin Chang

Pullbacks and Integrating Forms - Arya Vadnere

2019 Counselor Seminars on Functional Analysis

Zabrieko’s Lemma and Corollaries - Vijay Srinivasan

Extending Linear Functionals - Vijay Srinivasan

The Weak Topology and L^p spaces - Vijay Srinivasan

2019 Counselor Seminars on Lambda Calculus

Introduction to Lambda Calculus - Eileen Zhang

The Church-Rosser Theorem - Eileen Zhang

Combinatory Algebra - Eileen Zhang

2019 Counselor Seminars on Modular Forms

Introduction to Modular Forms - Adit Vishnu

The Ramanujan Congruences - Adit Vishnu

Algebraic Relations between Partition Functions and the j-function - Adit Vishnu

2019 Counselor Seminars on Probability and Stochastic Processes

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

2019 Miscellaneous Counselor Seminars

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


2018 Counselor Minicourses and Counselor Seminars on Riemann Surfaces, Algebraic Geometry, Algebraic Number Theory, Iwasawa Theory, Elliptic Curves, Topology, Representation Theory of Finite Groups, Intersection Theory, Commutative Algebra, Measure Theory, Random Matrix Theory, Representation Theory of the Symmetric Group, Matrix Lie Groups, Rigidity Theory, Tannaka Duality, and Miscellaneous Topics.

2018 Counselor Minicourses

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

2018 Counselor Seminars on Riemann Surfaces

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

2018 Counselor Seminars on Algebraic Geometry

What is Algebraic Geometry? – Ishan Levy

Divisors and Intersections – Ishan Levy

Dimension and Moduli- Ishan Levy

Gröbner Bases – Ishan Levy

2018 Counselor Seminars on Algebraic Number Theory

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

2018 Counselor Seminars on Iwasawa Theory

Iwasawa Theory I - Sam Mundy (alum)

Iwasawa Theory II - Sam Mundy (alum)

Iwasawa Theory III - Sam Mundy (alum)

2018 Counselor Seminars on Elliptic Curves

Introduction to Elliptic Curves – Alec Leng

Points of Order 13 on Elliptic Curves – Kevin Lin

Hasse Bound for Elliptic Curves – Seraphina Lee

2018 Counselor Seminars on Topology

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

2018 Counselor Seminars on Representation Theory of Finite Groups

Representation Theory of Finite Groups I - Hugo Jenkins

Representation Theory of Finite Groups II - Hugo Jenkins

2018 Counselor Seminars on Intersection Theory

Intersection Theory in Algebraic Geometry I – Adam Block

Intersection Theory in Algebraic Geometry II – Adam Block

Intersection Theory in Algebraic Geometry III – Adam Block

2018 Counselor Seminars on Commutative Algebra

Introduction to Commutative Algebra – Caitlyn Booms

Introduction to Minimal Free Resolutions – Caitlyn Booms

Linear Resolutions of Edge Ideals – Caitlyn Booms

2018 Counselor Seminars on Measure Theory

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

2018 Counselor Seminars on Random Matrix Theory

Random Matrix Theory I – Roger Van Peski

Random Matrix Theory II – Roger Van Peski

2018 Counselor Seminars on Representation Theory of the Symmetric Group

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

2018 Counselor Seminars on Matrix Lie Groups

Matrix Lie Groups I – Yichi Zhang

Matrix Lie Groups II – Yichi Zhang

2018 Counselor Seminars on Rigidity Theory

Rigidity Theory I - Rebecca Rohrlich

Rigidity Theory II - Rebecca Rohrlich

2018 Counselor Seminars on Tannaka Duality

Tannaka Duality I – Oron Propp

Tannaka Duality II – Oron Propp

2018 Miscellaneous Counselor Seminars

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


2017 Counselor Minicourses and Counselor Seminars on Algebraic Geometry, Complex Analysis, Characteristic Classes, Category Theory, Representation Theory and Combinatorics, Riemann Surfaces, Geometric Group Theory, and Miscellaneous Topics 

2017 Counselor Minicourses

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

2017 Counselor Seminars on Algebraic Geometry

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

2017 Counselor Seminars on Complex Analysis

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

2017 Counselor Seminars on Characteristic Classes

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

2017 Counselor Seminars on Category Theory

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

2017 Counselor Seminars on Representation Theory and Combinatorics

Representation Theory and Combinatorics, I - Adam Block

Representation Theory and Combinatorics, II - Adam Block

2017 Counselor Seminars on Riemann Surfaces

Riemann Surfaces, I - Alyosha Latyntsev

Riemann Surfaces, II - Alyosha Latyntsev

Riemann Surfaces, III - Alyosha Latyntsev

2017 Counselor Seminars on Geometric Group Theory

Ping Pong and Quasi-Isometry - Larsen Linov

The Word Problem and Hyperbolic Groups - Robert Huben (’15)

2017 Miscellaneous Counselor Seminars

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


2016 Functional Analysis Mini Seminars, Mini Courses, Seminars in Representation Theory, and One-Off Counselor Talks

2016 Counselor Mini Seminars in Functional Analysis

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

2016 Counselor Mini Courses

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

2016 Counselor Seminars in Representation Theory

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

2016 One-off Counselor Talks

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


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 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

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


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)