Spring 2018

Information

Founded in March 2014, the SCUM is a series of weekly math talks/panels by (mostly) undergraduates, for undergraduates, at MIT. Anyone is invited to speak about a math topic he or she finds interesting, sometimes but usually not original research, and talks are open to the MIT community (as well as interested visitors, e.g. from Harvard). With the support of the MIT Mathematics Department (and in past semesters, the Undergraduate Mathematics Association (UMA), Undergraduate Society of Women in Math (USWIM), and the Harvard-MIT Mathematics Tournament), SCUM also features free dinner each week! We'll meet weekly on Wednesdays, 5:30--6:30 PM, in room 2-143.

If you are interested in picking up a talk, please send a title and abstract, as well as any appropriate references (optional but recommended), to scum-exec@mit.edu. (If you have any food preferences, let us know!) In addition, please include a preference for dates, and any other accommodations you will need (e.g. projector). Talks should be fifty minutes long and accessible to first-year undergraduate math majors. We strongly recommend attending several SCUM talks before signing up to give one yourself.

(For logistical tips/advice on organizing such activities yourself, see below here.)

There are other math events that go on in the Cambridge area: at MIT, we have the Undergraduate Math Association, as well as the Harvard-MIT Math Tournament. There's also Tea with Mathematicians; we'll update this site with the dates for when undergraduates are invited to attend. (Harvard also has weekly tea in its math department.)

Upcoming Talks, Panels, etc.

To receive email announcements, make sure you are either a declared MIT math major (which by definition excludes all freshmen first semester), or on the scum-interest mailing list (possibly via UMA or USWIM). If you do not have MIT certificates, email scum-exec@mit.edu and we'll manually add you to the mailing list.

Alternatively, you can like or follow us on Facebook.

Organizers: Sanath Devalapurkar, Marisa Gaetz, Elizabeth Han, Brice Huang, Ahaan Rungta, and Henry Shackleton.
Meeting Time/Place: Wednesdays, 5:30 PM, in 4-145

Date: April 18, 5:45 pm
Title: Regenerating Codes
Speaker: Margalit Glasgow
Error-correcting codes allow us to encode a message into a redundant codeword, such that even when some of the symbols in the codeword are erased (or changed), we can recover the original message. In regenerating codes, which are often used in distributed storage, we care about recovering the full codeword. For example, in Reed-Solomon codes that encode k-symbol messages, if any symbol in the codeword is lost, we can recover that symbol exactly using polynomial interpolation from any other k-symbols of the codeword. But what about if the symbols are really large and stored in the cloud, and we don't have the bandwidth to download k full symbols? Can we recover the lost symbol using less information? (Spoiler: yes) Come learn how!
References:

• Repairing Reed-Solomon Codes. Venkatesan Guruswami and Mary Wootters. STOC 2016.
• Optimal repair of Reed-Solomon codes: Achieving the cut-set bound Itzhak Tamo, Min Ye, Alexander Barg 2017

Date: April 11, 5:45 pm
Title: Smoothness Classes of Minkowski Sums
Speaker: Yonah Borns-Weil
The Minkowski Sum of two sets is the set of all vector sums of elements in the sets. Somewhat surprisingly, the sum two convex sets in the plane with $C^{\infty}$ (infinitely differentiable) boundaries need not have $C^{\infty}$ boundary. However, the sum's boundary must be differentiable, and twice differentiable, and even three times differentiable... In this talk, we'll prove the astonishing cutoff" of just how smooth such a boundary must be. The proof will use only introductory analysis techniques, and the worst-case scenario will be perfectly simple and constructive.
Prerequisites: Basic (18.100 level) analysis.

Date: April 4, 5:45 pm
Title: Dimensionality Reduction While Preserving Distances
Speaker: Sandeep Silwal
Dimensionality reduction is an important tool in numerical linear algebra, statistics, and algorithms. In this talk, we present a nice proof of the Johnson Lindenstrauss lemma which allows us to reduce the size of vectors while preserving their pairwise distances. We will also look at some applications of this lemma to combinatorics and algorithms.
References:

Date: March 14, 5:30 pm
Title: Formulas for Pi
Speaker: Yang Liu
Ramanujan proved many absurd formulas for pi. We explain how one would go about deriving one of these formulas.

Date: March 7, 5:45 pm
Title: The integral of $e^{x^2}$ (or lack thereof)
Speaker: Ashwin Sah
We give a more or less complete proof of the classical and well-known, yet rarely proven fact that e^{x^2} and other functions have no elementary integrals.

Let us know if you (or someone you know) might like to give a talk, or if you have suggestions for topics/ideas you would like to see in future talks.

Past Talks, Panels, etc.

See the archive here.