## Department of Mathematics

## Math Integration Bee

Jan/20 | Thu | 06:00PM |

You are cordially invited to the 41st Annual MIT Integration Bee. Watch our top students compete for the chance to win prizes and the prestigious title of Grand Integrator! This tournament to end all tournaments will be held on Thursday, January 20th at 6:00pm in room 32-123. Come watch brilliant minds at work and invite your friends to behold the thrilling finale! Witness your classmates show off their mad integrating skills at the only Integration Bee of 2022. Bring your friends!

## Mathematics Lecture Series

Jan/10 | Mon | 01:00PM–02:30PM |

**The Study of Wave Interactions: Where Beautiful Mathematical Ideas Come Together**

**Abstract:** Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave packets in quantum physics. These phenomena are difficult to study in a rigorous mathematical manner, but maybe because of this challenge mathematicians have developed interdisciplinary approaches that are powerful and beautiful. I will describe some of these approaches and show for example how the need to understand certain multilinear and periodic interactions gave also the tools to prove a famous conjecture in number theory, or how classical tools in probability gave the right framework to still have viable theories behind certain deterministic counterexamples.

## Mathematics Lecture Series

Jan/12 | Wed | 01:00PM–02:30PM |

**What is a random surface?**

These constructions have deep roots in mathematics, drawing from classical graph theory (Tutte, Mullin), complex analysis (Gauss, Liouville, Riemann, Loewner), representation theory (Lie, Virasoro, Verma, Kac) and many areas of physics (string theory, Coulomb gas theory, quantum field theory, statistical mechanics, discrete quantum gravity).

We present here an informal, colloquium-level overview of the subject. We aim to answer, as cleanly as possible, the fundamental question. What is a random surface?

## Mathematics Lecture Series

Jan/14 | Fri | 01:00PM–02:30PM |

**Minimal Mathematical Models of Living Matter**

Recent advances in the live-imaging of multicellular systems pose a wide range of interesting mathematical problems, from the compression of video microscopy data to the modeling of gene expression, tissue dynamics and growth during embryonic development. After a brief review of recent experiments, we will introduce and analyze minimal ODE, SDE and PDE models to describe individual and collective cell behaviors.

## Mathematics Lecture Series

Jan/19 | Wed | 01:00PM–02:30PM |

**Factoring Huge Integers**

You learned many years ago that any integer N can be factored uniquely into primes. But the algorithm taught in elementary school -- iterate through primes and check whether N is divisible by each one -- quickly becomes impractical when N gets large. Computational number theorists have devised faster methods over the last several decades that make it possible to factor larger integers on a computer, but the problem is still very difficult: the 260 digit RSA-challenge factorization has stood for 30 years. I will give a broad overview of the methods in use today, together with a more detailed description of three: the Miller-Rabin primality test, the quadratic sieve factoring algorithm and the elliptic curve factorization method.

## Mathematics Lecture Series

Jan/21 | Fri | 01:00PM–02:30PM |

**The Odd-Town Theorem**

We will discuss the so-called "Odd-Town Theorem", a theorem in extremal combinatorics (or, more specifically, in extremal set theory). Perhaps surprisingly, the proof of this combinatorics theorem relies on linear algebra over the finite field F_2. We will introduce F_2 in the lecture, and discuss the relevant concepts from linear algebra. Using these linear algebra concepts, we will then prove the "Odd-Town Theorem".

## Mathematics Lecture Series

Jan/24 | Mon | 01:00PM–02:30PM |

**Fluidic Shaping of Optical Components**

Fabrication of optical components, such as lenses and mirrors, has not changed considerably in the past 300 years, and it relies on mechanical processing such as grinding, machining, and polishing. These fabrication processes are complex and require specialized equipment that prohibits rapid prototyping of optics, and puts a very high price tag on large lenses and freeform designs.

In this talk I will present a novel approach that leverages the basic physics of interfacial phenomena for rapidly fabricating a variety of lenses and freeform optical components without the need for any mechanical processing. We will see how such components can be obtained in liquid form, by minimizing the free energy functional of the system, allowing to design various freeform optical topographies.

Lastly, I will discuss our collaboration with NASA on the use of this technology of in-space fabrication of optics and for the creation of large space telescopes that overcomes launch constraints.

## Mathematics Lecture Series

Jan/26 | Wed | 01:00PM–02:30PM |

**Surface Tension**

Surface tension is a property of fluid interfaces that leads to myriad subtle and striking effects in nature and technology. We describe a number of surface-tension-dominated systems and how to rationalize their behavior via mathematical modeling. Particular attention is given to the role of surface tension in biological systems and in hydrodynamic quantum analogs.

## Music Recital

Jan/27 | Thu | 03:00PM–05:00PM |

The MIT math department music recital will be returning once again this IAP, taking place in Killian Hall on 1/27/2022 from 3pm-5pm. The recital is a yearly tradition where we gather to listen to music performed by the talented members of the math department. Classical (Indian and western), jazz, video game, Latin-American, and Scandinavian folk music, as well as original compositions have all previously been featured.