Fall 2021

Putnam Competition Post-Mortem

Speaker: Noam Elkies, Harvard University

Abstract:  Solutions, outlines, and/or mathematical context will be given for some of the problems from last Saturday's Putnam exam, starting with problems that lend themselves to discussion.

A Conversation on Borsuk-Ulam, Ham Sandwiches, and Necklaces

Speaker: Eric Tang

Abstract:  Topology, despite being an abstract branch of mathematics, sneakily finds its way into a variety of unique, fascinating problems. With this talk being an informal discussion on a famous result in topology, the Borsuk-Ulam theorem, we will muse over and appreciate the many distinct convenient guises the theorem takes on, as well as many of the short corollaries that follow. To wrap up the second half of the talk--as a little fun treat--we dissect the stolen necklace problem in two particularly interesting ways. Let's be some crafty mathematicians (thieves)! 

Graduate School Panel

Panelists: Levant Alpoge (Harvard), Anne Carlstein (MIT), Roderic Guigo (Harvard), and Andrew Rao (Harvard)

Abstract:  Come ask your questions about applying for and attending graduate school!

If you're planning to attend, please fill out this form to indicate your food preferences so that we have an accurate count of how many dinners to have.

Thinking in Categories: What Abstract Nonsense Can Do For You

Speaker: Rushil Mallarapu

Abstract:  What is category theory? Is there more to “functors” and “natural transformations” than these scary-looking diagrams? Categories provide a language for recognizing — and generalizing —patterns and constructions that may seem unrelated in different mathematical contexts, but have the same fundamental flavor. Because of this, category theory is useful, beautiful, and everywhere. In this talk, we’ll tour through the abstractions of category theory, give concrete examples as to where these abstractions come up, explain what all the pretty diagrams are good for, and go over an example of how categorical thinking can help demystify math you have never seen before!

If you're planning to attend, please fill out this form to indicate your food preferences so that we have an accurate count of how many dinners to have.

From Number Theory to the Solar System

Speaker: Forrest Flesher

Abstract:  One of the deepest questions of mathematics and physics in modern times is the following: is the solar system stable? After Isaac Newton invented calculus to understand the motion of the planets in the 17th century, this problem remained unanswered for hundreds of years. It wasn’t until the mid 20th century that this confounding problem was finally “solved.” Remarkably, the solution involves number theory in a fascinating way. In this talk, we’ll discuss what it means for the solar system to be stable, how number theory arises in the solution, why this “solution” to this stability problem is still fundamentally unsatisfying, and how this is an important example for the interaction between mathematics and physics. 

If you're planning to attend, please fill out this poll to indicate your food preferences so that we have an accurate count of how many dinners to have. 

Solving a Nerd Sniping Problem

Speaker: Richard Xu

Abstract:  We will examine the famous "nerd sniping" problem in xkcd.com/356/. After discussing the history and setup of the problem, as well as some important theorems regarding electrical resistance, we will solve the problem using some analysis and trigonometric functions.

If you're planning to attend, please fill out this poll to indicate your food preferences so that we have an accurate count of how many dinners to have. 

A Remarkable Geometric Spiral

Speaker: Kyle Fridberg

Abstract:  What can we learn from a spiral made out of regular n-gons? In this talk, we will construct such a spiral and characterize it using elementary algebraic techniques. This will lead to investigating the behavior of the spiral in the infinite limit. Surprisingly, we can use the spiral to define the convergence of the sum exp(2 π i Hk) / k from k = 1 to N as N goes to infinity (where exp() is the complex exponential function and Hk is the k-th Harmonic number). Finally, I will show some continuous generalizations of the spiral that have great aesthetic appeal! 

If you're planning to attend, please fill out this poll to indicate your food preferences so that we have an accurate count of how many dinners to have. 

Math and the Universe

Speaker: Cliff Taubes, Harvard University

Abstract:  It is like that all known aspects of our universe are amenable to mathematical analysis. Are there universes that aren't? If you have thought about this, come and join the discussion.

If you're planning to attend, please fill out this poll to indicate your food preferences so that we have an accurate count of how many dinners to have. Note the room change for the first talk!