# AWM Columbia Chapter

The Association for Women in Mathematics Columbia Chapter is a pre-professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment of women and girls in the mathematical sciences. We connect students and professors interested in mathematics at Columbia University and Barnard College together and encourage women’s participation in STEM.

Barnard students are encouraged to join. Learn more at the Association of Women in Mathematics Columbia Chapter website or email columbiaawm@gmail.com.

## Welcome Summer 2021

## AWM Presents: Summer Reading Groups

AWM is excited to be offering 3 reading groups this summer in advanced topics that can be accessible to most undergraduates!

This year we are pleased to be offering **Introduction to Topology**,** Introduction to Quantum Computing**, and **Introduction to Geometric Analysis!**

These groups will be fun and informal introductions to areas in mathematics that you may not have been able to take a course in yet.

This form is by no means a "binding contract," we just want to see what you might be interested in for a directed reading group this year!**Topology**: In the Topology reading group, we will introduce some of the fundamental concepts in the topic of topology. We will start by defining topological spaces and manifolds. We will discuss the classification of topological cases and the separation axioms. We will then highlight concepts from algebraic topology, such as the fundamental group. We will go on to prove some important theorems in algebraic topology, such as the Borsuk-Ulam theorem and the Seifert-Van Kampen theorem. This reading group assumes background knowledge in analysis (Modern Analysis I or equivalent) and some introductory knowledge about groups. It is a great way to gain exposure to topics in topology and to prepare to take a course in topology in upcoming semesters.**Quantum Computing**: Quantum Computing, Simulation, and Technology is growing at a rapid pace, and there’s no knowing where the next 10 years will take the field! In the Quantum reading group, we’ll do a survey of various topics to get you up to speed in the quantum world and give you a high-level introduction to all things quantum. We will start with the basics, covering the necessary linear algebra and postulates of quantum mechanics. Then, we jump right into the material! We will cover the physics of the hardware: superconducting qubits and neutral atom qubits. We will go over algorithms: Quantum Fourier Transform, Grover’s Search, and Shor’s Factoring. And also quantum physics simulation: Variational Quantum Eigensolver and analog quantum simulation. The goal is for you leave with working knowledge of these topics, and a newfound interest in these topics. While some linear algebra/quantum exposure would help, we will try to keep the readings and meetings at an introductory level so anyone can jump in!**Geometric Analysis**: Many of you have heard of the famed "Poincare Conjecture." This was a topological problem that actually had a geometric solution! In this reading group, we will explore the rudiments of geometric, partial differential equations, and ultimately get to geometric flows such as the Ricci Flow which was used to prove this Millenium math problem! The goal here is to leave you with some interest in geometric flows and hopefully dissuade any fears people have when they first study PDE! Some idea of Riemannian geometry (smooth manifolds, Levi-Civita connection, curvature, geodesics) would be really helpful BUT entirely not needed as there will be a crash course involved! If you have a background in PDE, great but to be honest, surprisingly little knowledge of PDE will be required! A working knowledge of calculus is required.